遺伝的アルゴリズムを使った簡単な実験を書きました。単純に正方形のグリッドを取り、それらの色を変化させてすべてを黄色にしようとします。それは惨めに失敗し、その理由を理解できないようです。動作するコードを示す JSFiddle へのリンクと、コード全体のコピーを含めました。
http://jsfiddle.net/mankyd/X6x9L/
<!DOCTYPE html>
<html lang="en">
<head>
</head>
<body>
<div class="container">
<h1>The randomly flashing squares <i>should</i> be turning yellow</h1>
<div class="row">
<canvas id="input_canvas" width="100" height="100"></canvas>
<canvas id="output_canvas" width="100" height="100"></canvas>
</div>
<div class="row">
<span id="generation"></span>
<span id="best_fitness"></span>
<span id="avg_fitness"></span>
</div>
</div>
</body>
</html>
以下の JavaScript は、いくつかの場所で jquery に依存していることに注意してください。
// A bit of code that draws several squares in a canvas
// and then attempts to use a genetic algorithm to slowly
// make those squares all yellow.
// Knobs that can be tweaked
var mutation_rate = 0.1; // how often should we mutate something
var crossover_rate = 0.6; // how often should we crossover two parents
var fitness_influence = 1; // affects the fitness's influence over mutation
var elitism = 1; // how many of the parent's generation to carry over
var num_offspring = 20; // how many spawn's per generation
var use_rank_selection = true; // false == roulette_selection
// Global variables for easy tracking
var children = []; // current generation
var best_spawn = null; // keeps track of our best so far
var best_fitness = null; // keeps track of our best so far
var generation = 0; // global generation counter
var clear_color = 'rgb(0,0,0)';
// used for output
var $gen_span = $('#generation');
var $best_fit = $('#best_fitness');
var $avg_fit = $('#avg_fitness');
var $input_canvas = $('#input_canvas');
var input_ctx = $input_canvas[0].getContext('2d');
var $output_canvas = $('#output_canvas');
var output_ctx = $output_canvas[0].getContext('2d');
// A spawn represents a genome - a collection of colored
// squares.
var Spawn = function(nodes) {
var _fitness = null; // a cache of our fitness
this.nodes = nodes; // the squares that make up our image
this.fitness = function() {
// fitness is simply a function of how close to yellow we are.
// This is defined through euclidian distance. Smaller fitnesses
// are better.
if (_fitness === null) {
_fitness = 0;
for (var i = 0; i < nodes.length; i++) {
_fitness += Math.pow(-nodes[i].color[0], 2) +
Math.pow(255 - nodes[i].color[1], 2) +
Math.pow(255 - nodes[i].color[2], 2);
}
_fitness /= 255*255*3*nodes.length; // divide by the worst possible distance
}
return _fitness;
};
this.mutate = function() {
// reset our cached fitness to unknown
_fitness = null;
var health = this.fitness() * fitness_influence;
var width = $output_canvas[0].width;
var height = $output_canvas[0].height;
for (var i = 0; i < nodes.length; i++) {
// Sometimes (most times) we don't mutate
if (Math.random() > mutation_rate) {
continue;
}
// Mutate the colors.
for (var j = 0; j < 3; j++) {
// colors can move by up to 32 in either direction
nodes[i].color[j] += 64 * (.5 - Math.random()) * health;
// make sure that our colors stay between 0 and 255
nodes[i].color[j] = Math.max(0, Math.min(255, nodes[i].color[j]));
}
}
};
this.draw = function(ctx) {
// This draw function is a little overly generic in that it supports
// arbitrary polygons.
ctx.save();
ctx.fillStyle = clear_color;
ctx.fillRect(0, 0, ctx.canvas.width, ctx.canvas.height);
for (var i = 0; i < nodes.length; i++) {
ctx.fillStyle = 'rgba(' + Math.floor(nodes[i].color[0]) + ',' + Math.floor(nodes[i].color[1]) + ',' + Math.floor(nodes[i].color[2]) + ',' + nodes[i].color[3] + ')';
ctx.beginPath();
ctx.moveTo(nodes[i].points[0][0], nodes[i].points[0][1]);
for (var j = 1; j < nodes[i].points.length; j++) {
ctx.lineTo(nodes[i].points[j][0], nodes[i].points[j][1]);
}
ctx.fill();
ctx.closePath();
}
ctx.restore();
};
};
Spawn.from_parents = function(parents) {
// Given two parents, mix them together to get another spawn
var nodes = [];
for (var i = 0; i < parents[0].nodes.length; i++) {
if (Math.random() > 0.5) {
nodes.push($.extend({}, parents[0].nodes[i]));
}
else {
nodes.push($.extend({}, parents[1].nodes[i]));
}
}
var s = new Spawn(nodes);
s.mutate();
return s;
};
Spawn.random = function(width, height) {
// Return a complete random spawn.
