A new game-theoretical multi-objective evolutionary approach for cash-in-transit vehicle routing problem with time windows (A Real life Case)

Multiobjective Particle Swarm Optimization Based on Cosine Distance Mechanism and Game Strategy

The optimization problems are taking place at all times in actual lives. They are divided into single objective problems and multiobjective problems. Single objective optimization has only one objective function, while multiobjective optimization has multiple objective functions that generate the Pareto set. Therefore, to solve multiobjective problems is a challenging task. A multiobjective particle swarm optimization, which combined cosine distance measurement mechanism and novel game strategy, has been proposed in this article. The cosine distance measurement mechanism was adopted to update Pareto optimal set in the external archive. At the same time, the candidate set was established so that Pareto optimal set deleted from the external archive could be effectively replaced, which helped to maintain the size of the external archive and improved the convergence and diversity of the swarm. In order to strengthen the selection pressure of leader, this article combined with the game update mechanism, and a global leader selection strategy that integrates the game strategy including the cosine distance mechanism was proposed. In addition, mutation was used to maintain the diversity of the swarm and prevent the swarm from prematurely converging to the true Pareto front. The performance of the proposed competitive multiobjective particle swarm optimizer was verified by benchmark comparisons with several state-of-the-art multiobjective optimizer, including seven multiobjective particle swarm optimization algorithms and seven multiobjective evolutionary algorithms. Experimental results demonstrate the promising performance of the proposed algorithm in terms of optimization quality.