The optimization problems are divided into a single objective and multi-objective. Single objective optimization has only one objective function; whereas, multi-objective optimization has multiple objective functions that generate the Pareto set; therefore, solving a multi-objective problem is a challenging problem. This paper presents a new multi-objective optimization method (called MWDEO) based on improved whale optimization algorithm (WOA) by combining the differential evolution (DE) algorithm and the opposition-based learning (OBL). The MWDEO uses the WOA to perform a global exploration, whereas DE is used to exploit the search space; while the OBL is applied to improve the exploration and exploitation by generating the opposite values. The proposed algorithm is evaluated using 32 multi-objective test problems besides a set of benchmark problems of CEC’2017. The experimental results are compared with nine state-of-the-art multi-objective methods. The analysis of the results showed that the proposed MWDEO outperformed all other algorithms in most of the test problems which indicates that the proposed MWDEO is competitive and effective in solving different types of multi-objective problems.

优化问题分为单目标和多目标。单目标优化只有一个目标函数。然而，多目标优化具有生成帕累托集的多个目标函数。因此，解决多目标问题是一个具有挑战性的问题。本文提出了一种基于改进的鲸鱼优化算法（WOA）的多目标优化方法（MWDEO），该方法将差分进化（DE）算法和基于对立的学习（OBL）相结合。MWDEO使用WOA进行全局探索，而DE用于开发搜索空间；OBL通过生成相反的值来改进勘探和开发。除了一组CEC'2017基准测试问题外，该算法还使用32个多目标测试问题进行了评估。将实验结果与九种最新的多目标方法进行了比较。结果分析表明，在大多数测试问题中，拟议的MWDEO优于所有其他算法，这表明拟议的MWDEO在解决不同类型的多目标问题方面具有竞争力和有效性。