How to implement simulated annealing algorithm with PHP

How to use PHP to implement simulated annealing algorithm

Introduction:
Simulated annealing algorithm (Simulated Annealing) is a commonly used global optimization algorithm that finds the solution to problems by simulating the behavior of the material annealing process. Optimal solution. It can overcome the problem of local optimal solutions and can be applied to many optimization problems, such as the traveling salesman problem, knapsack problem, etc. This article will introduce how to implement the simulated annealing algorithm with PHP and give code examples.

Algorithm steps:

1. Initialization parameters - set initial temperature, end temperature, cooling rate, current status, etc.
2. Generate Neighborhood Solution - Generate a neighborhood solution based on the current state.
3. Calculate function value - Calculate the function value of the neighborhood solution.
4. Determine whether to accept the neighborhood solution - Determine whether to accept the neighborhood solution by calculating the acceptance probability.
5. Update current status - Update the current status based on acceptance or rejection.
6. Cooling - Update the temperature value and reduce the temperature.
7. Iteration - Repeat the above steps until the termination condition is met.

Sample code:

<?php
function simulatedAnnealing($initState, $initTemp, $finalTemp, $coolRate) {
    $currentTemp = $initTemp;
    $currentState = $initState;
    $bestState = $initState;
    $currentEnergy = calculateEnergy($currentState);
    $bestEnergy = $currentEnergy;

    while ($currentTemp > $finalTemp) {
        $newState = generateNeighbor($currentState);
        $newEnergy = calculateEnergy($newState);
        $energyDifference = $newEnergy - $currentEnergy;

        if ($energyDifference < 0) {
            $currentState = $newState;
            $currentEnergy = $newEnergy;
            if ($newEnergy < $bestEnergy) {
                $bestState = $newState;
                $bestEnergy = $newEnergy;
            }
        } else {
            $random = mt_rand() / mt_getrandmax();
            $acceptProbability = exp(-$energyDifference / $currentTemp);
            if ($random < $acceptProbability) {
                $currentState = $newState;
                $currentEnergy = $newEnergy;
            }
        }

        $currentTemp *= $coolRate;
    }

    return $bestState;
}

function calculateEnergy($state) {
    // 计算函数值，根据具体问题进行定义
    // 这里以一个简单的函数为例
    $x = $state;
    $energy = pow($x, 2) - 10 * cos(2 * M_PI * $x);

    return $energy;
}

function generateNeighbor($state) {
    // 生成邻域解，根据具体问题进行定义
    // 这里以一个简单的生成随机数的方式为例
    $neighbor = $state + (mt_rand() / mt_getrandmax()) * 2 - 1;

    return $neighbor;
}

// 示例调用
$initState = 0;
$initTemp = 100;
$finalTemp = 0.1;
$coolRate = 0.9;

$bestState = simulatedAnnealing($initState, $initTemp, $finalTemp, $coolRate);
echo "Best state: " . $bestState . "
";
echo "Best energy: " . calculateEnergy($bestState) . "
";
?>

In this example, the simulated annealing algorithm is used to solve the minimum value of a simple function. By calling the simulatedAnnealing function and passing in parameters such as the initial state, initial temperature, termination temperature, and cooling rate, the optimal solution can be obtained.

Summary:
This article introduces how to use PHP to implement the simulated annealing algorithm, and gives a code example for a simple function optimization problem. Through this example, you can understand and master the basic principles and implementation process of the simulated annealing algorithm. In practical applications, corresponding function value calculation and neighborhood solution generation can be performed according to specific problems. I hope this article can help readers who want to understand and apply simulated annealing algorithms.

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