Solving TSP Problem Using Simulated Annealing Algorithm with Two-Point Swap Operation

This article explores how to solve the Traveling Salesman Problem (TSP) using the Simulated Annealing algorithm, specifically focusing on the two-point swap implementation. The TSP involves finding the shortest possible route that visits each given point exactly once and returns to the origin point. Simulated Annealing is a metaheuristic algorithm that mimics the physical process of annealing in metallurgy, where a material is heated and slowly cooled to reduce defects. The algorithm works by randomly exploring solution spaces while occasionally accepting worse solutions to escape local optima, using a temperature parameter that decreases over time. In this implementation, we utilize a two-point swap operation to generate neighboring solutions. This neighborhood search strategy involves selecting two random positions in the current route and swapping their positions to create a new candidate solution. The key algorithmic steps include: 1. Initialization: Generate an initial random tour and set initial temperature parameters 2. Energy Calculation: Compute the total distance (cost) of the current tour 3. Neighborhood Generation: Perform two-point swaps to create new candidate solutions 4. Acceptance Probability: Use the Metropolis criterion to determine whether to accept worse solutions based on current temperature 5. Cooling Schedule: Gradually reduce temperature according to a predefined cooling rate The core implementation typically involves functions for: - calculate_distance(): Computes total route distance using Euclidean distance - generate_neighbor(): Creates new solutions by swapping two random cities - acceptance_probability(): Determines whether to accept worse solutions based on temperature and cost difference This approach proves particularly valuable in logistics optimization, manufacturing process planning, and other combinatorial optimization problems where finding near-optimal routes is essential. The two-point swap operation provides an efficient way to explore the solution space while maintaining solution feasibility.