Solving TSP with Simulated Annealing Algorithm

In this article, we explore how to solve the Traveling Salesman Problem (TSP) using the Simulated Annealing algorithm. TSP involves finding the shortest possible route that visits each city exactly once and returns to the origin city, given a set of cities and distances between every pair. This classical combinatorial optimization problem represents a significant challenge in computer science.

The Simulated Annealing algorithm is a versatile optimization method applicable to various problems including TSP. As a heuristic algorithm, it mimics the annealing process in metallurgy where metals are heated and slowly cooled to reduce defects. The algorithm starts with an initial solution and performs random perturbations at a specific temperature, gradually cooling while converging toward an optimal solution. Key implementation aspects include: generating neighbor solutions through city swaps (using functions like swap() or reverse()), calculating energy differences (route length differences), and applying the Metropolis criterion (accepting worse solutions with probability exp(-ΔE/T)) to escape local optima.

The TSP solving process begins with a random initial route permutation. Through iterative neighbor generation and acceptance criteria, the algorithm explores the solution space while tolerating suboptimal solutions, ultimately converging to a near-optimal route. While computationally intensive (O(n²) per iteration for n cities), the algorithm's strength lies in finding high-quality approximate solutions rather than requiring global optimality. Critical parameters include: initial temperature (T0), cooling rate (α), and iteration count per temperature level, typically implemented through nested loops with temperature decay (T = α*T) and neighbor evaluation cycles.

In summary, Simulated Annealing provides an effective TSP solution methodology that balances solution quality with computational efficiency. By strategically accepting inferior solutions during the search process, it avoids premature convergence to local optima, yielding robust solutions for complex routing problems.