Hybrid Particle Swarm Optimization Algorithm to Solve Multi-Index Fixed Charge Transportation Problem

The transportation problem in which multiple products are transported from sources to destinations and some fixed-charge is levied on the transportation routes is called a Multi-Index Fixed Charge Transportation Problem (MIFCTP). This NP-hard discrete optimization problem has been solved by many researchers and an optimality condition was proposed. This paper solves the problem through a Particle Swarm Optimization (PSO) based procedure that is hybridized with three new algorithms. PSO is a population-based algorithm that searches for an optimal solution through an interaction of the particles. The three algorithms proposed in this paper address the issues of diverse initial population and obtaining non-negative integral solutions of the problem. This Hybrid PSO improves the optimal transportation cost thereby addressing the existing optimality condition for MIFCTP.