noc-book-2/content/09_ga.html

<section data-type="chapter">
<h1 id="chapter-9-evolutionary-computing">Chapter 9. Evolutionary Computing</h1>
<div class="chapter-opening-quote">
  <blockquote data-type="epigraph">
    <p>Time flies like an arrow; fruit flies like a banana.</p>
    <div class="chapter-opening-quote-source">
      <p>—Unknown</p>
    </div>
  </blockquote>
</div>
<div class="chapter-opening-figure">
  <figure>
    <img src="images/09_ga/09_ga_1.png" alt="">
    <figcaption></figcaption>
  </figure>
  <h3 id="pueblo-pottery-photo-courtesy-of-the-national-park-service">Pueblo pottery (photo courtesy of the National Park Service)</h3>
  <p>For centuries, pottery created by the Ancestral Puebloans and Mogollon cultures of the southwestern United States and northern Mexico has held great significance in both ceremonial and everyday contexts. Techniques and design elements like those used to create this Chaco Ancestral Pueblo bowl are passed down through generations, with each potter learning, preserving, and subtly adapting these designs. This ongoing process gives rise to a continually evolving tapestry of familial and cultural expression.</p>
</div>
<p>Take a moment to think back to a simpler time, when you wrote your first p5.js sketches and life was free and easy. Which fundamental programming concept did you likely use in those first sketches and continue to use over and over again to this day? <em>Variables</em>. Variables allow you to save data and reuse it while a program runs.</p>
<p>Of course, this is nothing new. In this book, you’ve moved far beyond sketches with just one or two simple variables, working up to sketches organized around more complex data structures: variables holding custom objects that include both data and functionality. You’ve used these complex data structures—classes—to build your own little worlds of movers and particles and vehicles and cells and trees. But there’s been a catch: in each and every example in this book, you’ve had to worry about initializing the properties of these objects. Perhaps you made a whole set of particles with random colors and sizes, or a list of vehicles all starting at the same (<em>x</em>, <em>y</em>) position.</p>
<p>What if, instead of acting as an intelligent designer, assigning the properties of the objects through randomness or thoughtful consideration, you could let a process found in nature—<strong>evolution</strong><em>—</em>decide the values for you? Can you think of the variables of a JavaScript object as the object’s DNA? Can objects give birth to other objects and pass down their DNA to a new generation? Can a p5.js sketch evolve?</p>
<p>The answer to all these questions is a resounding yes, and getting to that answer is the focus of this chapter. After all, this book would hardly be complete without tackling a simulation of one of the most powerful algorithmic processes found in nature itself, biological evolution. This chapter is dedicated to examining the principles behind evolutionary processes and finding ways to apply those principles in code.</p>
<h2 id="genetic-algorithms-inspired-by-actual-events">Genetic Algorithms: Inspired by Actual Events</h2>
<p>The primary means for developing code systems that evolve are <strong>genetic algorithms</strong> (<strong>GAs</strong> for short), which are inspired by the core principles of Darwinian evolutionary theory. In these algorithms, populations of potential solutions to a problem evolve over generations through processes that mimic natural selection in biological evolution. While computer simulations of evolutionary processes date back to the 1950s, much of our contemporary understanding of GAs stems from the work of John Holland, a professor at the University of Michigan whose 1975 book <em>Adaptation in Natural and Artificial Systems</em> (MIT Press) pioneered GA research. Today, GAs are part of a wider field that’s often referred to as <strong>evolutionary computing</strong>.</p>
<p>To be clear, GAs are only <em>inspired</em> by genetics and evolutionary theory, and aren’t intended to precisely implement the science behind these fields. As I explore GAs in this chapter, I won’t be making Punnett squares (sorry to disappoint), and there will be no discussion of nucleotides, protein synthesis, RNA, or other topics related to the biological processes of evolution. I don’t care so much about creating a scientifically accurate simulation of evolution as it happens in the physical world; rather, I care about methods for applying evolutionary strategies in software.</p>
<p>This isn’t to say that a project with more scientific depth wouldn’t have value. In fact, a whole field of computational biology research <em>does</em> take on the challenge of more accurately simulating biological evolutionary processes! I encourage readers with a particular interest in this topic to explore possibilities for expanding the examples provided with additional evolutionary features. Nevertheless, for the sake of keeping the projects manageable, I’m going to stick to the basics. And as it happens, the basics will be plenty complex and exciting.</p>
<p>I should also note that, strictly speaking, the term <em>genetic algorithm</em> refers to a specific algorithm implemented in a specific way to solve specific sorts of problems, and not all those specifics are important to this book. While the formal GA will serve as the foundation for the examples in this chapter, I won’t make a fuss about implementing the algorithm with perfect accuracy, given that I’m looking for creative applications of evolutionary theory in code. As such, this chapter will be broken into the following three parts:</p>
<ul>
  <li><strong>Traditional genetic algorithm:</strong> I’ll begin with the traditional, textbook GA. This algorithm was developed to solve problems in computer science for which the solution space is so vast that a <em>brute-force</em> algorithm would take too long. Here’s an example: I’m thinking of a number between one and one billion. How long will it take you to guess it? With a brute-force approach, you’d have to check every possible solution. Is it one? Is it two? Is it three? Is it four? . . . Luck plays a factor here (maybe I happened to pick five!), but on average, you would end up spending years counting up from one before hitting the correct answer. However, what if I could tell you whether your answer was good or bad? Warm or cold? Very warm? Hot? Ice frigid? If you could evaluate how close (or <em>fit</em>) your guesses are, you could start picking numbers accordingly and arrive at the answer more quickly. Your answer would <em>evolve</em>.</li>
  <li><strong>Interactive selection: </strong>After<strong> </strong>exploring the traditional computer science version, I’ll examine other applications of GAs in the visual arts. <em>Interactive selection</em> refers to the process of evolving something (often a computer-generated image) through user interaction. Let’s say you walk into a museum gallery and see 10 paintings. With interactive selection, you might pick your favorites and allow an algorithmic process to generate (or <em>evolve</em>) new paintings based on your preferences.</li>
  <li><strong>Ecosystem simulation:</strong> The traditional computer science GA and interactive selection technique are what you’ll likely find if you search online or read a textbook about artificial intelligence. But as you’ll soon see, they don’t really simulate the process of evolution as it happens in the physical world. In this chapter, I’ll also explore techniques for simulating evolution in an ecosystem of artificial creatures. How can the objects that move about a canvas meet each other, mate, and pass their genes on to a new generation? This could apply directly to the Ecosystem Project outlined at the end of each chapter. It will also be particularly relevant as I explore neuroevolution in <a href="/neuroevolution#">Chapter 11</a>.</li>
</ul>
<h2 id="why-use-genetic-algorithms">Why Use Genetic Algorithms?</h2>
<p>To help illustrate the utility of the traditional GA, I’m going to start with cats. No, not just your everyday feline friends. I’m going to start with some purr-fect cats that paw-sess a talent for typing, with the goal of producing the complete works of Shakespeare (Figure 9.1).</p>
<figure>
  <img src="images/09_ga/09_ga_2.png" alt="Figure 9.1: Infinite cats typing at infinite keyboards">
  <figcaption>Figure 9.1: Infinite cats typing at infinite keyboards</figcaption>
</figure>
<p>This is my meow-velous<em> </em>twist on the <strong>infinite monkey theorem</strong>,<strong> </strong>which<strong> </strong>is stated as follows: a monkey hitting keys randomly on a typewriter will eventually type the complete works of Shakespeare, given an infinite amount of time. It’s only a theory because in practice the number of possible combinations of letters and words makes the likelihood of the monkey <em>actually</em> typing Shakespeare minuscule. To put it in perspective, even if the monkey had started typing at the beginning of the universe, the probability that by now it would have produced just <em>Hamlet</em>, to say nothing of the <em>entire</em> <em>works</em> of Shakespeare, is still absurdly unlikely.</p>
<p>Consider a cat named Clawdius. Clawdius types on a reduced typewriter containing only 27 characters: the 26 English letters plus the spacebar. The probability of Clawdius hitting any given key is 1 in 27.</p>
<p>Next, consider the phrase “to be or not to be that is the question” (for simplicity, I’m ignoring capitalization and punctuation). The phrase is 39 characters long, including spaces. If Clawdius starts typing, the chance he’ll get the first character right is 1 in 27. Since the probability he’ll get the second character right is also 1 in 27, he has a 1 in 729 (<span data-type="equation">27 \times 27</span>) chance of landing the first two characters in correct order. (This follows directly from our discussion of probability in <a href="/random#">Chapter 0</a>.) Therefore, the probability that Clawdius will type the full phrase is 1 in 27 multiplied by itself 39 times, or <span data-type="equation">(1/27)^{39}</span>. That equals a probability of . . .</p>
<p><span data-type="equation">1 \text{ in } \text{66,555,937,033,867,822,607,895,549,241,096,482,953,017,615,834,735,226,163}</span></p>
<p>Needless to say, even hitting just this one phrase, let alone an entire play, let alone all 38 Shakespeare plays (yes, even <em>The Two Noble Kinsmen</em>) is highly unlikely. Even if Clawdius were a computer simulation and could type a million random phrases per second, for Clawdius to have a 99 percent probability of eventually getting just the one phrase right, he would have to type for 9,719,096,182,010,563,073,125,591,133,903,305,625,605,017 years. (For comparison, the universe is estimated to be a mere 13,750,000,000 years old.)</p>
<p>The point of all these unfathomably large numbers isn’t to give you a headache, but to demonstrate that a brute-force algorithm (typing every possible random phrase) isn’t a reasonable strategy for arriving randomly at “to be or not to be that is the question.” Enter GAs, which start with random phrases and swiftly find the solution through simulated evolution, leaving plenty of time for Clawdius to savor a cozy catnap.</p>
<p>To be fair, this particular problem (to arrive at the phrase “to be or not to be that is the question”) is a ridiculous one. Since you know the answer already, all you need to do is type it. Here’s a p5.js sketch that solves the problem:</p>
<pre class="codesplit" data-code-language="javascript">let s = "to be or not to be that is the question";
console.log(s);</pre>
<p>Nevertheless, it’s a terrific problem to start with since having a known answer will allow you to easily test the code and evaluate the success of the GA. Once you’ve successfully solved the problem, you can feel more confident in using GAs to do something actually useful: solving problems with <em>unknown</em> answers. This first example serves no real purpose other than to demonstrate how GAs work. If you test the GA results against the known answer and get “to be or not to be,” then you’ve succeeded in writing a GA.</p>
<div data-type="exercise">
  <h3 id="exercise-91">Exercise 9.1</h3>
  <p>Create a sketch that generates random strings. You’ll need to know how to do this in order to implement the GA example that will shortly follow. How long does it take for p5.js to randomly generate the string <code>cat</code>? How might you adapt this to generate a random design using p5.js’s shape-drawing functions?</p>
</div>
<h2 id="how-genetic-algorithms-work">How Genetic Algorithms Work</h2>
<p>Before I get to any code, I’d like to walk through the steps of the classic GA in a more general way. I’ll illustrate how a population of <em>creatures</em> (a generic term for the elements of a simulation) can evolve over a series of generations. To understand how this works, it’s important to outline three core principles of Darwinian evolution. If natural selection is to occur in code as it does in nature, all three of these elements must be present:</p>
<ul>
  <li><strong>Heredity:</strong> There must be a mechanism that allows <em>parent</em> creatures in one generation to pass their traits down to <em>child</em> creatures in the next generation.</li>
  <li><strong>Variation: </strong>There must be a variety of traits present in the population of creatures or a means to introduce variation for evolution to take place. Imagine a population of beetles that were exactly the same: same color, same size, same wingspan, same everything. Without any variety in the population, the children would always be identical to the parents and to each other. New combinations of traits could never occur, and nothing could evolve.</li>
  <li>
    <strong>Selection: </strong>There must be a mechanism by which some creatures have the opportunity to be parents and pass on their genetic information, while others don’t. This is commonly referred to as <em>survival of the fittest</em>. Take, for example, a population of gazelles that are chased by lions. The faster gazelles have a better chance of escaping the lions, increasing their chances of living longer, reproducing, and passing on their genetic information to offspring.
    The term <em>fittest</em> can be misleading, however. It’s often thought to mean biggest, fastest, or strongest, but while it can sometimes encompass physical attributes like size, speed, or strength, it doesn’t have to. The core of natural selection lies in whatever traits best suit an organism’s environment and increase its likelihood of survival and ultimately reproduction. Instead of asserting superiority, <em>fittest</em> can be better understood as “able to reproduce.” Take the <em>Dolania americana</em> (aka the American sand-burrowing mayfly), which is believed to have the shortest life span of any insect. An adult female lives for only five minutes, but as long as it has managed to deposit its egg in the water, it will pass its genetic information to the next generation. For the typing cats, a more <em>fit</em> cat, one that I will assign as more likely to reproduce, is one that has typed more characters present in a given phrase of Shakespeare.
  </li>
</ul>
<p>I want to emphasize the context in which I’m applying these Darwinian concepts: a simulated, artificial environment where specific goals can be quantified, all for the sake of creative exploration. Throughout history, the principles of genetics have been used to harm those who have been marginalized and oppressed by dominant societal structures. I believe it is essential to approach projects involving GAs with careful consideration of the language used, and to ensure that the documentation and descriptions of the work are framed inclusively.</p>
<p>With these concepts established, I’ll begin walking through the GA narrative. I’ll do this in the context of typing cats. The algorithm will be divided into several steps that unfold over two parts: a set of conditions for initialization, and the steps that are repeated over and over again until the correct phrase is found.</p>
<h3 id="step-1-population-creation">Step 1: Population Creation</h3>
<p>For typing cats, the first step of the GA is to create a population of phrases. I’m using the term <em>phrase</em> rather loosely to mean any string of characters. These phrases are the creatures of this example, though of course they aren’t very creature-like.</p>
<p>In creating the population of phrases, the Darwinian principle of <strong>variation</strong> applies. Let’s say for the sake of simplicity that I’m trying to evolve the phrase <em>cat</em> and that I have a population of three phrases:</p>
<table>
  <tbody>
    <tr>
      <td>rid</td>
    </tr>
    <tr>
      <td>won</td>
    </tr>
    <tr>
      <td>hug</td>
    </tr>
  </tbody>
</table>
<p>Sure, these phrases have variety, but try to mix and match the characters every which way and you’ll never get <em>cat</em>. There isn’t <em>enough</em> variety here to evolve the optimal solution. However, if I had a population of thousands of phrases, all generated randomly, chances are that at least one phrase would have a <em>c</em> as the first character, one would have an <em>a</em> as the second, and one a <em>t</em> as the third. A large population will most likely provide enough variety to generate the desired phrase. (In step 3 of the algorithm, I’ll also demonstrate another mechanism to introduce more variation in case there isn’t enough in the first place.) Step 1 can therefore be described as follows:</p>
<p><span class="highlight">Create a population of randomly generated elements.</span></p>
<p><em>Element</em> is perhaps a better, more general-purpose term than <em>creature</em>. But what is the element? As you move through the examples in this chapter, you’ll see several scenarios; you might have a population of images or a population of vehicles à la <a href="/autonomous-agents#">Chapter 5</a>. The part that’s new in this chapter is that each element, each member of the population, has <em>virtual DNA</em>, a set of properties (you could also call them <em>genes</em>) that describe how a given element looks or behaves. For the typing cats, for example, the DNA could be a string of characters. With this in mind, I can be even more specific and describe step 1 of the GA as follows:</p>
