Particle Swarm Optimization for Traveling Salesman Problem

Application Context

The Traveling Salesman Problem (TSP) is a classic NP-hard combinatorial optimization problem. A salesman must visit n cities exactly once and return to the starting point, with the objective of finding the shortest possible route.

Particle Swarm Optimization (PSO), introduced by American psychologist James Kennedy and electrical engineer Russell Eberhart in 1995, is a global optimization algorithm. This study utilizes a modified PSO algorithm to solve TSP. By incorporating swap operators and swap sequences, the PSO algorithm can address discrete TSP problems while exhibiting characteristics such as easy implementation, high precision, and fast convergence. The swap operators handle city permutations through position exchanges, while swap sequences manage multiple iterative swaps to explore solution spaces efficiently.

Key Technologies

Traditional TSP-solving algorithms often face limitations like susceptibility to local minima or slow convergence. To address these issues, this paper proposes a PSO-based approach for TSP. Since standard PSO only handles continuous problems, we introduce swap sequences to enable discrete problem-solving. Implementation involves coding swap operations to update particle positions (representing city tours) and velocities (guiding search directions). MATLAB simulations validate the enhanced PSO's effectiveness, with key functions including: 1) Initialization of particles with random city permutations, 2) Fitness evaluation using total tour distance calculation, 3) Velocity updates incorporating personal best (pbest) and global best (gbest) positions via swap sequences, and 4) Iterative optimization until convergence criteria are met.