Solving Traveling Salesman Problem Using Simulated Annealing Algorithm with Code Implementation

This project implements the simulated annealing algorithm to solve the traveling salesman problem (TSP) involving twenty cities. The primary objective is to identify the optimal route that minimizes the total traveling distance. Simulated annealing, a probabilistic heuristic algorithm, mimics the physical annealing process where materials slowly cool to reach minimal energy states. In our implementation, this translates to systematically exploring the solution space for the shortest path configuration. Key algorithm components include: - Temperature scheduling: Implementing a cooling scheme that gradually reduces the acceptance probability of worse solutions - Neighborhood generation: Creating new route configurations through operations like city swapping, inversion, or permutation - Energy function: Calculating total route distance as the optimization criterion The algorithm iteratively improves solutions by: 1. Initializing with a random or greedy route 2. Generating candidate solutions through local transformations 3. Accepting improved solutions unconditionally 4. Accepting worse solutions probabilistically based on current temperature 5. Gradually cooling the system to converge toward global optimum Technical implementation considerations: - Distance matrix computation between all city pairs - Parameter tuning for initial temperature, cooling rate, and iteration count - Termination criteria based on temperature threshold or solution stability This classical combinatorial optimization approach demonstrates practical applications in logistics, circuit design, and DNA sequencing. Through simulated annealing, we achieve near-optimal routing solutions enabling salespersons to visit all cities with minimal time and cost expenditure.