How can I implement simulated annealing in C++?

How can I implement simulated annealing in C++?

To implement simulated annealing in C++, you need to define your objective function, initial solution, and cooling schedule.

What is a cooling schedule, and how do I choose one?

A cooling schedule controls the temperature decrease over time. Common choices include linear, exponential, or logarithmic cooling.

Can you provide a simple code example?

Sure! Here's a basic structure:

#include <iostream>
#include <cmath>

// Objective function
double objectiveFunction(double x) {
    return x * x; // Example: minimize x^2
}

// Simulated Annealing function
void simulatedAnnealing() {
    double temperature = 1000;
    double coolingRate = 0.003;
    double currentSolution = ...; // Initial solution
    double bestSolution = currentSolution;

    while (temperature > 1) {
        // Generate new solution
        double newSolution = ...; // Perturb current solution
        double currentEnergy = objectiveFunction(currentSolution);
        double newEnergy = objectiveFunction(newSolution);

        // Acceptance probability
        if (newEnergy < currentEnergy || exp((currentEnergy - newEnergy) / temperature) > rand() / RAND_MAX) {
            currentSolution = newSolution;
        }

        // Update best solution
        if (currentEnergy < objectiveFunction(bestSolution)) {
            bestSolution = currentSolution;
        }

        // Cool down
        temperature *= 1 - coolingRate;
    }
    std::cout << "Best solution: " << bestSolution << std::endl;
}

What are some common applications of simulated annealing?

Simulated annealing is commonly used for optimization problems like traveling salesman, job scheduling, and circuit design.