Chaos quantum evolutionary algorithm for vehicle routing problem with simultaneous delivery and pickup

For the discrete value of the rotation gate, the quantum-inspired evolutionary algorithm (QEA) has jump phenomena in the search space. To improve the QEA, a hybrid algorithm with computing the rotation gate using elite mean values based on chaos theory is presented, which is applied to vehicle routing problem with simultaneous delivery and pickup (VRPSDP). The solution of VRPSDP is investigated, and the qualification of strong feasible solution and puny feasible solution is analyzed theoretically. An efficient population initialization based on nearest insertion algorithm (NIA) and chaos function is proposed to generate an initial population with certain quality and diversity. Simulation results and comparisons show the effectiveness of the proposed algorithm.