<p><span class="highlight">Create a population of <em>N</em> elements, each with randomly generated DNA.</span></p>
<p>The field of genetics makes an important distinction between the concepts of genotype and phenotype. The actual genetic code—the particular sequence of molecules in the DNA—is an organism’s <strong>genotype</strong>. This is what gets passed down from generation to generation. The <strong>phenotype</strong>, by contrast, is the <em>expression</em> of that data—this cat will be big, that cat will be small, that other cat will be a particularly fast and effective typist.</p>
<p>The genotype/phenotype distinction is key to creatively using GAs. What are the objects in your world? How will you design the genotype for those objects—the data structure to store each object’s properties, and the values those properties take on? And how will you use that information to design the phenotype? That is, what do <em>you</em> want these variables to actually express?</p>
<p>We do this all the time in graphics programming, taking values (the genotype) and interpreting them in a visual way (the phenotype). The simplest example is probably color:</p>
<table>
  <thead>
    <tr>
      <th style="width:100px">Genotype</th>
      <th>Phenotype</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>0</td>
      <td>
        <div style="display: inline-block; vertical-align: sub; height: 18px; width: 18px; background-color: #000000; border: 1px solid black;"></div>
      </td>
    </tr>
    <tr>
      <td>127</td>
      <td>
        <div style="display: inline-block; vertical-align: sub; height: 18px; width: 18px; background-color: #7F7F7F; border: 1px solid black;"></div>
      </td>
    </tr>
    <tr>
      <td>255</td>
      <td>
        <div style="display: inline-block; vertical-align: sub; height: 18px; width: 18px; background-color: #FFFFFF; border: 1px solid black;"></div>
      </td>
    </tr>
  </tbody>
</table>
<p>Think of the genotype as the digital information, the data that represents color—in the case of grayscale values, an integer from 0 to 255. The way you choose to express the data is arbitrary: a red value, a green value, and a blue value. It doesn’t even need to be color at all—in a different approach, you could use the same values to describe the length of a line, the weight of a force, and so on:</p>
<table>
  <thead>
    <tr>
      <th style="width:100px">Same Genotype</th>
      <th>Different Phenotype (Line Length)</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>0</td>
      <td></td>
    </tr>
    <tr>
      <td>127</td>
      <td>
        <div style="display: inline-block; vertical-align: sub; width: 127px; height: 1px; background-color: #000000;"></div>
      </td>
    </tr>
    <tr>
      <td>255</td>
      <td>
        <div style="display: inline-block; vertical-align: sub; width: 255px; height: 1px; background-color: #000000;"></div>
      </td>
    </tr>
  </tbody>
</table>
<p>A nice aspect of the cat-typing example is that there’s no difference between genotype and phenotype. The DNA data is a string of characters, and the expression of that data is that very string.</p>
<h3 id="step-2-selection">Step 2: Selection</h3>
<p>The second step of the GA is to apply the Darwinian principle of <strong>selection</strong>.<em> </em>This involves evaluating the population and determining which members are fit to be selected as parents for the next generation. The process of selection can be divided into two steps:</p>
<ol>
  <li><strong>Evaluate fitness.</strong></li>
  <li><strong>Create a mating pool.</strong></li>
</ol>
<p>For the first of these steps, I’ll need to design a <strong>fitness function</strong>, a function that produces a numeric score to describe the fitness of a given element of the population. This, of course, isn’t how the real world works at all. Creatures aren’t given a score; rather, they simply reproduce or they don’t reproduce. A traditional GA, however, aims to evolve an optimal solution to a problem, so a mechanism to numerically evaluate any given possible solution is required.</p>
<p>Consider the current scenario, the typing cats. Again, for simplicity, I’ll say the target phrase is <em>cat</em>. Assume three members of the population: <em>hut</em>, <em>car</em>, and <em>box</em>. <em>Car</em> is obviously the most fit, given that it has two correct characters in the correct positions, <em>hut</em> has only one, and <em>box</em> has zero. And there it is, a fitness function:</p>
<div data-type="equation">\text{fitness} = \text{the number of correct characters}</div>
<table>
  <thead>
    <tr>
      <th style="width:100px">DNA</th>
      <th>Fitness</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>car</td>
      <td>2</td>
    </tr>
    <tr>
      <td>hut</td>
      <td>1</td>
    </tr>
    <tr>
      <td>box</td>
      <td>0</td>
    </tr>
  </tbody>
</table>
<p>I’ll eventually want to look at examples with more sophisticated fitness functions, but this is a good place to start.</p>
<p>Once the fitness has been calculated for all members of the population, the next part of the selection process is to choose which members are fit to become parents and place them in a mating pool. This step has several approaches. For example, I could employ the <strong>elitist</strong> method and say, “Which two members of the population scored the highest? You two will make all the children for the next generation.” This is probably one of the easier methods to code, but it flies in the face of the principle of variation. If two members of the population (out of perhaps thousands) are the only ones available to reproduce, the next generation will have little variety, and this may stunt the evolutionary process.</p>
<p>I could instead make a mating pool out of a larger number of elements—for example, the top 50 percent of the population. This is another easy one to code, but it also won’t produce optimal results. In this case, the highest-scoring elements would have the same chance of being selected as the ones toward the middle. In a population of 1,000 phrases, why should the phrase ranked 500th have the same chance of reproducing as the phrase ranked 1st? For that matter, why should phrase 500 have a solid shot of reproducing, while phrase 501 has no shot at all?</p>
<p>A better solution for the mating pool is to use a <strong>probabilistic</strong> method, which I’ll call the <em>wheel of fortune</em> (aka the <em>roulette wheel</em>). To illustrate this method, let’s say a population has five elements, each with a fitness score:</p>
<table>
  <thead>
    <tr>
      <th style="width:100px">Element</th>
      <th>Fitness</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>A</td>
      <td>3</td>
    </tr>
    <tr>
      <td>B</td>
      <td>4</td>
    </tr>
    <tr>
      <td>C</td>
      <td>0.5</td>
    </tr>
    <tr>
      <td>D</td>
      <td>1</td>
    </tr>
    <tr>
      <td>E</td>
      <td>1.5</td>
    </tr>
  </tbody>
</table>
<p>The first step is to <strong>normalize</strong> all the scores. Remember normalizing a vector? That involved taking a vector and standardizing its length, setting it to 1. Normalizing a set of fitness scores standardizes their range from 0 to 1, as a percentage of total fitness. For that, first add up all the fitness scores:</p>
<div data-type="equation">\text{total fitness} = 3 + 4 + 0.5 + 1 + 1.5 = 10</div>
<p>Next, divide each score by the total fitness, resulting in the normalized fitness:</p>
<table>
  <thead>
    <tr>
      <th style="width:100px">Element</th>
      <th>Fitness</th>
      <th>Normalized Fitness</th>
      <th>Expressed as a Percentage</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>A</td>
      <td>3</td>
      <td>0.3</td>
      <td>30%</td>
    </tr>
    <tr>
      <td>B</td>
      <td>4</td>
      <td>0.4</td>
      <td>40%</td>
    </tr>
    <tr>
      <td>C</td>
      <td>0.5</td>
      <td>0.05</td>
      <td>5%</td>
    </tr>
    <tr>
      <td>D</td>
      <td>1</td>
      <td>0.1</td>
      <td>10%</td>
    </tr>
    <tr>
      <td>E</td>
      <td>1.5</td>
      <td>0.1</td>
      <td>15%</td>
    </tr>
  </tbody>
</table>
<p>Now it’s time for the wheel of fortune, shown in Figure 9.2.</p>
<div class="half-width-right">
  <figure>
    <img src="images/09_ga/09_ga_3.png" alt="Figure 9.2: In this wheel of fortune, each slice of the wheel is sized according to a fitness value.">
    <figcaption>Figure 9.2: In this wheel of fortune, each slice of the wheel is sized according to a fitness value.</figcaption>
  </figure>
</div>
<p>Spin the wheel and you’ll notice that element B has the highest chance of being selected, followed by A, then E, then D, and finally C. This probability-based selection according to fitness is an excellent approach. It guarantees that the highest-scoring elements will be most likely to reproduce, while also not entirely eliminating any variation from the population. Unlike with the elitist method, even the lowest-scoring element (in this case, C) has at least some chance of passing its information to the next generation. This is important because it’s quite possible (and often the case) that some low-scoring elements have tiny nuggets of genetic code that are truly useful and shouldn’t be removed from the population. For example, in the case of evolving “to be or not to be,” we might have the following elements:</p>
<table>
  <thead>
    <tr>
      <th style="width:100px">Element</th>
      <th>DNA</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>A</td>
      <td>to be or not to go</td>
    </tr>
    <tr>
      <td>B</td>
      <td>to be or not to pi</td>
    </tr>
    <tr>
      <td>C</td>
      <td>purrrrrrrrrrrrr be</td>
    </tr>
  </tbody>
</table>
<p>As you can see, elements A and B are clearly the most fit and would have the highest score. But neither contains the correct characters for the end of the phrase. Element C, even though it would receive a very low score, happens to have the genetic data for the end of the phrase. While I might want A and B to be picked to generate the majority of the next generation, I still want C to have a small chance to participate in the reproductive process too.</p>
<h3 id="step-3-reproduction">Step 3: Reproduction</h3>
<p>Now that I’ve demonstrated a strategy for picking parents, the last step is to use <strong>reproduction</strong> to create the population’s next generation, keeping in mind the Darwinian principle of heredity—that children inherit properties from their parents. Again, numerous techniques could be employed here. For example, one reasonable (and easy-to-program) strategy is <strong>cloning</strong>, meaning just one parent is picked and an exact copy of that parent is created as a child element. As with the elitist approach to selection, however, this runs counter to the goal of variation. Instead, the standard approach with GAs is to pick two parents and create a child according to two steps:</p>
<ol>
  <li><strong>Crossover</strong></li>
  <li><strong>Mutation</strong></li>
</ol>
<p>The first step, <strong>crossover</strong>, creates a child out of the genetic code of two parents. For the cat-typing example, say I’ve picked the following two parent phrases from the mating pool, as outlined in the selection step (I’m simplifying and using strings of length 6, instead of the 18 characters required for “to be or not to be”):</p>
<table>
  <tbody>
    <tr>
      <td>Parent A</td>
      <td>coding</td>
    </tr>
    <tr>
      <td>Parent B</td>
      <td>nature</td>
    </tr>
  </tbody>
</table>
<p>The task at hand is now to create a child phrase from these two. Perhaps the most obvious way (call it the <em>50/50 method</em>) would be to take the first three characters from A and the second three from B, as shown in Figure 9.3.</p>
<figure>
  <img src="images/09_ga/09_ga_4.png" alt="Figure 9.3: A 50/50 crossover">
  <figcaption>Figure 9.3: A 50/50 crossover</figcaption>
</figure>
<p>A variation of this technique is to pick a random midpoint. In other words, I don’t always have to pick exactly half of the characters from each parent. I could use a combination of 1 and 5, or 2 and 4. This is preferable to the 50/50 approach, since it increases the variety of possibilities for the next generation (see Figure 9.4).</p>
<figure>
  <img src="images/09_ga/09_ga_5.png" alt="Figure 9.4: Two examples of crossover from a random midpoint ">
  <figcaption>Figure 9.4: Two examples of crossover from a random midpoint </figcaption>
</figure>
<p>Another possibility is to randomly select a parent for each character in the child string, as in Figure 9.5. You can think of this as flipping a coin six times: heads, take a character from parent A; tails, from parent B. This yields even more possible outcomes: <em>codurg</em>, <em>natine</em>, <em>notune</em>, <em>cadune</em>, and so on.</p>
<figure>
  <img src="images/09_ga/09_ga_6.png" alt="Figure 9.5: Crossover with a coin-flipping approach ">
  <figcaption>Figure 9.5: Crossover with a coin-flipping approach </figcaption>
</figure>
<p>This strategy won’t significantly change the outcome from the random midpoint method; however, if the order of the genetic information plays a role in the fitness function, you may prefer one solution over the other. Other problems may benefit more from the randomness introduced by the coin-flipping approach.</p>
<p>Once the child DNA has been created via crossover, an extra, optional process can be applied before adding the child to the next generation: <strong>mutation</strong>. This second reproduction stage is unnecessary in some cases, but it exists to further uphold the Darwinian principle of variation. The initial population was created randomly, ensuring a variety of elements at the outset. However, this variation is limited by the size of the population, and the variation narrows over time by virtue of selection. Mutation introduces additional variety throughout the evolutionary process.</p>
<div class="half-width-right">
  <figure>
    <img src="images/09_ga/09_ga_7.png" alt="Figure 9.6: Mutating the child phrase">
    <figcaption>Figure 9.6: Mutating the child phrase</figcaption>
  </figure>
</div>
<p>Mutation is described in terms of a <em>rate</em>. A given GA might have a mutation rate of 5 percent, or 1 percent, or 0.1 percent, for example. Say I’ve arrived through crossover at the child phrase <em>catire</em>. If the mutation rate is 1 percent, this means that each character in the phrase has a 1 percent chance of mutating before being “born” into the next generation. What does it mean for a character to mutate? In this case, mutation could be defined as picking a new random character. A 1 percent probability is fairly low, so most of the time mutation won’t occur at all in a six-character string (about 94 percent of the time, in fact). However, when it does, the mutated character is replaced with a randomly generated one (see Figure 9.6).</p>
<p>As you’ll see in the coming examples, the mutation rate can greatly affect the behavior of the system. A very high mutation rate (such as, say, 80 percent) would negate the entire evolutionary process and leave you with something more akin to a brute-force algorithm. If the majority of a child’s genes are generated randomly, you can’t guarantee that the more fit genes occur with greater frequency with each successive generation.</p>
<p>Overall, the process of selection (picking two parents) and reproduction (crossover and mutation) is repeated <em>N</em> times until you have a new population of <em>N</em> child elements.</p>
<h3 id="step-4-repetition">Step 4: Repetition!</h3>
<p>At this point, the new population of children becomes the current population. Then the process returns to step 2 and starts all over again, evaluating the fitness of each element, selecting parents, and producing another generation of children. Hopefully, as the algorithm cycles through more and more generations, the system evolves closer and closer to the desired solution.</p>
<h2 id="coding-the-genetic-algorithm">Coding the Genetic Algorithm</h2>
<p>Now that I’ve described all the steps of the GA, it’s time to translate them into code. Before I dive into the details of the implementation, let’s think about how these steps fit into the overall standard structure of a p5.js sketch. What goes into <code>setup()</code>, and what goes into <code>draw()</code>?</p>
<p><code><strong>setup()</strong></code></p>
<p>Step 1, <strong>Initialization</strong>: Create a starting population of <em>N</em> elements, each with randomly generated DNA.</p>
<p><code><strong>draw()</strong></code></p>
<p>Step 2, <strong>Selection</strong>: Evaluate the fitness of each element of the population and build a mating pool.</p>
<p>Step 3, <strong>Reproduction</strong>: Repeat <em>N</em> times:</p>
<ul>
  <li>Pick two parents with probability according to relative fitness.        </li>
  <li><strong>Crossover:</strong> Create a child by combining the DNA of these two parents.</li>
  <li><strong>Mutation:</strong> Modify the child’s DNA based on a given probability.</li>
  <li>Add the new child to a new population.</li>
</ul>
<p>Step 4: Replace the old population with the new population and return to step 2.</p>
<p>With this plan in place, I can start writing the code.</p>
<h3 id="step-1-initialization">Step 1: Initialization</h3>
<p>If I’m going to create a population, I need a data structure to store a list of elements in the population:</p>
<pre class="codesplit" data-code-language="javascript">// An array for the population of elements
let population = [];</pre>
<p>Choosing an array to represent a list is straightforward, but the question remains: An array of what? An object is an excellent choice for storing the genetic information, as it can hold multiple properties and methods. These genetic objects will be structured according to a class that I’ll call <code>DNA</code>:</p>
<pre class="codesplit" data-code-language="javascript">class DNA {

