Velocity Tentative Particle Swarm Optimization to solve TSP

Abstract

Particle Swarm Optimization (PSO) is a population based optimization technique on metaphor of social behavior of flocks of birds or schools of fishes and has found popularity in solving difficult optimization problems. A number of PSO based methods have been investigated for solving Traveling Salesman Problem (TSP), the popular combinatorial problem. The velocity for solving TSP is the Swap Sequence (SS) with several Swap Operators (SOs) and all SOs of a SS are applied maintaining order on a particle and gives a new tour i.e., a particle having new solution in the PSO. This study investigates a new PSO based method, called Velocity Tentative PSO (VTPSO), for solving TSP where calculated velocity SS is considered as tentative velocity. VTPSO evaluates a number of tentative tours applying SOs one after another sequentially and the final tour is considered as the best tentative tour. VTPSO is shown to produce optimal solution within a minimal time when compared with traditional PSO based methods in solving benchmark TSPs. The reason behind the less time requirement is revealed from the experimental analysis is that VTPSO converge faster due to intermediate tour evaluation.