Solving fixed-charge transportation problem using a modified particle swarm optimization algorithm

Particle Swarm Optimization (PSO) has emulated the social behaviour of some animals such as a flock of birds and a school of fish, searching for food. This communicative sociality when modelled as computational procedure has solved a wide range of complex problems. Over the years, PSO has undergone transformations and numerous variants have come up. In this paper, PSO has been hybridized with two new algorithms to solve the fixed charge transportation problem to minimize the transportation cost (variable and fixed) of delivering goods while satisfying supply/demand constraints. The method considers the reduction of objective function defined by Balinski, Adlakha et al., Yousefi et al. and is incorporated within the PSO. An independent approach of solving the problem on the basis of variable cost initially followed by addition of fixed cost has also been explored. It was observed that proposed PSO works best without reducing the objective function. The simulation results reveal a substantial gain of the proposed method in terms of its efficiency and effectiveness examined on different test problems. To validate the claims, the proposed PSO has also been compared with the solutions attained by other existing methods (either exact or heuristics).