}</pre>
<p>What should go in the <code>DNA</code> class? For a typing cat, its DNA would be the random phrase it types, a string of characters. However, using an array of characters (rather than a string object) provides a more generic template that can extend easily to other data types. For example, the DNA of a creature in a physics system could be an array of vectors—or for an image, an array of numbers (RGB pixel values). Any set of properties can be listed in an array, and even though a string is convenient for this particular scenario, an array will serve as a better foundation for future evolutionary examples.</p>
<p>The GA specifies that I create a population of <em>N</em> elements, each with <em>randomly generated genes</em>. The DNA constructor therefore includes a loop to fill in each element of the <code>genes</code> array:</p>
<pre class="codesplit" data-code-language="javascript">class DNA {
  constructor(length) {
    //{!1} The individual genes are stored in an array. 
    this.genes = [];
    // There are length genes.
    for (let i = 0; i &#x3C; length; i++) {
      // Each gene is a random character.
      this.genes[i] = randomCharacter(); 
    }
  }
}</pre>
<p>To randomly generate a character, I’ll write a helper function called <code>randomCharacter()</code> for each individual gene:</p>
<pre class="codesplit" data-code-language="javascript">// Return a random character (letter, number, symbol, space, and so forth).
function randomCharacter() {
  let c = floor(random(32, 127));
  return String.fromCharCode(c);
}</pre>
<p>The random numbers picked correspond to a specific character according to a standard known as <strong>ASCII</strong> (American Standard Code for Information Interchange), and <code>String.fromCharCode()</code> is a native JavaScript method that converts a number into its corresponding character based on that standard. The range I’ve specified encompasses upper- and lowercase letters, numbers, punctuation marks, and special characters. An alternative approach could use the Unicode standard, which includes emojis and characters from various world languages, providing a more extensive range of characters for a different target string.</p>
<p>Now that I have the constructor, I can return to <code>setup()</code> and initialize each <code>DNA</code> object in the <code>population</code> array:</p>
<pre class="codesplit" data-code-language="javascript">let population = [];

function setup() {
  for (let i = 0; i &#x3C; population.length; i++) {
    //{!1} Initialize each element of the population; 18 is hardcoded for now as the length of the <code>genes</code> array.
    population[i] = new DNA(18);
  }
}</pre>
<p>The <code>DNA</code> class is not at all complete. I need to give it methods that perform all the other tasks in the GA. I’ll do that as I walk through steps 2 and 3.</p>
<h3 id="step-2-selection-1">Step 2: Selection</h3>
<p>Step 2 reads, “Evaluate the fitness of each element of the population and build a mating pool.” I’ll start with the first part, evaluating each object’s fitness. Earlier I stated that one possible fitness function for the typed phrases is the total number of correct characters. Now I’ll revise this fitness function a little bit and state it as the <em>percentage</em> of correct characters—that is, the number of correct characters divided by the total number of characters:</p>
<div data-type="equation">\text{fitness} = \frac{\text{correct characters}}{\text{total characters}}</div>
<p>Where should I calculate the fitness? Since the <code>DNA</code> class contains the genetic information (the phrase I will test against the target phrase), I can write a method inside the <code>DNA</code> class to score its own fitness. Let’s assume a target phrase:</p>
<pre class="codesplit" data-code-language="javascript">let target = "to be or not to be";</pre>
<p>I can now compare each gene against the corresponding character in the target phrase, incrementing a counter each time I find a correct character in the correct position. For example, a <code>t</code> is found in several places in <code>target</code>, but it increases the fitness only if it is in the <code>genes</code> array at the correct corresponding index:</p>
<p></p>
<pre class="codesplit" data-code-language="javascript">class DNA {
  constructor(length) {
    this.genes = [];
    //{!1} Add a variable to track fitness.
    this.fitness = 0;
    for (let i = 0; i &#x3C; length; i++) {
      this.genes[i] = randomCharacter();
    }
  }

  // Compute fitness as a percentage of correct characters.
  calculateFitness(target) {
    let score = 0;
    for (let i = 0; i &#x3C; this.genes.length; i++) {
      if (this.genes[i] === target.charAt(i)) {
        score++;
      }
    }
    this.fitness = score / target.length;
  }
}</pre>
<p>Since fitness is calculated for each subsequent generation, the very first step I’ll take inside the <code>draw()</code> loop is to call the fitness function for each member of the population:</p>
<pre class="codesplit" data-code-language="javascript">function draw() {
  for (let phrase of population) {
    phrase.calculateFitness(target);
  }
}</pre>
<p>Once the fitness scores have been computed, the next step is to build the <em>mating pool</em> for the reproduction process. The mating pool is a data structure from which two parents are repeatedly selected. Recalling the description of the selection process, the goal is to pick parents with probabilities calculated according to fitness. The members of the population with the highest fitness scores should be the most likely to be selected; those with the lowest scores, the least likely.</p>
<p>In <a href="/random#">Chapter 0</a>, I covered the basics of probability and generating a custom distribution of random numbers. I’m going to use the same techniques here to assign a probability to each member of the population, picking parents by spinning the wheel of fortune. Revisiting Figure 9.2, your mind might immediately go back to <a href="/oscillation#">Chapter 3</a> and contemplate coding a simulation of an actual spinning wheel. As fun as this might be (and you should make one!), it’s quite unnecessary.</p>
<div class="half-width-right">
  <figure>
    <img src="images/09_ga/09_ga_8.png" alt="Figure 9.7: A bucket full of letters A, B, C, D, and E. The higher the fitness, the more instances of the letter in the bucket.">
    <figcaption>Figure 9.7: A bucket full of letters A, B, C, D, and E. The higher the fitness, the more instances of the letter in the bucket.</figcaption>
  </figure>
</div>
<p>One solution that could work here is to pick from the five options depicted in Figure 9.2 (A, B, C, D, E) according to their probabilities by filling an array with multiple instances of each parent. In other words, imagine you have a bucket of wooden letters, as in Figure 9.7. Based on the earlier probabilities, it should contain 30 As, 40 Bs, 5 Cs, 10 Ds, and 15 Es. If you were to pick a random letter out of that bucket, you’d have a 30 percent chance of getting an A, a 5 percent chance of getting a C, and so on.</p>
<p>For the GA code, that bucket could be an array, and each wooden letter a potential parent <code>DNA</code> object. The mating pool is therefore created by adding each parent to the array a certain number of times, scaled according to that parent’s fitness score:</p>
<pre class="codesplit" data-code-language="javascript">  //{!1} Start with an empty mating pool.
  let matingPool = [];

  for (let phrase of population) {
    //{!1} <code>n</code> is equal to fitness times 100.
    // 100 is an arbitrary way to scale the percentage of fitness to a larger integer value.
    let n = floor(phrase.fitness * 100);
    for (let j = 0; j &#x3C; n; j++) {
      //{!1} Add each member of the population to the mating pool <code>n</code> times.
      matingPool.push(phrase);
    }
  }</pre>
<p>With the mating pool ready to go, it’s time to select two parents! Picking two parents for each child is a somewhat arbitrary decision. It certainly mirrors human reproduction and is the standard means in the textbook GA, but in terms of creative applications, there really aren’t restrictions here. You could choose only one parent for cloning, or devise a reproduction methodology for picking three or four parents from which to generate child DNA. For this demonstration, I’ll stick to two parents and call them <code>parentA</code> and <code>parentB</code>.</p>
<p>I can select two random instances of DNA from the mating pool by using the p5.js <code>random()</code> function. When an array is passed as an argument to <code>random()</code>, the function returns a single random element from the array:</p>
<pre class="codesplit" data-code-language="javascript">  let parentA = random(matingPool);
  let parentB = random(matingPool);</pre>
<p>This method of building a mating pool and choosing parents from it works, but it isn’t the only way to perform selection. Other, more memory-efficient techniques don’t require an additional array full of multiple references to each element. For example, think back to the discussion of nonuniform distributions of random numbers in <a href="/random#">Chapter 0</a>. There, I implemented the accept-reject method. If applied here, the approach would be to randomly pick an element from the original <code>population</code> array, and then pick a second, qualifying random number to check against the element’s fitness value. If the fitness is less than the qualifying number, start again and pick a new element. Keep going until two parents are deemed fit enough.</p>
<p>Yet another excellent alternative is worth exploring that similarly capitalizes on the principle of fitness-proportionate selection. To understand how it works, imagine a relay race in which each member of the population runs a given distance tied to its fitness. The higher the fitness, the farther they run. Let’s also assume that the fitness values have been normalized to all add up to 1 (just as with the wheel of fortune). The first step is to pick a <em>starting line—</em>a random distance from the finish. This distance is a random number from 0 to 1. (You’ll see in a moment that the finish line<em> </em>is assumed to be at 0.)</p>
<pre class="codesplit" data-code-language="javascript">let start = random(1);</pre>
<p>Then the relay race begins at the starting line with the first member of the population:</p>
<pre class="codesplit" data-code-language="javascript">let index = 0;</pre>
<p>The runner travels a distance defined by its normalized fitness score, then hands the baton to the next runner:</p>
<pre class="codesplit" data-code-language="javascript">
while (start > 0) {
  // Move a distance according to fitness.
  start = start - population[index].fitness;
  // Pass the baton to the next element.
  index++;
}</pre>
<p>The steps are repeated over and over again in a <code>while</code> loop until the race ends (<code>start</code> is less than or equal to <code>0</code>, the finish line). The runner who crosses the finish threshold is selected as a parent.</p>
<p>Here are all the steps together in a function that returns the selected element:</p>
<pre class="codesplit" data-code-language="javascript">function weightedSelection() {
  // Start with the first element.
  let index = 0;
  // Pick a starting point.
  let start = random(1);
  // At the finish line?
  while (start > 0) {
    // Move a distance according to fitness.
    start = start - population[index].fitness;
    // Pass the baton to the next element.
    index++;
  }
  // Undo moving to the next element since the finish has been reached.
  index--;
  return population[index];
}</pre>
<p>This works well for selection because every member has a shot at crossing the finish line (the elements’ fitness scores all add up to 1), but those who run longer distances (that is, those with higher fitness scores) have a better chance of making it there. However, while this method is more memory efficient, it can be more <em>computationally </em>demanding, especially for large populations, as it requires iterating through the population for each selection. By contrast, the original <code>matingPool</code> array method needs only a single random lookup into the array per parent.</p>
<p>Depending on the specific requirements and constraints of your application of GAs, one approach might prove more suitable than the other. I’ll alternate between them in the examples outlined in this chapter.</p>
<div data-type="exercise">
  <h3 id="exercise-92">Exercise 9.2</h3>
  <p>Revisit the accept-reject algorithm from <a href="/random#">Chapter 0</a> and rewrite the <code>weightedSelection()</code> function to use accept-reject instead. Like the relay race method, this technique can also end up being computationally intensive, since several potential parents may be rejected as unfit before one is finally chosen.</p>
</div>
<div data-type="exercise">
  <h3 id="exercise-93">Exercise 9.3</h3>
  <p>In some cases, the wheel-of-fortune algorithm will have an extraordinarily high preference for some elements over others. Take the following probabilities:</p>
  <table>
    <thead>
      <tr>
        <th style="width:200px">Element</th>
        <th>Probability</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td>A</td>
        <td>98%</td>
      </tr>
      <tr>
        <td>B</td>
        <td>1%</td>
      </tr>
      <tr>
        <td>C</td>
        <td>1%</td>
      </tr>
    </tbody>
  </table>
  <p>This is sometimes undesirable, given that it will decrease the amount of variety in this system. A solution to this problem is to replace the calculated fitness scores with the ordinals of scoring (meaning their rank):</p>
  <table>
    <thead>
      <tr>
        <th style="width:100px">Element</th>
        <th style="width:100px">Rank</th>
        <th>Probability</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td>A</td>
        <td>1</td>
        <td>50% (1/2)</td>
      </tr>
      <tr>
        <td>B</td>
        <td>2</td>
        <td>33% (1/3)</td>
      </tr>
      <tr>
        <td>C</td>
        <td>3</td>
        <td>17% (1/6)</td>
      </tr>
    </tbody>
  </table>
  <p>How can you implement an approach like this? Hint: You don’t need to modify the selection algorithm. Instead, your task is to calculate the probabilities from the rank rather than the raw fitness score.</p>
</div>
<p>For any of these algorithms, the same parent could be picked twice for a given child. If I wanted, I could enhance the algorithm to ensure that this isn’t possible. This would likely have very little impact on the end result, but it may be worth exploring as an exercise.</p>
<div data-type="exercise">
  <h3 id="exercise-94">Exercise 9.4</h3>
  <p>Pick any of the weighted selection algorithms and adapt the algorithm to guarantee that two unique parents are picked.</p>
</div>
<h3 id="step-3-reproduction-crossover-and-mutation">Step 3: Reproduction (Crossover and Mutation)</h3>
<p>Once I have the two parents, the next step is to perform a <strong>crossover</strong> operation to generate child DNA, followed by <strong>mutation</strong>:</p>
<pre class="codesplit" data-code-language="javascript">// A function for crossover
let child = parentA.crossover(parentB);
// A function for mutation
child.mutate();</pre>
<p>Of course, the <code>crossover()</code> and <code>mutate()</code> methods don’t magically exist in the <code>DNA</code> class; I have to write them. The way I’ve called <code>crossover()</code> indicates that it should receive an instance of <code>DNA</code> as an argument (<code>parentB</code>) and return a new instance of <code>DNA</code>, the <code>child</code>:</p>
<pre class="codesplit" data-code-language="javascript">crossover(partner) {
  // The child is a new instance of <code>DNA</code>.
  // (Note that the genes are generated randomly in the <code>DNA</code> constructor,
  // but the crossover method will override the array.)
  let child = new DNA(this.genes.length);

