A modified particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery

The vehicle routing problem with simultaneous pickup and delivery (VRPSPD) is an extension to the classical vehicle routing problem (VRP) where customers require pickup and delivery service simultaneously. The objective of this problem is to determine the optimal set of routes to totally satisfy both the pickup and delivery. We propose a modified particle swarm optimization to solve this problem. The solution representation for VRPSPD with m customers is several (m + 1)-dimensional particles. In the decoding process, particles will be transformed to vehicle allocation matrices with the sweep algorithm, and then the priority matrices of customers served by the same vehicle are evaluated. Based on the two matrices, the vehicle routes are constructed. The proposed algorithm is evaluated using some benchmark datasets which are publicly available, and the experimental results prove that our proposed method is effective and efficient.