ABSTRACT

This paper proposes a new Multi-Objective Equilibrium Optimizer (MOEO) to handle complex optimization problems, including real-world engineering design optimization problems. The Equilibrium Optimizer (EO) is a recently reported physics-based metaheuristic algorithm, and it has been inspired by the models used to predict equilibrium state and dynamic state. A similar procedure is utilized in MOEO by combining models in a different target search space. The crowding distance mechanism is employed in the MOEO algorithm to balance exploitation and exploration phases as the search progresses. In addition, a non-dominated sorting strategy is also merged with the MOEO algorithm to preserve the population diversity and it has been considered as a crucial problem in multi-objective metaheuristic algorithms. An archive with an update function is used to uphold and improve the coverage of Pareto with optimal solutions. The performance of MOEO is validated for 33 contextual problems with 6 constrained, 12 unconstrained, and 15 practical constrained engineering design problems, including non-linear problems. The result obtained by the proposed MOEO algorithm is compared with other state-of-the-art multi-objective optimization algorithms. The quantitative and qualitative results indicate that the proposed MOEO provides more competitive outcomes than the different algorithms. From the results obtained for all 33 benchmark optimization problems, the efficiency, robustness, and exploration ability to solve multi-objective problems of the MOEO algorithm are well defined and clarified. The paper is further supported with extra online service and guideline at https://premkumarmanoharan.wixsite.com/mysite.

中文翻译：

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多目标均衡优化器：解决多目标优化问题的框架和开发

摘要

本文提出了一种新的多目标平衡优化器 (MOEO) 来处理复杂的优化问题，包括现实世界的工程设计优化问题。平衡优化器 (EO) 是最近报道的一种基于物理的元启发式算法，它受到用于预测平衡状态和动态状态的模型的启发。通过在不同的目标搜索空间中组合模型，在 MOEO 中使用了类似的过程。MOEO 算法中采用拥挤距离机制来平衡搜索过程中的开发和探索阶段。此外，非支配排序策略也与 MOEO 算法相结合以保持种群多样性，并被认为是多目标元启发式算法中的关键问题。具有更新功能的存档用于通过最佳解决方案维护和改进 Pareto 的覆盖范围。MOEO 的性能经过 33 个上下文问题的验证，其中 6 个受约束、12 个不受约束和 15 个实际受约束的工程设计问题，包括非线性问题。将提出的 MOEO 算法获得的结果与其他最先进的多目标优化算法进行比较。定量和定性结果表明，提出的 MOEO 提供了比不同算法更具竞争力的结果。从所有 33 个基准优化问题获得的结果来看，MOEO 算法解决多目标问题的效率、鲁棒性和探索能力得到了很好的定义和阐明。