  //{!1} Pick a random midpoint in the <code>genes</code> array.
  let midpoint = floor(random(this.genes.length));

  for (let i = 0; i &#x3C; this.genes.length; i++) {
    // Before the midpoint, take genes from this DNA.
    if (i &#x3C; midpoint) {
      child.genes[i] = this.genes[i];
      // After the midpoint, take from the partner DNA.
    } else {
      child.genes[i] = partner.genes[i];
    }
  }
  return child;
}</pre>
<p>This implementation uses the random midpoint method of crossover, in which the first section of genes is taken from parent A and the second from parent B.</p>
<div data-type="exercise">
  <h3 id="exercise-95">Exercise 9.5</h3>
  <p>Rewrite the crossover function to use the coin-flipping method instead, in which each gene has a 50 percent chance of coming from parent A and a 50 percent chance of coming from parent B.</p>
</div>
<p>The <code>mutate()</code> method is even simpler to write than <code>crossover()</code>. All I need to do is loop through the array of genes and randomly pick a new character according to the defined mutation rate. With a mutation rate of 1 percent, for example, a new character would be generated only 1 out of 100 times:</p>
<pre class="codesplit" data-code-language="javascript">let mutationRate = 0.01;

if (random(1) &#x3C; mutationRate) {
  /* Any code here would be executed 1% of the time. */
}</pre>
<p>The entire method therefore reads as follows:</p>
<pre class="codesplit" data-code-language="javascript">mutate(mutationRate) {
  //{!1} Look at each gene in the array.
  for (let i = 0; i &#x3C; this.genes.length; i++) {
    //{!1} Check a random number against the mutation rate.
    if (random(1) &#x3C; mutationRate) {
      //{!1} Mutation means choosing a new random character.
      this.genes[i] = randomCharacter();
    }
  }
}</pre>
<p>Once again, I’m able to use the <code>randomCharacter()</code> helper function to simplify the mutation process.</p>
<h3 id="putting-it-all-together">Putting It All Together</h3>
<p>I’ve now walked through the steps of the GA twice—once describing the algorithm in narrative form, and another time with code snippets implementing each of the steps. Now I’m ready to put it all together and show you the complete code alongside the basic steps of the algorithm.</p>
<div data-type="example">
  <h3 id="example-91-genetic-algorithm-for-evolving-shakespeare">Example 9.1: Genetic Algorithm for Evolving Shakespeare</h3>
  <figure>
    <div data-type="embed" data-p5-editor="https://editor.p5js.org/natureofcode/sketches/q4F192JCV" data-example-path="examples/09_ga/9_1_ga_shakespeare"><img src="examples/09_ga/9_1_ga_shakespeare/screenshot.png"></div>
    <figcaption></figcaption>
  </figure>
</div>
<pre class="codesplit" data-code-language="javascript">
// Mutation rate
let mutationRate = 0.01;
// Population size
let populationSize = 150;

// Population array
let population = [];

// Target phrase
let target = "to be or not to be";

function setup() {
  createCanvas(640, 360);
  // <strong>Step 1: Initialization</strong><span class="blank"><strong><em>
</em></strong></span>  for (let i = 0; i &#x3C; populationSize; i++) {
    population[i] = new DNA(target.length);
  }
}

function draw() {

  //{!0} <strong>Step 2: Selection</strong>
  //{!3} Step 2a: Calculate fitness.
  for (let phrase of population) {
    phrase.calculateFitness(target);
  }

  // Step 2b: Build the mating pool.
  let matingPool = [];

  for (let phrase of population) {
    //{!4} Add each member <code>n</code> times according to its fitness score.
    let n = floor(phrase.fitness * 100);
    for (let j = 0; j &#x3C; n; j++) {
      matingPool.push(phrase);
    }
  }

  // <strong>Step 3: Reproduction</strong>
  for (let i = 0; i &#x3C; population.length; i++) {
    let parentA = random(matingPool);
    let parentB = random(matingPool);
    // Step 3a: Crossover
    let child = parentA.crossover(parentB);
    // Step 3b: Mutation
    child.mutate(mutationRate);

    //{!1} Note that you are overwriting the population with the new
    // children.  When <code>draw()</code> loops, you will perform all the same
    // steps with the new population of children.
    population[i] = child;
  }

	// <strong>Step 4: Repetition. Go back to the beginning of </strong><code><strong>draw()</strong></code><strong>!</strong>
}</pre>
<p>The <em>sketch.js</em> file precisely mirrors the steps of the GA. However, most of the functionality called upon is encapsulated in the <code>DNA</code> class:</p>
<pre class="codesplit" data-code-language="javascript">
class DNA {
  //{.code-wide} Constructor (makes a random DNA)
  constructor(length) {
    this.genes = [];
    this.fitness = 0;
    for (let i = 0; i &#x3C; length; i++) {
      this.genes[i] = randomCharacter();
    }
  }

  //{.code-wide} Converts the array to a string of the phenotype.
  getPhrase() {
    return this.genes.join("");
  }

  //{.code-wide} Calculate fitness.
  calculateFitness(target) {
    let score = 0;
    for (let i = 0; i &#x3C; this.genes.length; i++) {
      if (this.genes[i] === target.charAt(i)) {
        score++;
      }
    }
    this.fitness = score / target.length;
  }

  //{.code-wide} Crossover
  crossover(partner) {
    let child = new DNA(this.genes.length);
    let midpoint = floor(random(this.genes.length));
    for (let i = 0; i &#x3C; this.genes.length; i++) {
      if (i &#x3C; midpoint) {
        child.genes[i] = this.genes[i];
      } else {
        child.genes[i] = partner.genes[i];
      }
    }
    return child;
  }

  //{.code-wide} Mutation
  mutate(mutationRate) {
    for (let i = 0; i &#x3C; this.genes.length; i++) {
      if (random(1) &#x3C; mutationRate) {
        this.genes[i] = randomCharacter();
      }
    }
  }
}