var nodes = [];
for (var i = 0; i < width * height; i += 10) {
var n = {
color: [Math.random() * 256, Math.random() * 256, Math.random() * 256, 1],
points: [
[i % width, Math.floor(i / width) * 10],
[(i % width) + 10, Math.floor(i / width) * 10],
[(i % width) + 10, Math.floor(i / width + 1) * 10],
[i % width, Math.floor(i / width + 1) * 10],
]
};
nodes.push(n);
}
return new Spawn(nodes);
};
var select_parents = function(gene_pool) {
if (use_rank_selection) {
return rank_selection(gene_pool);
}
return roulette_selection(gene_pool);
};
var roulette_selection = function(gene_pool) {
var mother = null;
var father = null;
gene_pool = gene_pool.slice(0);
var sum_fitness = 0;
var i = 0;
for (i = 0; i < gene_pool.length; i++) {
sum_fitness += gene_pool[i].fitness();
}
var choose = Math.floor(Math.random() * sum_fitness);
for (i = 0; i < gene_pool.length; i++) {
if (choose <= gene_pool[i].fitness()) {
mother = gene_pool[i];
break;
}
choose -= gene_pool[i].fitness();
}
// now remove the mother and repeat for the father
sum_fitness -= mother.fitness();
gene_pool.splice(i, 1);
choose = Math.floor(Math.random() * sum_fitness);
for (i = 0; i < gene_pool.length; i++) {
if (choose <= gene_pool[i].fitness()) {
father = gene_pool[i];
break;
}
choose -= gene_pool[i].fitness();
}
return [mother, father];
};
var rank_selection = function(gene_pool) {
gene_pool = gene_pool.slice(0);
gene_pool.sort(function(a, b) {
return b.fitness() - a.fitness();
});
var choose_one = function() {
var sum_fitness = (gene_pool.length + 1) * (gene_pool.length / 2);
var choose = Math.floor(Math.random() * sum_fitness);
for (var i = 0; i < gene_pool.length; i++) {
// figure out the sume of the records up to this point. if we exceed
// our chosen spot, we've found our spawn.
if ((i + 1) * (i / 2) >= choose) {
return gene_pool.splice(i, 1)[0];
}
}
return gene_pool.pop(); // last element, if for some reason we get here
};
var mother = choose_one();
var father = choose_one();
return [mother, father];
};
var start = function() {
// Initialize our first generation
var width = $output_canvas[0].width;
var height = $output_canvas[0].height;
generation = 0;
children = [];
for (var j = 0; j < num_offspring; j++) {
children.push(Spawn.random(width, height));
}
// sort by fitness so that our best comes first
children.sort(function(a, b) {
return a.fitness() - b.fitness();
});
best_spawn = children[0];
best_fitness = best_spawn.fitness();
best_spawn.draw(output_ctx);
};
var generate = function(spawn_pool) {
// generate a new set of offspring
var offspring = [];
for (var i = 0; i < num_offspring; i++) {
var parents = select_parents(spawn_pool);
// odds of crossover decrease as we get closer
if (Math.random() * best_fitness < crossover_rate) {
var s = Spawn.from_parents(parents);
}
else {
// quick hack to copy our mother, with possible mutation
var s = Spawn.from_parents([parents[0], parents[0]]);
}
offspring.push(s);
}
// select a number of best from the parent pool (elitism)
for (var i = 0; i < elitism; i++) {
offspring.push(spawn_pool[i]);
}
// sort our offspring by fitness (this includes the parents from elitism). Fittest first.
offspring.sort(function(a, b) {
return a.fitness() - b.fitness();
});
// pick off the number that we want
offspring = offspring.slice(0, num_offspring);
best_spawn = offspring[0];
best_fitness = best_spawn.fitness();
best_spawn.draw(output_ctx);
generation++;
return offspring;
};
var average_fitness = function(generation) {
debugger;
var a = 0;
for (var i = 0; i < generation.length; i++) {
a += generation[i].fitness();
}
return a / generation.length;
};
//Draw yellow and then initialize our first generation
input_ctx.fillStyle = 'yellow';
input_ctx.fillRect(0, 0, input_ctx.canvas.width, input_ctx.canvas.height);
start();
// Our loop function. Use setTimeout to prevent things from freezing
var gen = function() {
children = generate(children);
$gen_span.text('Generation: ' + generation);
$best_fit.text('Best Fitness: ' + best_fitness);
$avg_fit.text('Avg. Fitness: ' + average_fitness(children));
if (generation % 100 === 0) {
console.log('Generation', generation);
console.log('Fitness', best_fitness);
}
setTimeout(gen, 1);
};
gen();
解析を容易にするために、コードにコメントを付けました。基本的な考え方は非常に単純です。
- 現在の世代から 1 つまたは 2 つの親を選択してください
- それらの1つまたは2つの親を一緒に混ぜます
- 結果を少し変異させて次世代に追加する
- 最良の数の親 (例では 1 つ) を選択し、それらを次の世代に追加します
- N 個の結果を並べ替えてスライスし、次世代に使用します (親と子が混在する可能性があります)。
- すすいで繰り返す
出力が黄色に近づくことはありません。それはすぐに、ひどく見えるような安定した状態に陥ります。どこで間違ったのですか？