遺伝アルゴリズムを用いた最適化関数。ここでは旅程問題の最小コストの最適化を試みていますが、他の問題にも応用できます。かなり強力なアルゴリズムなのでオススメです。肌感としては、世代数を増やすよりも人口（ポピュレーション）を増やしたほうが良い解に辿り着ける可能性が高い気がします。

PHPで学ぶ集合知プログラミング5.7

function geneticoptimize($domain, $origin, $people, $flights, $destination, $popsize = 50, $step=1, $mutprob=0.2, $elite=0.2, $maxiter = 100) {
    function mutate($vec, $domain, $step) { 
        $i = rand(0, (count($domain) - 1));
        $rand = rand(1,10000)/10000;
        if(($rand < 0.5) && ($vec[$i] > $domain[$i][0])) {
            $vec[$i] = $vec[$i] - $step;
            return $vec;
        } elseif($vec[$i] < $domain[$i][1]) {
            $vec[$i] = $vec[$i] + $step;
            return $vec;
        }
    }

    function crossover($r1, $r2, $domain) {
        $i = rand(1, (count($domain) - 2));
        for($k = 0; $k < $i; $k++){
            $r2[$k] = $r1[$k];
        }
        return $r2;
    }


    $pop = array();

    for($y = 0; $y < $popsize; $y++){
        $vec = array();
        for($s = 0; $s < count($domain); $s++) {
            $vec[] = rand($domain[$s][0], $domain[$s][1]);
        }
        $pop[] = $vec;
    }

    $topelite = floor($elite*$popsize);
    for($g=0; $g<$maxiter; $g++){
        $scores = array();
        foreach($pop as $key => $v){
            if(!empty($v)){
            $scores[]=array(schedulecost($v, $origin, $people, $flights, $destination), $v);
            }
       }
        sort($scores);
        $pop = $ranked = array();
        foreach($scores as $key => $v) {

            $ranked[] = $v[1];
        }
        foreach($ranked as $v){
            $pop[] = $v;
            if(count($pop) == $topelite) {
                break;
            }
        }
        while(count($pop) <= $popsize) {
            $randrand = rand(1,10000)/10000;
            if($randrand  < $mutprob){
                $c = rand(0, $topelite);
                $pop[] = mutate($ranked[$c], $domain, $step);
            }else{
                $c1 = rand(0, $topelite);
                $c2 = rand(0, $topelite);
                $pop[] = crossover($ranked[$c1], $ranked[$c2], $domain);
            }
        }
        print $scores[0][0] . '<br />';
    }
    return $scores[0][1];
}
$result = geneticoptimize($domain, $origin, $people, $flights, $destination, $popsize = 50, $step=1, $mutprob=0.2, $elite=0.2, $maxiter = 100);
var_dump($result);
die();
$cost = schedulecost($result, $origin, $people, $flights, $destination);
var_dump($cost);
$schedule = printschedule($result, $people, $flights, $destination);
var_dump($schedule);