// Return a random character (letter, number, symbol, space, and so forth).
function randomCharacter() {
  let c = floor(random(32, 127));
  return String.fromCharCode(c);
}</pre>
<p>In Example 9.1, you might notice that new child elements are directly added to the <code>population</code> array. This approach is possible because I have a separate mating pool array that contains references to the original parent elements. However, if I were to instead use the relay-race <code>weightedSelection()</code> function, I’d need to create a temporary array for the new population. This temporary array would hold the child elements and replace the original population array only after the reproduction step is completed. You’ll see this implemented in Example 9.2.</p>
<div data-type="exercise">
  <h3 id="exercise-96">Exercise 9.6</h3>
  <p>Add features to Example 9.1 to report more information about the progress of the GA itself. For example, show the phrase closest to the target in each generation, as well as a report on the number of generations, the average fitness, and so on. Stop the GA after it has solved the phrase. Consider writing a <code>Population</code> class to manage the GA, instead of including all the code in <code>draw()</code>.</p>
  <figure>
    <div data-type="embed" data-p5-editor="https://editor.p5js.org/natureofcode/sketches/ZwT5cPix2" data-example-path="examples/09_ga/exercise_9_6_annotated_ga_shakespeare"><img src="examples/09_ga/exercise_9_6_annotated_ga_shakespeare/screenshot.png"></div>
    <figcaption></figcaption>
  </figure>
</div>
<div data-type="exercise">
  <h3 id="exercise-97">Exercise 9.7</h3>
  <p>Explore the idea of a dynamic mutation rate. For example, try calculating a mutation rate that inversely correlates with the average fitness of the parent phrases so that higher fitness results in fewer mutations. Does this change affect the behavior of the overall system and how quickly the target phrase is found?</p>
</div>
<p></p>
<h2 id="customizing-genetic-algorithms">Customizing Genetic Algorithms</h2>
<p>The nice thing about using GAs in a project is that example code can easily be ported from application to application. The core mechanics of selection and reproduction don’t need to change. However, you, the creator, will have to customize three key components of GAs for each use. This is crucial to moving beyond trivial demonstrations of evolutionary simulations (as in the Shakespeare example) to creative uses in projects that you make in p5.js and other programming environments.</p>
<h3 id="key-1-the-global-variables">Key 1: The Global Variables</h3>
<p>The GA doesn’t have a lot of variables. If you look at the code in Example 9.1, you’ll see only two global variables (not including the arrays to store the population and mating pool):</p>
<pre class="codesplit" data-code-language="javascript">let mutationRate = 0.01;
let populationSize = 150;</pre>
<p>These two variables can greatly affect the behavior of the system, and it’s not such a good idea to arbitrarily assign them values (though tweaking them through trial and error is a perfectly reasonable way to arrive at optimal values).</p>
<p>I chose the values for the Shakespeare demonstration to virtually guarantee that the GA would solve for the phrase, but not too quickly (approximately 1,000 generations on average), so as to demonstrate the process over a reasonable period of time. A much larger population, however, would yield faster results (if the goal were algorithmic efficiency rather than demonstration). Here’s a table of some results:</p>
<table>
  <thead>
    <tr>
      <th style="width:100px">Population</th>
      <th style="width:100px">Mutation</th>
      <th>Number of Generations Until the Phrase Is Solved</th>
      <th>Total Time (in Seconds) Until the Phrase Is Solved</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>150</td>
      <td>1%</td>
      <td>1,089</td>
      <td>18.8</td>
    </tr>
    <tr>
      <td>300</td>
      <td>1%</td>
      <td>448</td>
      <td>8.2</td>
    </tr>
    <tr>
      <td>1,000</td>
      <td>1%</td>
      <td>71</td>
      <td>1.8</td>
    </tr>
    <tr>
      <td>50,000</td>
      <td>1%</td>
      <td>27</td>
      <td>4.3</td>
    </tr>
  </tbody>
</table>
<p>Notice that increasing the population size drastically reduces the number of generations needed to solve for the phrase. However, it doesn’t necessarily reduce the amount of time. Once the population balloons to 50,000 elements, the sketch begins to run slowly, given the amount of time required to process fitness and build a mating pool out of so many elements. (Of course, optimizations could be made should you require such a large population.)</p>
<p>In addition to the population size, the mutation rate can greatly affect performance:</p>
<table>
  <thead>
    <tr>
      <th style="width:100px">Population</th>
      <th style="width:100px">Mutation</th>
      <th>Number of Generations Until the Phrase Is Solved</th>
      <th>Total Time (in Seconds) Until the Phrase Is Solved</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>1,000</td>
      <td>0%</td>
      <td>37 or never?</td>
      <td>1.2 or never?</td>
    </tr>
    <tr>
      <td>1,000</td>
      <td>1%</td>
      <td>71</td>
      <td>1.8</td>
    </tr>
    <tr>
      <td>1,000</td>
      <td>2%</td>
      <td>60</td>
      <td>1.6</td>
    </tr>
    <tr>
      <td>1,000</td>
      <td>10%</td>
      <td>Never?</td>
      <td>Never?</td>
    </tr>
  </tbody>
</table>
<p>Without any mutation at all (0 percent), you just have to get lucky. If all the correct characters are present somewhere in an element of the initial population, you’ll evolve the phrase very quickly. If not, there’s no way for the sketch to ever reach the exact phrase. Run it a few times and you’ll see both instances. In addition, once the mutation rate gets high enough (10 percent, for example), so much randomness is involved (1 out of every 10 letters is random in each new child) that the simulation is pretty much back to a randomly typing cat. In theory, it will eventually solve the phrase, but you may be waiting much, much longer than is reasonable.</p>
<h3 id="key-2-the-fitness-function">Key 2: The Fitness Function</h3>
<p>Playing around with the mutation rate or population size is pretty easy and involves little more than typing numbers in your sketch. The real hard work of developing a GA is in writing the fitness function. If you can’t define your problem’s goals and evaluate numerically how well those goals have been achieved, you won’t have successful evolution in your simulation.</p>
<p>Before I move on to other scenarios exploring more sophisticated fitness functions, I want to look at flaws in my Shakespearean fitness function. Consider solving for a phrase that isn’t 18 characters long, but 1,000. And take two elements of the population, one with 800 characters correct and one with 801. Here are their fitness scores:</p>
<table>
  <thead>
    <tr>
      <th style="width:100px">Phrase</th>
      <th style="width:200px">Characters Correct</th>
      <th>Fitness</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>A</td>
      <td>800</td>
      <td>80.0%</td>
    </tr>
    <tr>
      <td>B</td>
      <td>801</td>
      <td>80.1%</td>
    </tr>
  </tbody>
</table>
<p>This scenario has a couple of problems. First, I’m adding elements to the mating pool <em>N</em> times, where <em>N</em> equals fitness multiplied by 100. But objects can be added to an array only a whole number of times, so A and B will both be added 80 times, giving them an equal probability of being selected. Even with an improved solution that takes floating-point probabilities into account, 80.1 percent is only a teeny tiny bit higher than 80 percent. But getting 801 characters right is a whole lot better than 800 in the evolutionary scenario. I really want to make that additional character count. I want the fitness score for 801 characters to be <em>substantially</em> better than the score for 800.</p>
<p>To put it another way, Figure 9.8 shows graphs of two possible fitness functions.</p>
<figure>
  <img src="images/09_ga/09_ga_9.png" alt="Figure 9.8: A fitness graph of y = x (left) and of y = x^2 (right)">
  <figcaption>Figure 9.8: A fitness graph of <span data-type="equation">y = x</span> (left) and of <span data-type="equation">y = x^2</span> (right)</figcaption>
</figure>
<p>On the left is a linear graph; as the number of characters goes up, so does the fitness score. By contrast, in the graph on the right, as the number of characters goes up, the fitness score goes <em>way</em> up. That is, the fitness increases at an accelerating rate as the number of correct characters increases.</p>
<p>I can achieve this second type of result in various ways. For example, I could say this:</p>
<div data-type="equation">\text{fitness} = \text{(correct characters)}^2</div>
<p>Here, the fitness scores increase <strong>quadratically</strong>, meaning proportional to the square of the number of correct characters. Say I have two members of the population, one with five correct characters and one with six. The number 6 is a 20 percent increase over the number 5. However, by squaring the correct characters, the fitness value will go from 25 to 36, a 44 percent increase:</p>
<table>
  <thead>
    <tr>
      <th style="width:200px">Correct Characters</th>
      <th>Fitness</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>5</td>
      <td>25</td>
    </tr>
    <tr>
      <td>6</td>
      <td>36</td>
    </tr>
  </tbody>
</table>
<p>Here’s another formula:</p>
<div data-type="equation">\text{fitness} = 2^\text{correct characters}</div>
<p>And here’s how that formula plays out as the number of correct characters increases:</p>
<table>
  <thead>
    <tr>
      <th style="width:200px">Correct Characters</th>
      <th>Fitness</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>1</td>
      <td>2</td>
    </tr>
    <tr>
      <td>2</td>
      <td>4</td>
    </tr>
    <tr>
      <td>3</td>
      <td>8</td>
    </tr>
    <tr>
      <td>4</td>
      <td>16</td>
    </tr>
  </tbody>
</table>
<p>Here, the fitness scores increase <strong>exponentially</strong>, doubling with each additional correct character.</p>
<div data-type="exercise">
  <h3 id="exercise-98">Exercise 9.8</h3>
  <p>Rewrite the fitness function to increase quadratically or exponentially, according to the number of correct characters. Note that you’ll likely have to normalize the fitness values to a range from 0 to 1 so they can be added to the mating pool a reasonable number of times, or use a different weighted-selection method.</p>
</div>
<p>While this rather specific discussion of exponential versus linear equations is an important detail in the design of a good fitness function, I don’t want you to miss the more important point here: <em>design your own fitness function!</em> I seriously doubt that any project you undertake in p5.js with GAs will involve counting the correct number of characters in a string. In the context of this book, you’ll more likely be looking to evolve a creature that’s part of a physics system. Perhaps you’re looking to optimize the weights of steering behaviors so a creature can best escape a predator or avoid an obstacle or make it through a maze. You have to ask yourself what you’re hoping to evaluate.</p>
<p>Consider a racing simulation in which a vehicle is evolving a design optimized for speed:</p>
<div data-type="equation">\text{fitness} = \text{total number of frames required for vehicle to reach race finish}</div>
<p>How about a mouse that’s evolving the optimal way to find a piece of cheese?</p>
<div data-type="equation">\text{fitness} = \text{mouse distance to cheese}</div>
<p>The design of computer-controlled players in a game is also a common scenario. Say you’re programming a soccer game in which the user is the goalie. The rest of the players are controlled by your program and have a set of parameters that determine how they kick a ball toward the goal. What would be the fitness score for any given player?</p>
<div data-type="equation">\text{fitness} = \text{total goals scored}</div>
<p>This, of course, is a simplistic take on the game of soccer, but it illustrates the point. The more goals a player scores, the higher its fitness, and the more likely its genetic information will appear in the next game. Even with a fitness function as simple as the one described here, this scenario is demonstrating something powerful—the adaptability of a system. If the players continue to evolve from game to game to game, when a new <em>human</em> user enters the game with a completely different strategy, the system will quickly discover that the fitness scores are going down and evolve a new optimal strategy. It will adapt. (Don’t worry, there’s very little danger of this resulting in sentient, soccer-playing robots that will enslave all humans.)</p>
<p>In the end, if you don’t have a fitness function that effectively evaluates the performance of the individual elements of your population, you won’t have any evolution. And the fitness function from one example will likely not apply to a totally different project. You have to design a function, sometimes from scratch, that works for your particular project. And where do you do this? All you have to edit are those few lines of code inside the method that computes the <code>fitness</code> variable:</p>
<pre class="codesplit" data-code-language="javascript">calculateFitness() {
  ????????????
  ????????????
  this.fitness = ??????????
}</pre>
<p>Filling in those question marks is the part where you get to shine!</p>
<h3 id="key-3-the-genotype-and-phenotype">Key 3: The Genotype and Phenotype</h3>
<p>The final key to designing your own GA relates to the way you choose to encode the properties of your system. What are you trying to express, and how can you translate that expression into a bunch of numbers? What is the genotype and phenotype?</p>
<p>I started with the Shakespeare example because of how easy it is to design both the genotype (an array of characters) and its expression, the phenotype (the string displayed on the canvas). It isn’t always this easy, however. For example, when talking about the fitness function for a soccer game, I happily assumed the existence of computer-controlled kickers that each have a “set of parameters that determine how they kick a ball toward the goal,” but actually determining what those parameters are and how you choose to encode them would require some thought and creativity. And of course, there’s no one correct answer: how you design the system is up to you.</p>
<p>The good news—and I hinted at this earlier in the chapter—is that you’ve been translating genotypes (data) into phenotypes (expression) all along. Anytime you write a class in p5.js, you make a whole bunch of variables:</p>
<div class="snip-below">
  <pre class="codesplit" data-code-language="javascript">class Vehicle {
  constructor() {
    this.maxspeed = ????;
    this.maxforce = ????;
    this.size = ????;
    this.separationWeight = ????;
    /* and more... */
  }
  </pre>
</div>
<p>All you need to do to evolve those variables is to turn them into an array, so that the array can be used with all the methods—<code>crossover()</code>, <code>mutate()</code>, and the like—found in the <code>DNA</code> class. One common solution is to use an array of floating-point numbers from 0 to 1:</p>
<pre class="codesplit" data-code-language="javascript">class DNA {
  constructor(length) {
    // An empty array
    this.genes = [];
    for (let i = 0; i &#x3C; length; i++) {
      // Always pick a number from 0 to 1.
      this.genes[i] = random(1);
    }
  }
}</pre>
<p>Notice that I’ve now put the raw genetic data (genotype) and its expression (phenotype) into two separate classes. The <code>DNA</code> class is the genotype—it’s just a bunch of numbers. The <code>Vehicle</code> class is the phenotype—it’s an expression of how to turn those numbers into animated, visual behaviors. The two can be linked by including a <code>DNA</code> instance inside the <code>Vehicle</code> class:</p>
<div class="snip-below">
  <pre class="codesplit" data-code-language="javascript">class Vehicle {
  constructor() {
    //{!1} A <code>DNA</code> object embedded into the <code>Vehicle</code> class
    this.dna = new DNA(4);
    //{!4} Use the genes to set variables.
    this.maxspeed = dna.genes[0];
    this.maxforce = dna.genes[1];
    this.size = dna.genes[2];
    this.separationWeight = dna.genes[3];
    /* and more... */
  }</pre>
</div>
<p>Of course, you most likely don’t want all your variables to have a range from 0 to 1. But rather than try to remember how to adjust those ranges in the <code>DNA</code> class, it’s easier to pull the original genetic information from the <code>DNA</code> object and then use p5.js’s <code>map()</code> function to change the range as needed for your phenotype. For example, if you want a <code>size</code> variable between 10 and 72, you would say this:</p>
<pre class="codesplit" data-code-language="javascript">    this.size = map(this.dna.genes[2], 0, 1, 10, 72);</pre>
<p>In other cases, you may want to design a genotype that’s an array of objects. Consider the design of a rocket with a series of thruster engines. You could consider each thruster to be a vector that describes its direction and relative strength:</p>
<pre class="codesplit" data-code-language="javascript">class DNA {
  constructor(length) {
    // The genotype is an array of vectors.
    this.genes = [];
    for (let i = 0; i &#x3C; length; i++) {
      //{!1} A vector pointing in a random direction
      this.genes[i] = p5.Vector.random2D();
      //{!1} And scaled randomly
      this.genes[i].mult(random(10));
    }
  }
}</pre>
<p>The phenotype would be a <code>Rocket</code> class that participates in a physics system:</p>
<pre class="codesplit" data-code-language="javascript">class Rocket {
  constructor() {
    this.dna = ????;
    /* and more... */
  }
}  </pre>
<p>What’s great about dividing the genotype and phenotype into separate classes (<code>DNA</code> and <code>Rocket</code>, for example) is that when it comes time to build all the code, you’ll notice that the <code>DNA</code> class I developed earlier remains intact. The only thing that changes is the kind of data stored in the array (numbers, vectors, and so on) and the expression of that data in the phenotype class.</p>
<p>In the next section, I’ll follow this idea a bit further and walk through the necessary steps to implement an example that involves moving bodies and an array of vectors as DNA.</p>
<h2 id="evolving-forces-smart-rockets">Evolving Forces: Smart Rockets</h2>
<p>I mentioned rockets for a specific reason: in 2009, Jer Thorp released a GAs example on his blog titled “Smart Rockets.” Thorp pointed out that the National Aeronautics and Space Administration (NASA) uses evolutionary computing techniques to solve all sorts of problems, from satellite antenna design to rocket-firing patterns. This inspired him to create a Flash demonstration of evolving rockets.</p>
<p>Here’s the scenario: a population of rockets launches from the bottom of the screen with the goal of hitting a target at the top of the screen. Obstacles block a straight-line path to the target (see Figure 9.9).</p>
<figure>
  <img src="images/09_ga/09_ga_10.png" alt="Figure 9.9: A population of smart rockets seeking a delicious strawberry planet">
  <figcaption>Figure 9.9: A population of smart rockets seeking a delicious strawberry planet</figcaption>
</figure>
<p>Each rocket is equipped with five thrusters of variable strength and direction (Figure 9.10). The thrusters don’t fire all at once and continuously; rather, they fire one at a time in a custom sequence.</p>
<div class="half-width-right">
  <figure>
    <img src="images/09_ga/09_ga_11.png" alt="Figure 9.10: A single smart rocket with five thrusters, carrying Clawdius the astronaut">
    <figcaption>Figure 9.10: A single smart rocket with five thrusters, carrying Clawdius the astronaut</figcaption>
  </figure>
</div>
<p>In this section, I’m going to evolve my own simplified smart rockets, inspired by Thorp’s. When I get to the end of the section, I’ll leave implementing some of Thorp’s additional advanced features as an exercise.</p>
<p>My rockets will have only one thruster, which will be able to fire in any direction with any strength for every frame of animation. This isn’t particularly realistic, but it will make building out the example a little easier. (You can always make the rocket and its thrusters more advanced and realistic later.)</p>
<h3 id="developing-the-rockets">Developing the Rockets</h3>
<p>To implement my evolving smart rockets, I’ll start by taking the <code>Mover</code> class from <a href="/forces#">Chapter 2</a> and renaming it <code>Rocket</code>:</p>
<pre class="codesplit" data-code-language="javascript">class Rocket {
  constructor(x, y) {
    // A rocket has three vectors: position, velocity, and acceleration.
    this.position = createVector(x, y);
    this.velocity = createVector();
    this.acceleration = createVector();
  }

  // Accumulate forces into acceleration (Newton’s second law).
  applyForce(force) {
    this.acceleration.add(force);
  }

  // A simple physics engine (Euler integration)
  update() {
    // Velocity changes according to acceleration.
    this.velocity.add(this.acceleration);
    //{!1} Position changes according to velocity.
    this.position.add(this.velocity);
    this.acceleration.mult(0);
  }
}</pre>
<p>With this class, I can move the rocket by calling <code>applyForce()</code> with a new force for every frame of animation. The thruster applies a single force to the rocket each time through <code>draw()</code>. But at this point, I’m far from done. To make my rockets “smart” and evolvable, I need to think about the three keys to programming a custom GA, as outlined in the previous section.</p>
<p><strong>Key 1</strong> is to define the right global variables for the population size and mutation rate. I’m going to hold off on worrying too much about these variables for now and arbitrarily choose reasonable-sounding numbers—perhaps a population of 50 rockets and a mutation rate of 1 percent. Once I’ve built out the system and have my sketch up and running, I can experiment with these numbers.</p>
<p><strong>Key 2</strong> is to develop an appropriate fitness function. In this case, the goal of a rocket is to reach its target. The closer a rocket gets to the target, the higher its fitness. Fitness is therefore inversely proportional to distance: the smaller the distance, the greater the fitness, and the greater the distance, the smaller the fitness.</p>
<p>To put this into practice, I first need to add a property to the <code>Rocket</code> class to store its fitness:</p>
<div class="snip-below">
  <pre class="codesplit" data-code-language="javascript">class Rocket {
  constructor(x, y) {
    //{!1} A rocket has fitness.
    this.fitness = 0;

