Extension of particle swarm optimization algorithm for solving transportation problem in fuzzy environment

Abstract

Transportation problem is one of the most common real life optimization problems seeking to minimize the total transportation cost while delivering a product from a number of sources to a number of destinations. In this paper, the transportation costs have been considered as generalized trapezoidal fuzzy numbers representing the uncertainty therein whereas the supply and the demand levels are crisp numbers. Particle Swarm Optimization has been extended to solve this fuzzy transportation problem. To illustrate the proposed extension of PSO, two numerical examples from existing literature have been solved and the results have been compared with those of the existing approaches. A few randomly generated problems of different dimensions have also been solved and the convergence rate of the proposed PSO has also been studied with respect to the variants of inertia weight, population size and the number of iterations. It has been observed that the proposed PSO works efficiently to obtain the optimal solutions and also removes the barricades of the traditional solution techniques.