Adaptive Tunning of All Parameters in a Multi-Swarm Particle Swarm Optimization Algorithm: An Application to the Probabilistic Traveling Salesman Problem

摘要

One of the main issues in the application of a Particle SwarmOptimization (PSO) algorithm and of every evolutionary opti-mization algorithm is the finding of the suitable parameters ofthe algorithm. In this paper, we use a parameter free version of aMulti-Swarm PSO algorithm where random values are assignedin the initialization of all parameters (including the number ofswarms) of the algorithm and, then, during the iterations theparameters are optimized together and simultaneously with theoptimization of the objective function of the problem. This ideais used for the solution of the Probabilistic Traveling SalesmanProblem (PTSP). The PTSP is a variation of the classic Trav-eling Salesman Problem (TSP) and one of the most significantstochastic routing problems. In the PTSP, only a subset of poten-tial customers needs to be visited on any given instance of theproblem. The number of customers to be visited each time is arandom variable. The proposed algorithm is tested on numer-ous benchmark problems from TSPLIB with very satisfactoryresults. It is compared with other algorithms from the literature,and, mainly with a Multi-Swarm Particle Swarm Optimizationwith parameters calculated with a classic trial - and - error pro-cedure and they are the same for all instances.