    this.position = createVector(x, y);
    this.velocity = createVector();
    this.acceleration = createVector();
  }
  </pre>
</div>
<p>Next, I need to add a method to calculate the fitness to the <code>Rocket</code> class. After all, only a <code>Rocket</code> object knows how to compute its distance to the target, so the fitness function should live in this class. Assuming I have a <code>target</code> vector, I can write the following:</p>
<pre class="codesplit" data-code-language="javascript">  calculateFitness() {
    // How close did the rocket get?
    let distance = p5.Vector.dist(this.position, target);
    //{!1} Fitness is inversely proportional to distance.
    this.fitness = 1 / distance;
  }</pre>
<p>This is perhaps the simplest fitness function I could write. By dividing <code>1</code> by the distance, large distances become small numbers and small distances become large. If I want to use my quadratic trick from the previous section, I could divide <code>1</code> by the distance squared instead:</p>
<pre class="codesplit" data-code-language="javascript">  calculateFitness() {
    let distance = p5.Vector.dist(position, target);
    //{!1} 1 divided by distance squared
    this.fitness = 1 / (distance * distance);
  }</pre>
<p>I’ll want to make several additional improvements to the fitness function, but this is a good start.</p>
<p>Finally, <strong>Key 3</strong> is to think about the relationship between the genotype and the phenotype. I’ve stated that each rocket has a thruster that fires in a variable direction with a variable magnitude—in other words, a vector! The genotype, the data required to encode the rocket’s behavior, is therefore an array of vectors, one for each frame of the animation:</p>
<pre class="codesplit" data-code-language="javascript">class DNA {
  constructor(length) {
    this.genes = [];
    for (let i = 0; i &#x3C; length; i++) {
      this.genes[i] = createVector();
    }
  }
}</pre>
<p>The happy news here is that I don’t really have to do anything else to the <code>DNA</code> class. All the functionality for the typing cat (crossover and mutation) still applies. The one difference I do have to consider is how to initialize the array of genes. With the typing cat, I had an array of characters and picked a random character for each element of the array. Now I’ll do exactly the same thing and initialize a DNA sequence as an array of random vectors.</p>
<p>Your instinct in creating a random vector might be as follows:</p>
<pre class="codesplit" data-code-language="javascript">let v = createVector(random(-1, 1), random(-1, 1));</pre>
<p>This code is perfectly fine and will likely do the trick. However, if I were to draw every single possible vector that could be picked, the result would fill a square (see Figure 9.11, left). In this case, it probably doesn’t matter, but there’s a slight bias to the diagonals given that a vector from the center of a square to a corner is longer than a purely vertical or horizontal one.</p>
<figure>
  <div class="col-list">
    <div>
      <img src="images/09_ga/09_ga_12.png" alt="Figure 9.11: Vectors created with random x and y values (left) and using p5.Vector.random2D() (right)">
    </div>
    <div>
      <img src="images/09_ga/09_ga_13.png" alt="">
    </div>
  </div>
  <figcaption>Figure 9.11: Vectors created with random <em>x</em> and <em>y</em> values (left) and using <code>p5.Vector.random2D()</code> (right)</figcaption>
</figure>
<p>As you may recall from <a href="/oscillation#">Chapter 3</a>, a better choice is to pick a random angle and create a vector of length 1 from that angle. This produces results that form a circle (see the right of Figure 9.11) and can be achieved with polar-to-Cartesian conversion or the trusty <code>p5.Vector.random2D()</code> method:</p>
<pre class="codesplit" data-code-language="javascript">for (let i = 0; i &#x3C; length; i++) {
  //{!1} A random unit vector
  this.genes[i] = p5.Vector.random2D();
}</pre>
<p>A vector of length 1 would actually create quite a large force. Remember, forces are applied to acceleration, which accumulates into velocity 30 times per second (or whatever the frame rate is). Therefore, for this example, I’ll add another variable to the <code>DNA</code> class, a maximum force, and randomly scale all the vectors to be somewhere from 0 to the maximum. This will control the thruster power:</p>
<div class="snip-below">
  <pre class="codesplit" data-code-language="javascript">class DNA {
  constructor() {
    // The genetic sequence is an array of vectors.
    this.genes = [];
    // How strong can the thrusters be?
    this.maxForce = 0.1;
    // Notice that the length of <code>genes</code> is equal to a global <code>lifeSpan</code> variable.
    for (let i = 0; i &#x3C; lifeSpan; i++) {
      this.genes[i] = p5.Vector.random2D();
      //{!1} Scale the vectors randomly, but not stronger than the maximum force.
      this.genes[i].mult(random(0, maxforce));
    }
  }</pre>
</div>
<p>Notice that I’m using <code>lifeSpan</code> to set the length of <code>genes</code>, the array of vectors. This global variable stores the total number of frames in each generation’s life cycle, allowing me to create a vector for each frame of the rocket’s life.</p>
<p>The expression of this array of vectors, the phenotype, is my <code>Rocket</code> class. To cement the connection, I need to add an instance of a <code>DNA</code> object to the class:</p>
<div class="snip-below">
  <pre class="codesplit" data-code-language="javascript">class Rocket {
  constructor(x, y, dna) {
    // A rocket has DNA.
    this.dna = dna;
    //{!1} A rocket has fitness.
    this.fitness = 0;

    this.position = createVector(x, y);
    this.velocity = createVector();
    this.acceleration = createVector();
  }</pre>
</div>
<p>What am I using <code>this.dna</code> for? As the rocket launches, it marches through the array of vectors and applies them one at a time as a force. To achieve this, I’ll need to include the variable <code>this.geneCounter</code> to help step through the array:</p>
<pre class="codesplit" data-code-language="javascript">class Rocket {
  constructor(x, y, dna) {
    // A rocket has DNA.
    this.dna = dna;
    // A rocket has fitness.
    this.fitness = 0;
    //{!1} A counter for the DNA <code>genes</code> array
    this.geneCounter = 0;
    this.position = createVector(x, y);
    this.velocity = createVector();
    this.acceleration = createVector();
  }

  run() {
    // Apply a force from the <code>genes</code> array.
    this.applyForce(this.dna.genes[this.geneCounter]);
    // Go to the next force in the <code>genes</code> array.
    this.geneCounter++;
    //{!1} Update the rocket’s physics.
    this.update();
  }
}</pre>
<p>Now I have a <code>DNA</code> class (genotype) and a <code>Rocket</code> class (phenotype). The last piece of the puzzle is a mechanism for managing the population of rockets and implementing selection and reproduction.</p>
<h3 id="managing-the-population">Managing the Population</h3>
<p>To keep my <em>sketch.js</em> file tidier, I’ll put the code for managing the array of <code>Rocket</code> objects in a <code>Population</code> class. As with the <code>DNA</code> class, the happy news is that I barely have to change anything from the typing cats example. I’m just organizing the code in a more object-oriented way, with a <code>selection()</code> method and a <code>reproduction()</code> method. For the sake of demonstrating a different technique, I’ll also normalize the fitness values in <code>selection()</code> and use the weighted-selection (relay-race) algorithm in <code>reproduction()</code>. This eliminates the need for a separate mating-pool array. The <code>weightedSelection()</code> code is the same as that written earlier in the chapter:</p>
<div class="snip-below">
  <pre class="codesplit" data-code-language="javascript">class Population {
  // <code>Population</code> has variables to keep track of the mutation rate, current
  // population array, and number of generations.
  constructor(mutation, length) {
    // Mutation rate
    this.mutationRate = mutation; 
    // Array to hold the current population
    this.population = [];
    //{!1} Number of generations
    this.generations = 0;
    for (let i = 0; i &#x3C; length; i++) {
      this.population[i] = new Rocket(320, 220, new DNA());
    }
  }

  // Calculate the fitness for each rocket.
  fitness() {
    for (let rocket of this.population) {
      rocket.calculateFitness();
    }
  }

  // The selection method normalizes all the fitness values.
  selection() {
    // Sum all the fitness values.
    let totalFitness = 0;
    for (let rocket of this.population) {
      totalFitness += rocket.fitness;
    }
    // Divide by the total to normalize the fitness values.
    for (let rocket of this.population) {
      rocket.fitness /= totalFitness;
    }
  }

  reproduction() {
    //{!1} Separate the array for the next generation.
    let newPopulation = [];
    for (let i = 0; i &#x3C; this.population.length; i++) {
      //{!2} Now use the weighted selection algorithm.
      let parentA = this.weightedSelection();
      let parentB = this.weightedSelection();
      let child = parentA.crossover(parentB);
      child.mutate(this.mutationRate);
      // <code>Rocket</code> goes in the new population.
      newPopulation[i] = new Rocket(320, 240, child);
    }
    // Now the new population is the current one.
    this.population = newPopulation;
  }</pre>
</div>
<p>I need to make one more fairly significant change, however. With typing cats, a random phrase was evaluated as soon as it was created. The string of characters had no life span; it existed purely for the purpose of calculating its fitness. The rockets, however, need to live for a period of time before they can be evaluated—that is, they need to be given a chance to make their attempt at reaching the target. Therefore, I need to add one more method to the <code>Population</code> class that runs the physics simulation. This is identical to what I did in the <code>run()</code> method of a particle system—update all the particle positions and draw them:</p>
<div class="snip-above">
  <pre class="codesplit" data-code-language="javascript">  live() {
    for (let rocket of this.population) {
      //{!1} The <code>run()</code> method takes care of the simulation, updates the rocket’s
      // position, and draws it to the canvas.
      rocket.run();
    }
  }
}</pre>
</div>
<p>Finally, I’m ready for <code>setup()</code> and <code>draw()</code>. Here, my primary responsibility is to implement the steps of the GA in the appropriate order by calling the methods from the <code>Population</code> class:</p>
<pre class="codesplit" data-code-language="javascript">    population.fitness();
    population.selection();
    population.reproduction();</pre>
<p>However, unlike the Shakespeare example, I don’t want to do this every frame. Rather, my steps work as follows:</p>
<ol>
  <li>Create a population of rockets.</li>
  <li>Let the rockets live for <em>N</em> frames.</li>
  <li>Evolve the next generation:
    <ul>
      <li>Selection</li>
      <li>Reproduction</li>
    </ul>
  </li>
  <li>Return to step 2.</li>
</ol>
<p>To know when to go from step 2 to 3, I need a <code>lifeCounter</code> variable that tracks the current generation’s progress, along with the <code>lifeSpan</code> variable. In <code>draw()</code>, while <code>lifeCounter</code> is less than <code>lifeSpan</code>, the population’s <code>live()</code> method is called to run the simulation. Once <code>lifeCounter</code> hits <code>lifeSpan</code>, it’s time for <code>fitness()</code>, <code>selection(),</code> and <code>reproduction()</code> to evolve a new generation of rockets.</p>
<div data-type="example">
  <h3 id="example-92-smart-rockets">Example 9.2: Smart Rockets</h3>
  <figure>
    <div data-type="embed" data-p5-editor="https://editor.p5js.org/natureofcode/sketches/jzfy_9p1ES" data-example-path="examples/09_ga/9_2_smart_rockets_basic"><img src="examples/09_ga/9_2_smart_rockets_basic/screenshot.png"></div>
    <figcaption></figcaption>
  </figure>
</div>
<pre class="codesplit" data-code-language="javascript">// How many frames does a generation live for?
let lifeSpan = 500;

// Keep track of the life span.
let lifeCounter = 0;

// The population
let population;

function setup() {
  createCanvas(640, 240);

  //{!1} Step 1: Create the population. Try different values for
  // the mutation rate and population size.
  population = new Population(0.01, 50);
}

function draw() {
  background(255);
  // The revised GA
  if (lifeCounter &#x3C; lifeSpan) {
    // Step 2: The rockets live their lives until <code>lifeCounter</code> reaches <code>lifeSpan</code>.
    population.live();
    lifeCounter++;
  } else {
    // When <code>lifeSpan</code> is reached, reset <code>lifeCounter</code> and evolve the next
    // generation (steps 3 and 4, selection and reproduction).
    lifeCounter = 0;
    population.fitness();
    population.selection();
    population.reproduction();
  }
}

// Move the target if the mouse is clicked. The rockets will adapt to the new target.
function mousePressed() {
  target.x = mouseX;
  target.y = mouseY;
}</pre>
<p>At the bottom of the code, you’ll see that I’ve added a new feature: when the mouse is clicked, the target position is moved to the coordinates of the mouse cursor. This change allows you to observe how the rockets adapt and adjust their trajectories toward the new target position as the system continuously evolves in real time.</p>
<h3 id="making-improvements">Making Improvements</h3>
<p>My smart rockets work but aren’t particularly exciting yet. After all, the rockets simply evolve toward having DNA with a bunch of vectors that point straight at the target. To make the example more interesting, I’m going to suggest two improvements. For starters, when I first introduced the smart rocket scenario, I said the rockets should evolve the ability to avoid obstacles. Adding this feature will make the system more complex and demonstrate the power of the evolutionary algorithm more effectively.</p>
<p>To evolve obstacle avoidance, I need some obstacles to avoid. I can easily create rectangular, stationary obstacles by implementing a class of <code>Obstacle</code> objects that store their own position and dimensions:</p>
<div class="snip-below">
  <pre class="codesplit" data-code-language="javascript">class Obstacle {
  constructor(x, y, w, h) {
    this.position = createVector(x, y);
    this.w = w;
    this.h = h;
  }</pre>
</div>
<p>I’ll add a <code>contains()</code> method to the <code>Obstacle</code> class that returns <code>true</code> if a rocket has hit the obstacle, or <code>false</code> otherwise:</p>
<div class="snip-below snip-above">
  <pre class="codesplit" data-code-language="javascript">  contains(spot) {
    return (
      spot.x > this.position.x &#x26;&#x26;
      spot.x &#x3C; this.position.x + this.w &#x26;&#x26;
      spot.y > this.position.y &#x26;&#x26;
      spot.y &#x3C; this.position.y + this.h
    );
  }</pre>
</div>
<p>If I create an array of <code>Obstacle</code> objects, I can then have each rocket check to see whether it has collided with each obstacle. If a collision occurs, the rocket can set the Boolean flag <code>hitObstacle</code> to <code>true</code>. To achieve this, I need to add a method to the <code>Rocket</code> class:</p>
<pre class="codesplit" data-code-language="javascript">  // This new method lives in the <code>Rocket</code> class and checks whether a rocket has
  // hit an obstacle.
  checkObstacles(obstacles) {
    for (let obstacle of obstacles) {
      if (obstacle.contains(this.position)) {
        this.hitObstacle = true;
      }
    }
  }</pre>
<p>If the rocket hits an obstacle, I’ll stop the rocket from updating its position. The revised <code>run()</code> method now receives an <code>obstacles</code> array as an argument:</p>
<pre class="codesplit" data-code-language="javascript">  run(obstacles) {
    // Stop the rocket if it has hit an obstacle.
    if (!this.hitObstacle) {
      this.applyForce(this.dna.genes[this.geneCounter]);
      this.geneCounter = (this.geneCounter + 1);
      this.update();
      // Check whether the rocket has hit an obstacle.
      this.checkObstacles(obstacles);
    }
    this.show();
  }</pre>
<p>I also have an opportunity to adjust the fitness of the rocket. If the rocket hits an obstacle, the fitness should be penalized and greatly reduced:</p>
<pre class="codesplit" data-code-language="javascript">  calculateFitness() {
    let distance = p5.Vector.dist(this.position, target);
    this.fitness = 1 / (distance * distance);
    // {.bold !3}
    if (this.hitObstacle) {
      this.fitness *= 0.1;
    }
  }</pre>
<p>With that, the rockets should be able to evolve to avoid obstacles. But I won’t stop now. I’d like to make another improvement.</p>
<p>If you look closely at Example 9.2, you’ll notice that the rockets aren’t rewarded for getting to the target faster. The only variable in the fitness calculation is the distance to the target at the end of the generation’s life. In fact, in the event that a rocket gets very close to the target but overshoots it and flies past, it may actually be penalized for getting to the target faster. Slow and steady wins the race in this case.</p>
<p>I could improve the algorithm in several ways to optimize for speed to reach the target. First, I could calculate a rocket’s fitness based on the closest it comes to the target at any point during its life, instead of using its distance to the target at the end of the generation. I’ll call this variable the rocket’s <code>recordDistance</code> and update it as part of a <code>checkTarget()</code> method on the <code>Rocket</code> class:</p>
<div class="snip-below">
  <pre class="codesplit" data-code-language="javascript">  checkTarget() {
    let distance = p5.Vector.dist(this.position, target);
    // Check whether the distance is closer than the record distance. If it is, set a new record.
    if (distance &#x3C; this.recordDistance) {
      this.recordDistance = distance;
    }</pre>
</div>
<p>Additionally, a rocket deserves a reward based on the speed with which it reaches its target. For that, I need a way of knowing when a rocket has hit the target. Actually, I already have one: the <code>Obstacle</code> class has a <code>contains()</code> method, and there’s no reason the target can’t also be implemented as an obstacle. It’s just an obstacle that the rocket <em>wants</em> to hit! I can use the <code>contains()</code> method to set a new <code>hitTarget</code> flag on each <code>Rocket</code> object. A rocket will stop if it hits the target, just as it stops if it hits an obstacle:</p>
<div class="snip-above snip-below">
  <pre class="codesplit" data-code-language="javascript">    // If the object reaches the target, set a Boolean flag to <code>true</code>.
    if (target.contains(this.position)) {
      this.hitTarget = true;
    }</pre>
</div>
<p>Remember, I also want the rocket to have a higher fitness the faster it reaches the target. Conversely, the slower it reaches the target, the lower its fitness score. To implement this, a <code>finishCounter</code> can be incremented every cycle of the rocket’s life until it reaches the target. At the end of its life, the counter will equal the amount of time the rocket took to reach the target:</p>
<div class="snip-above">
  <pre class="codesplit" data-code-language="javascript">    // Increase the finish counter if the rocket hasn’t hit the target.
    if (!this.hitTarget) {      
      this.finishCounter++;
    }
  }</pre>
</div>
<p>I want the fitness to be inversely proportional to <code>finishCounter</code> as well. To achieve this, I can improve the fitness function with the following changes:</p>
<pre class="codesplit" data-code-language="javascript">  calculateFitness() {
    // Reward finishing faster and getting close.
    this.fitness = 1 / (this.finishTime * this.recordDistance);

