本文目录导读：
在PHP中实现模拟退火算法，虽然没有某些语言那么高效，但对于问题规模不是特别大的场景仍然可行,下面是一个完整的实现方案：
基础模拟退火算法实现
<?php
class SimulatedAnnealing {
private $temperature;
private $coolingRate;
private $minTemperature;
public function __construct($initialTemp = 1000, $coolingRate = 0.95, $minTemp = 0.001) {
$this->temperature = $initialTemp;
$this->coolingRate = $coolingRate;
$this->minTemperature = $minTemp;
}
// 目标函数 - 根据实际问题定义
protected function objectiveFunction($solution) {
// 示例：求解函数 f(x) = x^2 + 2x + 1 的最小值
// 实际使用时替换为你的目标函数
$x = $solution['x'];
return $x * $x + 2 * $x + 1;
}
// 生成邻域解
protected function generateNeighbor($currentSolution) {
// 在当前位置附近随机扰动
$neighbor = $currentSolution;
$neighbor['x'] += mt_rand(-100, 100) / 100.0; // 随机步长
return $neighbor;
}
// 初始化解
protected function generateInitialSolution() {
return ['x' => mt_rand(-1000, 1000) / 100.0];
}
// 运行模拟退火
public function run($iterations = 1000) {
$currentSolution = $this->generateInitialSolution();
$currentEnergy = $this->objectiveFunction($currentSolution);
$bestSolution = $currentSolution;
$bestEnergy = $currentEnergy;
$temperature = $this->temperature;
echo "初始解: x = {$currentSolution['x']}, 能量 = $currentEnergy\n";
for ($i = 0; $i < $iterations; $i++) {
if ($temperature < $this->minTemperature) {
break;
}
// 生成新解
$newSolution = $this->generateNeighbor($currentSolution);
$newEnergy = $this->objectiveFunction($newSolution);
// 计算能量差
$delta = $newEnergy - $currentEnergy;
// 接受新解的条件
if ($delta < 0 || exp(-$delta / $temperature) > mt_rand() / mt_getrandmax()) {
$currentSolution = $newSolution;
$currentEnergy = $newEnergy;
// 更新最优解
if ($currentEnergy < $bestEnergy) {
$bestSolution = $currentSolution;
$bestEnergy = $currentEnergy;
}
}
// 降温
$temperature *= $this->coolingRate;
// 输出进度
if ($i % 100 == 0) {
echo "迭代 {$i}: 温度 = {$temperature}, 当前最优 = {$bestEnergy}\n";
}
}
return [
'solution' => $bestSolution,
'energy' => $bestEnergy,
'iterations' => $i
];
}
}
// 使用示例
$sa = new SimulatedAnnealing(1000, 0.98, 0.001);
$result = $sa->run(2000);
echo "最终结果:\n";
print_r($result);
针对旅行商问题(TSP)的实现
<?php
class TSP_SimulatedAnnealing extends SimulatedAnnealing {
private $cities = [];
private $distanceMatrix = [];
public function __construct($cities, $initialTemp = 10000, $coolingRate = 0.999, $minTemp = 0.001) {
parent::__construct($initialTemp, $coolingRate, $minTemp);
$this->cities = $cities;
$this->calculateDistanceMatrix();
}
private function calculateDistanceMatrix() {
$n = count($this->cities);
for ($i = 0; $i < $n; $i++) {
for ($j = 0; $j < $n; $j++) {
$dx = $this->cities[$i]['x'] - $this->cities[$j]['x'];
$dy = $this->cities[$i]['y'] - $this->cities[$j]['y'];
$this->distanceMatrix[$i][$j] = sqrt($dx * $dx + $dy * $dy);
}
}
}
protected function objectiveFunction($solution) {
$totalDistance = 0;
$n = count($solution['route']);
for ($i = 0; $i < $n - 1; $i++) {
$totalDistance += $this->distanceMatrix[$solution['route'][$i]][$solution['route'][$i+1]];
}
// 返回起点的距离
$totalDistance += $this->distanceMatrix[$solution['route'][$n-1]][$solution['route'][0]];
return $totalDistance;
}
protected function generateInitialSolution() {
$n = count($this->cities);
$route = range(0, $n - 1);
shuffle($route);
return ['route' => $route];
}
protected function generateNeighbor($currentSolution) {
