A hybrid particle swarm algorithm with artificial immune learning for solving the fixed charge transportation problem

Fixed Charge Transportation Problem (FCTP) is an NP‐hard problem with many applications in both traditional and modern industrial situations. This paper introduces a Hybrid Particle Swarm algorithm with artificial Immune Learning (HPSIL) for solving fixed FCTPs. In HPSIL algorithm a flexible particle (chromosome) structure, decoding procedure and allocation procedure are used instead of a Prüfer number and a spanning tree that used with genetic algorithms. The proposed allocation procedure guarantees finding a feasible solution for each generated particle. The HPSIL algorithm can be used for solving both balanced and unbalanced FCTPs without introducing dummy supplier or dummy demand. With regard to solution quality, the HPSIL algorithm can be considered as a viable alternative for solving FCTPs in addition to the recent algorithms.