Investigating the performance of various PSO variants on VRPPD and VRPSPD

This study considers different PSO variants, that have been previously studied in literature, to solve the vehicle routing problem with pickup and delivery and its simultaneous variant. We consider two PSO frameworks: GLN-PSO, and opposition based GLN-PSO. We combine these main algorithms with four existing solution representations SR-1, SR-1*, SR-2 and SR-P. Three of which use vehicle orientation points to construct feasible routes and one uses probabilities to construct feasible routes. Additionally, we propose a new solution representation SR-C, based on customer priorities and radii, and investigate its competitiveness. As opposed to previous research, we compare solution representations under similar PSO frameworks and local improvement procedures, resulting in a fair comparison. In this comparison there exists an important trade-off between computation time and solution quality. We conclude from the behaviour of the PSO methods that SR-2 and SR-1* are, generally, the best PSO methods depending on the specifics of the data instance. Additionally, the proposed SR-C is not competitive to the other solution representations.