$neighbor = $currentSolution;
$n = count($neighbor['route']);
// 随机选择两个城市进行交换
$i = mt_rand(0, $n - 1);
$j = mt_rand(0, $n - 2);
if ($j >= $i) $j++; // 确保i != j
// 交换
$temp = $neighbor['route'][$i];
$neighbor['route'][$i] = $neighbor['route'][$j];
$neighbor['route'][$j] = $temp;
return $neighbor;
}
}
// 使用示例
$cities = [
['x' => 0, 'y' => 0],
['x' => 1, 'y' => 5],
['x' => 2, 'y' => 2],
['x' => 4, 'y' => 1],
['x' => 5, 'y' => 3],
['x' => 3, 'y' => 4]
];
$tsp = new TSP_SimulatedAnnealing($cities);
$result = $tsp->run(10000);
echo "最优路径: " . implode(' -> ', $result['solution']['route']) . "\n";
echo "路径长度: " . round($result['energy'], 3) . "\n";
优化和变体实现
<?php
class AdvancedSimulatedAnnealing extends SimulatedAnnealing {
// 自适应降温策略
private $reheatThreshold = 5; // 连续无改进次数触发重加热
private $noImprovementCount = 0;
// 多种邻域生成策略
private function generateNeighborV1($solution) {
// 小范围扰动
$neighbor = $solution;
$neighbor['x'] += mt_rand(-10, 10) / 100.0;
return $neighbor;
}
private function generateNeighborV2($solution) {
// 大范围跳跃
$neighbor = $solution;
if (mt_rand(0, 1)) {
$neighbor['x'] += mt_rand(-100, 100) / 10.0;
}
return $neighbor;
}
protected function generateNeighbor($currentSolution) {
// 根据当前温度选择策略
if ($this->temperature > 100) {
return $this->generateNeighborV2($currentSolution);
} else {
return $this->generateNeighborV1($currentSolution);
}
}
// 加入重加热机制
protected function reheatIfNeeded() {
if ($this->noImprovementCount >= $this->reheatThreshold) {
$this->temperature *= 2; // 加倍温度
$this->noImprovementCount = 0;
echo "触发重加热，温度变为: {$this->temperature}\n";
}
}
public function run($iterations = 1000) {
// 记录最优解
$bestSolution = null;
$bestEnergy = PHP_FLOAT_MAX;
for ($trial = 0; $trial < 3; $trial++) { // 多次尝试
$currentSolution = $this->generateInitialSolution();
$currentEnergy = $this->objectiveFunction($currentSolution);
$this->temperature = $this->initialTemp;
for ($i = 0; $i < $iterations; $i++) {
if ($this->temperature < $this->minTemperature) break;
$newSolution = $this->generateNeighbor($currentSolution);
$newEnergy = $this->objectiveFunction($newSolution);
$delta = $newEnergy - $currentEnergy;
if ($delta < 0 || exp(-$delta / $this->temperature) > mt_rand() / mt_getrandmax()) {
$currentSolution = $newSolution;
$currentEnergy = $newEnergy;
if ($currentEnergy < $bestEnergy) {
$bestEnergy = $currentEnergy;
$bestSolution = $currentSolution;
$this->noImprovementCount = 0;
} else {
$this->noImprovementCount++;
}
}
$this->temperature *= $this->coolingRate;
$this->reheatIfNeeded();
}
}
return ['solution' => $bestSolution, 'energy' => $bestEnergy];
}
}
使用建议
-
参数调优：
- 初始温度：应足够高以允许广泛搜索
- 降温速率：0.8-0.99之间，越接近1搜索越精细
- 最小温度：决定何时停止
-
性能优化：
- 使用
mt_rand()而非rand() - 考虑使用
SplFixedArray提高数组性能 - 对于大规模问题，考虑改用C扩展
- 使用
-
实际应用：
// 适配自己的问题 class MyProblemSA extends SimulatedAnnealing { private $params; public function __construct($params) { $this->params = $params; parent::__construct(500, 0.98, 0.01); } protected function objectiveFunction($solution) { // 实现你的目标函数 // 调度、路径规划、参数优化等 } protected function generateInitialSolution() { // 生成初始可行解 } protected function generateNeighbor($currentSolution) { // 生成邻域解的方法 } }
这个实现提供了基础的框架，你可以根据具体问题调整目标函数和解的表示方式，对于性能敏感的应用,建议使用PHP的JIT编译或在必要时考虑使用其他语言实现核心计算。