    // Let’s try to the power of 4 instead of squared!
    this.fitness = pow(this.fitness, 4);

    //{!3} Lose 90% of fitness for hitting an obstacle.
    if (this.hitObstacle) {
      this.fitness *= 0.1;
    }
    //{!3} Double the fitness for finishing!
    if (this.hitTarget) {
      this.fitness *= 2;
    }
  }</pre>
<p>Both improvements are incorporated into the code for Example 9.3.</p>
<div data-type="example">
  <h3 id="example-93-smarter-rockets">Example 9.3: Smarter Rockets</h3>
  <figure>
    <div data-type="embed" data-p5-editor="https://editor.p5js.org/natureofcode/sketches/565K_KXSA" data-example-path="examples/09_ga/9_3_smart_rockets"><img src="examples/09_ga/9_3_smart_rockets/screenshot.png"></div>
    <figcaption></figcaption>
  </figure>
</div>
<p>This example could be improved and further expanded in many ways. The following exercises offer ideas and challenges to explore GAs in more depth. What else can you try?</p>
<div data-type="exercise">
  <h3 id="exercise-99">Exercise 9.9</h3>
  <p>Create a more complex obstacle course. As you make it more difficult for the rockets to reach the target, do you need to improve other aspects of the GA—for example, the fitness function?</p>
</div>
<div data-type="exercise">
  <h3 id="exercise-910">Exercise 9.10</h3>
  <p>Implement the rocket-firing pattern of Thorp’s original smart rockets. Each rocket gets only five thrusters (of any direction and strength) that follow a firing sequence (of arbitrary length). Thorp’s simulation also gives the rockets a finite amount of fuel.</p>
</div>
<div data-type="exercise">
  <h3 id="exercise-911">Exercise 9.11</h3>
  <p>Visualize the simulation differently. Can you draw a line for the shortest path to the target? Can you draw the rockets in a more interesting way? What about adding particle systems that act as smoke in the direction of the rocket thrusters?</p>
</div>
<div data-type="exercise">
  <h3 id="exercise-912">Exercise 9.12</h3>
  <p>Another way to teach a rocket to reach a target is to evolve a flow field. Can you make the genotype of a rocket a flow field of vectors?</p>
</div>
<h2 id="interactive-selection">Interactive Selection</h2>
<p>Karl Sims is a computer graphics researcher and visual artist who worked extensively with GAs. (He’s also well known for his work with particle systems!) One of his innovative evolutionary projects is the museum installation <em>Galapagos</em>. Originally installed in the NTT InterCommunication Center in Tokyo in 1997, the installation consists of 12 monitors displaying computer-generated images. These images evolve over time, following the GA steps of selection and reproduction.</p>
<p>The innovation here isn’t the use of the GA, but rather the strategy behind the fitness function. In front of each monitor is a sensor on the floor that can detect the presence of a visitor viewing the screen. The fitness of an image is tied to the length of time that viewers look at the image. This is known as <strong>interactive selection</strong>, a GA with fitness values assigned by people.</p>
<p>Far from being confined to art installations, interactive selection is quite prevalent in the digital age of user-generated ratings and reviews. Could you imagine evolving the perfect song based on your Spotify ratings? Or the ideal book according to Goodreads reviews? In keeping with the book’s nature theme, however, I’ll illustrate how interactive selection works by using a population of digital flowers like the ones in Figure 9.12.</p>
<figure>
  <img src="images/09_ga/09_ga_14.png" alt="Figure 9.12: Flower design for interactive selection">
  <figcaption>Figure 9.12: Flower design for interactive selection</figcaption>
</figure>
<p>Each flower will have a set of properties: petal color, petal size, petal count, center color, center size, stem length, and stem color. A flower’s DNA (genotype) is an array of floating-point numbers from 0 to 1, with a single value for each property:</p>
<div class="snip-below">
  <pre class="codesplit" data-code-language="javascript">class DNA {
  constructor() {
    // The genetic sequence (14 properties for each flower)
    this.genes = [];
    for (let i = 0; i &#x3C; 14; i++) {
      // Each gene is a random floating-point value from 0 to 1.
      this.genes[i] = random(0, 1);
    }
  }</pre>
</div>
<p>The phenotype is a <code>Flower</code> class that includes an instance of a <code>DNA</code> object:</p>
<div class="snip-below">
  <pre class="codesplit" data-code-language="javascript">class Flower {
  constructor(dna) {
    // Flower DNA
    this.dna = dna;
    // How fit is this flower?
    this.fitness = 1; 
  }</pre>
</div>
<p>When it comes time to draw the flower, I’ll use p5.js’s <code>map()</code> function to convert any gene value to the appropriate range for pixel dimensions or color values. (I’ll also use <code>colorMode()</code> to set the RGB ranges from 0 to 1.)</p>
<div class="snip-below">
  <pre class="codesplit" data-code-language="javascript">  show() {
    //{.offset-top}
    // The DNA values are assigned to flower properties
    // such as petal color, petal size, and number of petals.
    let genes = this.dna.genes;
    // I’ll set the RGB range from 0 to 1 with <code>colorMode()</code> and use <code>map()</code> as needed elsewhere for drawing the flower.
    let petalColor  = color(genes[0], genes[1], genes[2], genes[3]);
    let petalSize   = map(genes[4], 0, 1, 4, 24); 
    let petalCount  = floor(map(genes[5], 0, 1, 2, 16)); 
    let centerColor = color(genes[6], genes[7], genes[8]); 
    let centerSize  = map(genes[9], 0, 1, 24, 48);
    let stemColor   = color(genes[10], genes[11], genes[12]); 
    let stemLength  = map(genes[13], 0, 1, 50, 100); </pre>
</div>
<p>Up to this point, I haven’t done anything new. This is the same process I’ve followed in every GA example so far. What’s different is that I won’t be writing a <code>fitness()</code> function that computes the score based on a mathematical formula. Instead, I’ll ask the user to assign the fitness.</p>
<p>How exactly to ask a user to assign fitness is best approached as an interaction design problem and isn’t really within the scope of this book. I’m not going to launch into an elaborate discussion of how to program sliders or build your own hardware dials or create a web app enabling people to submit online scores. How you choose to acquire fitness scores is up to you and the particular application you’re developing. For this demonstration, I’ll take inspiration from Sims’s <em>Galapagos</em> installation and simply increase a flower’s fitness whenever the mouse is over it. Then the next generation of flowers is created when an Evolve Next Generation button is pressed.</p>
<p>Look at how the steps of the GA—selection and reproduction—are applied in the <code>nextGeneration()</code> function, which is triggered by the <code>mousePressed()</code> event attached to the p5.js <code>button</code> element. Fitness is increased as part of the <code>Population</code> class’s <code>rollover()</code> method, which detects the presence of the mouse over any given flower design. You can find more details about the sketch in the accompanying example code on the book’s website.</p>
<div data-type="example">
  <h3 id="example-94-interactive-selection">Example 9.4: Interactive Selection</h3>
  <figure>
    <div data-type="embed" data-p5-editor="https://editor.p5js.org/natureofcode/sketches/dUeAaapkQ" data-example-path="examples/09_ga/9_4_interactive_selection"><img src="examples/09_ga/9_4_interactive_selection/screenshot.png"></div>
    <figcaption></figcaption>
  </figure>
</div>
<pre class="codesplit" data-code-language="javascript">let population;

function setup() {
  createCanvas(640, 240);
  colorMode(RGB, 1);
  // This is a very small population!
  let populationSize = 8;
  // A pretty high mutation rate here. Because our population is rather small, we need to enforce variety.
  let mutationRate = 0.05;
  // Create the population.
  population = new Population(mutationRate, populationSize);
  // A p5.js button
  button = createButton("evolve new generation");
  button.mousePressed(nextGeneration);
  button.position(10, 210);
}

function draw() {
  background(1);
  // Draw the flowers.
  population.show();
  // Check for increasing fitness.
  population.rollover(mouseX, mouseY);
  textAlign(LEFT);
  text("Generation " + population.generations, 12, height - 40);
}

// If the button is pressed, evolve the next generation.
function nextGeneration() {
  population.selection();
  population.reproduction();
}</pre>
<p>This example is just a demonstration of the idea of interactive selection and doesn’t achieve a particularly meaningful result. For one, I didn’t take much care in the visual design of the flowers; they’re just a few simple shapes with different sizes and colors. (See if you can spot the use of polar coordinates in the code, though!) Sims used more elaborate mathematical functions as the genotype for his images. You might also consider a vector-based approach, in which a design’s genotype is a set of points or paths.</p>
<p>The more significant problem here, however, is one of time. In the natural world, evolution occurs over millions of years. In the computer simulation world of the chapter’s first examples, the populations are able to evolve behaviors relatively quickly because the new generations are being produced algorithmically. In the typing cat example, a new generation is born in each cycle through <code>draw()</code> (approximately 60 per second). Each generation of smart rockets has a life span of 250 frames—still a mere blink of the eye in evolutionary time. In the case of interactive selection, however, you have to sit and wait for a person to rate each and every member of the population before you can get to the next generation. A large population would be unreasonably tedious for the user to evaluate—not to mention, how many generations could you stand to sit through?</p>
<p>You can certainly get around this problem in clever ways. Sims’s <em>Galapagos</em> exhibit concealed the rating process from the viewers, as it occurred through the normal behavior of looking at artwork in a gallery setting. Building a web application that would allow many people to rate a population in a distributed fashion is also a good strategy for achieving ratings for large populations quickly.</p>
<p>In the end, the key to a successful interactive selection system boils down to the same keys previously established. What are the genotype and phenotype? And how do you calculate fitness—or in this case, what’s your strategy for assigning fitness according to interaction?</p>
<div data-type="exercise">
  <h3 id="exercise-913">Exercise 9.13</h3>
  <p>Build your own interactive selection project. In addition to a visual design, consider evolving sounds—for example, a short sequence of tones. Can you devise a strategy, such as a web application or physical sensor system, to acquire ratings from many people over time?</p>
</div>
<div data-type="exercise">
  <h3 id="exercise-914">Exercise 9.14</h3>
  <p>Another of Karl Sims’s seminal works in the field of GAs is “Evolved Virtual Creatures.” In this project, a population of digital creatures in a simulated physics environment is evaluated for their ability to perform tasks, such as swimming, running, jumping, following, and competing for a green cube. The project uses a node-based genotype: the creature’s DNA isn’t a linear list of vectors or numbers, but a map of nodes (much like the soft-body simulation in <a href="/physics-libraries#">Chapter 6</a>). The phenotype is the creature’s body itself, a network of limbs connected with muscles.</p>
  <div class="half-width-right">
    <figure>
      <img src="images/09_ga/09_ga_15.png" alt="">
      <figcaption></figcaption>
    </figure>
  </div>
  <p>Can you design the DNA for a flower, plant, or creature as a network of parts? One idea is to use interactive selection to evolve the design. Alternatively, you could incorporate spring forces, perhaps with Toxiclibs.js or Matter.js, to create a simplified 2D version of Sims’s creatures. What if they were to evolve according to a fitness function associated with a specific goal? For more about Sims’s techniques, <a href="https://www.karlsims.com/papers/siggraph94.pdf">you can read his 1994 paper</a> and watch the <a href="https://youtu.be/RZtZia4ZkX8">“Evolved Virtual Creatures” video on YouTube</a>.</p>
</div>
<h2 id="ecosystem-simulation">Ecosystem Simulation</h2>
<p>You may have noticed something a bit odd about the evolutionary systems I’ve built so far in this chapter. In the real world, a population of babies isn’t born all at the same time. Those babies don’t then grow up and all reproduce at exactly the same time, then instantly die, leaving the population size perfectly stable. That would be ridiculous. Not to mention that certainly no one is running around the forest with a calculator crunching numbers and assigning fitness values to all the creatures.</p>
<p>In the real world, as I discussed at the start of the chapter, you don’t really have survival of the fittest; you have <em>survival of the reproducers</em>. Creatures that happen to live longer, in many cases, have a greater chance of reproducing. Babies are born, they live for a while, maybe they themselves have babies, maybe they don’t, and then they die. Could I write a sketch that captures this more realistic take on evolutionary biology?</p>
<p>You won’t necessarily find simulations of real-world evolution in artificial intelligence textbooks. GAs are generally used in the more formal manner outlined earlier in this chapter. However, since you’re reading this book to develop simulations of natural systems, it’s worth looking at how you might use a GA to build something that resembles a living ecosystem, much like the one I’ve described in the project prompts at the end of each chapter.</p>
<p>I’ll begin by imagining a simple scenario. I’ll create a creature called a <em>bloop</em>, a circle that moves about the canvas according to Perlin noise. The creature will have a radius and a maximum speed. The bigger it is, the slower it moves; the smaller, the faster:</p>
<pre class="codesplit" data-code-language="javascript">class Bloop {
  constructor(x, y) {
    this.position = createVector(x, y);
    //{!2} Each bloop will use a different part of the 1D noise space.
    this.xoff = random(1000); 
    this.yoff = random(1000);
    this.maxSpeed = 5;
    this.r = 8;
  }

