Abstract

Aims: The main goal of this paper is to address the issues of low-quality offspring solutions generated by traditional evolutionary operators, as well as the evolutionary algorithm's inability to solve multi-objective optimization problems (MOPs) with complicated Pareto fronts (PFs).

Background: For some complicated multi-objective optimization problems, the effect of the multi-objective evolutionary algorithm based on decomposition (MOEA/D) is poor. For specific complicated problems, there is less research on how to improve the performance of the algorithm by setting and adjusting the direction vector in the decomposition-based evolutionary algorithm. Considering that in the existing algorithms, the optimal solutions are selected according to the selection strategy in the selection stage, without considering whether it could produce the better solutions in the stage of individual generation to achieve the optimization effect faster. As a result, a multi-objective evolutionary algorithm based on two reference points decomposition and historical information prediction is proposed.

Objective: In order to verify the feasibility of the proposed strategy, the F-series test function with complicated PFs is used as the test function to simulate the proposed strategy.

Methods: Firstly, the evolutionary operator based on historical information prediction (EHIP) is used to generate better offspring solutions to improve the convergence of the algorithm; secondly, the decomposition strategy based on ideal point and nadir point is used to select solutions to solve the MOPs with complicated PFs, and the decomposition method with augmentation term is used to improve the population diversity when selecting solutions according to the nadir point. Finally, the proposed algorithm is compared to several popular algorithms by the F-series test function, and the comparison is made according to the corresponding performance metrics.

Results: The performance of the algorithm is improved obviously compared with the popular algorithms after using the EHIP. When the decomposition method with augmentation term is added, the performance of the proposed algorithm is better than the algorithm with only the EHIP on the whole, but the overall performance is better than the popular algorithms.

Conclusion: The experimental results show that the overall performance of the proposed algorithm is superior to the popular algorithms. The EHIP can produce better quality offspring solutions, and the decomposition strategy based on two reference points can well solve the MOPs with complicated PFs. This paper mainly demonstrates the theory without testing the practical problems. The following research mainly focuses on the application of the proposed algorithm to practical problems such as robot path planning.