Solving TSP with Simulated Annealing Algorithm

We employ the simulated annealing algorithm to solve the Traveling Salesman Problem (TSP). Simulated annealing is a probabilistic global optimization technique that explores the solution space to find near-optimal solutions. TSP represents a classic combinatorial optimization challenge aiming to discover the shortest possible route enabling a salesman to visit all cities exactly once and return to the starting point. Our implementation involves key components including: 1) Initial solution generation using random permutation or nearest-neighbor heuristic, 2) Temperature scheduling with exponential decay (T = T0 * α^k), 3) Neighbor solution creation through 2-opt swaps or inversion mutations, and 4) Acceptance probability calculation using the Metropolis criterion (P = exp(-ΔE/T)). The algorithm iteratively explores alternative paths while gradually reducing the temperature parameter to refine the solution. This approach finds practical applications in logistics planning, route optimization, and resource allocation scenarios. The method's effectiveness stems from its ability to escape local optima through controlled probabilistic acceptance of worse solutions during early stages. Thus, applying simulated annealing to TSP constitutes a robust and computationally feasible optimization strategy.