  // Assign simple movement and velocity with Perlin noise.
  update() {
    let vx = map(noise(this.xoff), 0, 1, -this.maxspeed, this.maxspeed);
    let vy = map(noise(this.yoff), 0, 1, -this.maxspeed, this.maxspeed);
    this.xoff += 0.01;
    this.yoff += 0.01;

    let velocity = createVector(vx, vy);
    this.position.add(velocity);
  }

  //{!3} A bloop is a circle.
  show() {
    stroke(0);
    fill(127);
    circle(this.position.x, this.position.y, this.r * 2);
  }
}</pre>
<p>As usual, the population of bloops can be stored in an array, which in turn can be managed by a class called <code>World</code>:</p>
<div class="snip-below">
  <pre class="codesplit" data-code-language="javascript">class World {
  //{!1} A list of bloops
  constructor(populationSize) {
    // An array of bloops
    this.bloops = []; 
    for (let i = 0; i &#x3C; populationSize; i++) {
      // Create each bloop with a starting position.
      this.bloops.push(new Bloop(random(width), random(height)));
    }
  }</pre>
</div>
<p>So far, I’m just rehashing the particle systems from <a href="/particles#">Chapter 4</a>. I have an entity called <code>Bloop</code> that moves around the canvas, and a class called <code>World</code> that manages a variable quantity of these entities. To turn this into a system that evolves, I need to add two additional features to my world:</p>
<ul>
  <li><strong>Bloops die.</strong></li>
  <li><strong>Bloops are born.</strong></li>
</ul>
<p>Bloops dying is my replacement for a fitness function and the process of selection. If a bloop dies, it can’t be selected to be a parent, because it no longer exists! One way I can build a mechanism to ensure bloop deaths in the world is by adding a <code>health</code> variable to the <code>Bloop</code> class:</p>
<div class="snip-below">
  <pre class="codesplit" data-code-language="javascript">class Bloop {
  constructor(position, dna) {
    //{!1} A variable to track the bloop’s health
    this.health = 100;  
    /* All the rest of the constructor */</pre>
</div>
<p>Each time through <code>update()</code>, a bloop loses some of its health:</p>
<div class="snip-below">
  <pre class="codesplit" data-code-language="javascript">  update() {
    // Death is always looming.
    this.health -= 0.2;
    /* All the rest of <code>update()</code> */</pre>
</div>
<p>If <code>health</code> drops below <code>0</code>, the bloop dies:</p>
<pre class="codesplit" data-code-language="javascript">  // A method to test whether the bloop is alive or dead
  dead() {
    return (this.health &#x3C; 0.0);
  }</pre>
<p>This is a good first step, but I haven’t really achieved anything. After all, if all bloops start with 100 health points and lose health at the same rate, then all bloops will live for the exact same amount of time and die together. If every single bloop lives the same amount of time, each one has an equal chance of reproducing, and therefore no evolutionary change will occur.</p>
<p>You can achieve variable life spans in several ways with a more sophisticated world. One approach is to introduce predators that eat bloops. Faster bloops would be more likely to escape being eaten, leading to the evolution of increasingly faster bloops. Another option is to introduce food. When a bloop eats food, its health points increase, extending its life.</p>
<p>Let’s assume I have an array of vector positions called <code>food</code>. I could test each bloop’s proximity to each food position. If the bloop is close enough, it eats the food (which is then removed from the world) and increases its health:</p>
<pre class="codesplit" data-code-language="javascript">  eat(food) {
    // Check all the food vectors.
    for (let i = food.length - 1; i >= 0; i--) {
      // How far away is the bloop?
      let distance = p5.Vector.dist(this.position, food[i]);
      // If the food is within its radius . . .
      if (distance &#x3C; this.r) {
        //{!2} . . . increase health and remove the food!
        this.health += 100;
        food.splice(i, 1);
      }
    }
  }</pre>
<p>In this scenario, bloops that eat more food are expected to live longer and have a greater likelihood of reproducing. As a result, the system should evolve bloops with an optimal ability to find and consume food.</p>
<p>Now that the world has been built, it’s time to add the components necessary for evolution. The first step is to establish the genotype and phenotype.</p>
<h3 id="genotype-and-phenotype">Genotype and Phenotype</h3>
<div class="half-width-right">
  <figure>
    <img src="images/09_ga/09_ga_16.png" alt="Figure 9.13: Small and big bloop creatures. The example will use simple circles, but you should try being more creative!">
    <figcaption>Figure 9.13: Small and big bloop creatures. The example will use simple circles, but you should try being more creative!</figcaption>
  </figure>
</div>
<p>The ability for a bloop to find food is tied to two variables: size and speed (see Figure 9.13). Bigger bloops will find food more easily simply because their size will allow them to intersect with food positions more often. And faster bloops will find more food because they can cover more ground in a shorter period of time.</p>
<p>Since size and speed are inversely related (large bloops are slow, small bloops are fast), I need a genotype with only a single number.</p>
<div class="snip-below">
  <pre class="codesplit" data-code-language="javascript">class DNA {
  constructor() {
    // The genetic sequence is a single value!
    // Using an array for just one number may seem absurd, but this will
    // scale for more sophisticated bloop designs.
    this.genes = [];
    for (let i = 0; i &#x3C; 1; i++) {
      this.genes[i] = random(0, 1);
    }
  }</pre>
</div>
<p>The phenotype is the bloop itself, whose size and speed are assigned by adding an instance of a <code>DNA</code> object to the <code>Bloop</code> class:</p>
<div class="snip-below">
  <pre class="codesplit" data-code-language="javascript">class Bloop {
  constructor(x, y, dna) {
    this.dna = dna;
    // DNA will determine size and max speed.
    // The bigger the bloop, the slower it is.
    this.maxSpeed = map(this.dna.genes[0], 0, 1, 15, 0);
    this.r = map(this.dna.genes[0], 0, 1, 0, 25);

    /* All the rest of the bloop initialization */</pre>
</div>
<p>Note that the <code>maxSpeed</code> property is mapped to a range from <code>15</code> to <code>0</code>. A bloop with a gene value of <code>0</code> will move at a speed of <code>15</code>, while a bloop with a gene value of <code>1</code> won’t move at all (speed of <code>0</code>).</p>
<h3 id="selection-and-reproduction">Selection and Reproduction</h3>
<p>Now that I have the genotype and phenotype, I need to move on to devising a method for selecting bloops as parents. I stated before that the longer a bloop lives, the more chances it has to reproduce. The length of a bloop’s life is its fitness.</p>
<p>One option would be to say that whenever two bloops come into contact with each other, they make a new bloop. The longer a bloop lives, the more likely it is to come into contact with another bloop. This would also affect the evolutionary outcome, since the likelihood of giving birth, in addition to eating food, depends on a bloop’s ability to locate other bloops.</p>
<p>A simpler option would be for bloops to clone themselves without needing a partner bloop, creating another bloop with the same genetic makeup instantly. For example, what if I said that at any given moment, a bloop has a 1 percent chance of reproducing? With this selection algorithm, the longer a bloop lives, the more likely it will clone itself. This is equivalent to saying the more times you play the lottery, the greater the likelihood you’ll win (though I’m sorry to say your chances of winning the lottery are still essentially zero).</p>
<p>To implement this selection algorithm, I can write a method in the <code>Bloop</code> class that picks a random number every frame. If the number is less than 0.01 (1 percent), a new bloop is born:</p>
<pre class="codesplit" data-code-language="javascript">  // This method will return a new child bloop.
  reproduce() {
    // A 1% chance of executing the code inside the <code>if</code> statement
    if (random(1) &#x3C; 0.01) {
      /* A Bloop baby! */
    }
  }</pre>
<p>How does a bloop reproduce? In previous examples, the reproduction process involved calling the <code>crossover()</code> method in the <code>DNA</code> class and creating a new object from the resulting array of genes. However, in this case, since I’m making a child from a single parent, I’ll call a method called <code>copy()</code> instead:</p>
<pre class="codesplit" data-code-language="javascript">  reproduce() {
    if (random(1) &#x3C; 0.005) {
      // A child is an exact copy of a single parent.      
      let childDNA = this.dna.copy();
      // 1% mutation rate
      childDNA.mutate(0.01);
      // The new bloop starts at this bloop’s position.
      return new Bloop(this.position.copy(), childDNA);
    }
  }</pre>
<p>Note that I’ve lowered the probability of reproduction from 1 percent to 0.05 percent. This change makes a significant difference; with a high reproduction probability, the system will rapidly become overpopulated. Too low a probability, and everything will likely die out quickly.</p>
<p>Writing the <code>copy()</code> method into the <code>DNA</code> class is easy with the JavaScript array method <code>slice()</code>, a standard JavaScript method that makes a new array by copying elements from an existing array:</p>
<pre class="codesplit" data-code-language="javascript">class DNA {
  //{!1} This <code>copy()</code> method replaces <code>crossover()</code>.
  copy() {
    // Create new <code>DNA</code> (with random genes).
    let newDNA = new DNA();
    //{!1} Overwrite the random genes with a copy of this DNA’s genes.
    newDNA.genes = this.genes.slice();
    return newDNA;
  }
}</pre>
<p>With the selection and reproduction pieces in place, I can finalize the <code>World</code> class to manage a list of all <code>Bloop</code> objects, as well as a <code>Food</code> object that contains a list of positions for the food (which I’ll draw as small squares).</p>
<p>Before you run the example, take a moment to guess which size and speed of bloops the system will evolve toward. I’ll discuss these details following the code.</p>
<div data-type="example">
  <h3 id="example-95-an-evolving-ecosystem">Example 9.5: An Evolving Ecosystem</h3>
  <figure>
    <div data-type="embed" data-p5-editor="https://editor.p5js.org/natureofcode/sketches/1HDlp_tKF" data-example-path="examples/09_ga/9_5_evolving_bloops"><img src="examples/09_ga/9_5_evolving_bloops/screenshot.png"></div>
    <figcaption></figcaption>
  </figure>
</div>
<pre class="codesplit" data-code-language="javascript">let world;

function setup() {
  createCanvas(640, 240);
  //{!1} The world starts with 20 bloops and 20 pieces of food.
  world = new World(20);
}

function draw() {
  background(255);
  world.run();
}

class World {
  //{!2} The <code>World</code> class manages the
  // population of bloops and all the food.
  constructor(populationSize) {
    // Create the population.
    this.bloops = [];
    for (let i = 0; i &#x3C; populationSize; i++) {
      let position = createVector(random(width), random(height));
      let dna = new DNA();
      this.bloops.push(new Bloop(position, dna));
    }
    // Create the food.
    this.food = new Food(populationSize);
  }

  // Run the world.
  run() {
    // This method draws the food and adds new food when necessary.
    this.food.run();

    // Manage the bloops (cycle through the array backward since bloops are deleted).
    for (let i = this.bloops.length - 1; i >= 0; i--) {
      // All bloops run and eat.
      let bloop = this.bloops[i];
      bloop.run();
      bloop.eat(this.food);
      // If the bloop is dead, remove it and create food.
      if (bloop.dead()) {
        this.bloops.splice(i, 1);
        this.food.add(bloop.position);
      } else {
        //{!4} Here is where each living bloop has a chance to reproduce.
        // If it does, the child is added to the population.
        // The value of the child is undefined if the parent does not reproduce.
        let child = this.bloops[i].reproduce();
        if (child) {
          this.bloops.push(child);
        }
      }
    }
  }
}</pre>
<p>If you guessed medium-sized bloops with medium speed, you’re right. With the design of this system, bloops that are large are simply too slow to find food. And bloops that are fast are too small to find food. The ones that are able to live the longest tend to be in the middle, large enough and fast enough to find food (but not too large or too fast). Some anomalies also exist. For example, if a bunch of large bloops happen to end up in the same position (and barely move because they are so large), they may all die out suddenly, leaving a lot of food for one large bloop that happens to be there to eat and allowing a mini population of large bloops to sustain themselves for a period of time in one position.</p>
<p>This example is rather simplistic given its single gene and cloning instead of crossover. Here are some suggestions for applying the bloop example in a more elaborate ecosystem simulation.</p>
<div data-type="project">
  <h3 id="the-ecosystem-project-10">The Ecosystem Project</h3>
  <p>Add evolution to your ecosystem, building from the examples in this chapter:</p>
  <ul>
    <li>Add a population of predators to your ecosystem. Biological evolution between predators and prey (or parasites and hosts) is often referred to as an <em>arms race</em>, in which the creatures continuously adapt and counter-adapt to one another. Can you achieve this behavior in a system of multiple creatures?</li>
    <li>How would you implement crossover and mutation between two parents in an ecosystem modeled after the bloops? Try implementing an algorithm so that two creatures mate when within a certain proximity.</li>
    <li>Try using the weights of multiple steering forces as a creature’s DNA. Can you create a scenario in which creatures evolve to cooperate with one another?</li>
    <li>One of the greatest challenges in ecosystem simulations is achieving balance. You will likely find that most of your attempts result in either mass overpopulation (followed by mass extinction) or mass extinction straight away. What techniques can you employ to achieve balance? Consider using the GA to evolve optimal parameters for an ecosystem.</li>
  </ul>
  <figure>
    <img src="images/09_ga/09_ga_17.png" alt="">
    <figcaption></figcaption>
  </figure>
</div>
</section>