In order to improve supply chain's operation efficiency, shorten delivery time and decrease distribution costs, two-stage cross docking scheduling problem under direct shipment mode was studied in this paper. Taking into consideration the influence of numbers of vehicles in distribution center on cross docking problem, three models were established based on different assumptions including only one vehicle in distribution center, many vehicles in distribution center and the location of distribution center to be determined, and the objective was to minimize transportation time. Hybrid particle swarm optimization was proposed to solve the model on the basis of PSO and GA. The algorithm introduced clone selection operator to make particles multiply and mutate by calculating the affinity between individuals so that the best individual can be reserved and the poor can be improved. Clone operator, crossover operator, antibody reorganization operator and mutation operator were designed to improve the performance of the algorithm. Computational experiments showed that the hybrid particle swarm optimization algorithm has faster convergence speed and better solution precision compared with other algorithms. The result of the present work implied that the model in this paper was accord with the reality, and it was effective and feasible.

Due to conflicts among objectives of multi-objective optimization (MO) problems, it remains challenging to gain high-quality Pareto fronts for different MO issues. Attempt to handle this challenge and obtain high-performance Pareto fronts, this paper proposes a novel MO optimizer via leveraging particle swarm optimization (PSO) with evolutionary game theory (EGT). Firstly, a modified self-adaptive PSO (MSAPSO) adopting a novel self-adaptive parameter adaption rule determined by the evolutionary strategy of EGT to tune the three key parameters of each particle is proposed in order to well balance the exploration and exploitation abilities of MSAPSO. Then, a parameter selection principle is provided to sufficiently guarantee convergence of MSAPSO followed after the analytical convergence investigation of this optimizer so as to assure convergence of the searched Pareto front toward the true Pareto front as far as possible. Subsequently, a MSAPSO-based MO optimizer is developed, in which an external archive is applied to preserve the searched non-dominated solutions and a circular sorting method is amalgamated with the elitistsaving method to update the external archive. Lastly, the performance of the proposed method is examined by 16 benchmark test functions against 4 well-known MOO methods. The simulation results reveal that the proposed method dominates its peers regarding the quality of the Pareto fronts for most of the studied benchmarks. Furthermore, the results of the non-parametric analysis confirm that the proposed method significantly outperforms its contenders at the confidential level of 95% over the 16 benchmarks.