Simulated Annealing Algorithm for Solving the Traveling Salesman Problem

The simulated annealing algorithm is a widely-used optimization technique applicable to various problems, including the Traveling Salesman Problem (TSP). In TSP, the objective is to find the shortest possible route that enables a salesperson to visit each city exactly once and return to the starting city. Our MATLAB implementation employs simulated annealing to achieve this goal through systematic path modifications. The program operates by initially generating a random route and calculating its total distance. Through iterative temperature-controlled randomization, the algorithm generates neighboring solutions by swapping city positions using functions like randperm() for permutation generation. At each iteration, the Metropolis criterion determines whether to accept inferior solutions based on current temperature and energy difference calculations, preventing premature convergence to local optima. Key MATLAB functions include: - Temperature scheduling using geometric cooling: T_new = alpha * T_old - Energy calculation through path distance summation - Neighbor generation via 2-opt or city-swap operations - Acceptance probability computation: exp(-ΔE/T) As the temperature decreases according to a predefined cooling schedule, the algorithm reduces exploration intensity while increasing exploitation, gradually converging toward the optimal route. The implementation includes convergence monitoring through plot() visualization of distance evolution and temperature decay, providing real-time optimization progress tracking. This approach effectively navigates the solution space by balancing exploration and exploitation, systematically refining the path until discovering the optimal traveling salesman route with minimized total distance.