In this work, we explore a novel multi-objective optimization algorithm to identify a set of solutions that could be optimal for more than one task. The proposed approach is used to generate a set of solutions that balance the tradeoff between convergence and diversity in multi-objective optimization problems. Equilibrium Optimizer (EO) algorithm is a novel developed meta-heuristic algorithm inspired by the physics laws. In this paper, we propose a Multi-objective Equilibrium Optimizer Algorithm (MEOA) for tackling multi-objective optimization problems. We suggest an enhancement for exploration and exploitation factors of the EO algorithm to randomize the values of these factors with decreasing the initial value of the exploration factor with the iteration and increasing the exploitation factor to accelerate the convergence toward the best solution. To achieve good convergence and well-distributed solutions, the proposed algorithm is integrated with the Improvement-Based Reference Points Method (IBRPM). The proposed approach is applied to the CEC 2020, CEC 2009, DTLZ, and ZDT test functions. Also, the inverted generational and spread spacing metrics are used to compare the proposed algorithm with the most recent evolutionary algorithms. It's obvious from the results that the proposed algorithm is better in both convergence and diversity.

在这项工作中，我们探索了一种新颖的多目标优化算法，以识别对于多个任务可能是最优的一组解决方案。所提出的方法用于生成一组解决方案，在多目标优化问题中平衡收敛和多样性之间的权衡。均衡优化器（EO）算法是一种受物理定律启发而开发的新颖的元启发式算法。在本文中，我们提出了一种用于解决多目标优化问题的多目标均衡优化器算法（MEOA）。我们建议对EO算法的探索和利用因子进行增强，以随机化这些因子的值，同时随着迭代减小探索因子的初始值，并增加利用因子以加速收敛，以达到最佳解决方案。为了实现良好的收敛性和分布均匀的解决方案，该算法与基于改进的参考点方法（IBRPM）集成在一起。提议的方法适用于CEC 2020，CEC 2009，DTLZ和ZDT测试功能。同样，倒置的世代和扩展间隔度量用于将提出的算法与最新的进化算法进行比较。从结果可以明显看出，该算法在收敛性和多样性方面都更好。为了实现良好的收敛性和分布均匀的解决方案，该算法与基于改进的参考点方法（IBRPM）集成在一起。提议的方法适用于CEC 2020，CEC 2009，DTLZ和ZDT测试功能。同样，倒置的世代和扩展间隔度量用于将提出的算法与最新的进化算法进行比较。从结果可以明显看出，该算法在收敛性和多样性方面都更好。为了实现良好的收敛性和分布均匀的解决方案，该算法与基于改进的参考点方法（IBRPM）集成在一起。提议的方法适用于CEC 2020，CEC 2009，DTLZ和ZDT测试功能。同样，倒置的世代和扩展间隔度量用于将提出的算法与最新的进化算法进行比较。从结果可以明显看出，该算法在收敛性和多样性方面都更好。