论文标题

一种用于多模式多目标优化的简单进化算法

A Simple Evolutionary Algorithm for Multi-modal Multi-objective Optimization

论文作者

Ray, Tapabrata, Mamun, Mohammad Mohiuddin, Singh, Hemant Kumar

论文摘要

在解决多模式,多目标优化问题(MMOP)时,该目标不仅是在目标空间中找到帕托托最佳前沿(PF)的良好表示,而且还可以在可变空间中找到所有等效的帕累托 - 最佳子集(PSS)。当决策者(DM)有兴趣确定具有相似性能的替代设计时,此类问题实际上是相关的。近年来,人们对开发有效的算法来处理MMOP的研究兴趣很大。但是,现有的算法仍然需要大量的功能评估(通常为数千个)来处理涉及两个目标和两个变量的问题。这些算法通常嵌入了复杂的自定义机制,这些机制需要其他参数来管理变量和目标空间中的多样性和收敛性。在这封信中,我们引入了一种用于求解MMOP的稳态进化算法,具有简单的设计,并且与标准EA相比,无需调整的其他用户定义参数。我们报告了其在来自各种测试套件的21毫米摩托车上的性能,这些套件被广泛用于使用1000个功能评估的低计算预算进行基准测试。将所提出的算法的性能与六种最先进的算法(Mo Ring PSO SCD,DN-NSGAII,Trimoea-Ta&r,CPDEA,MMOEA/MMOEA/DC和MMEA-WI)进行了比较。所提出的算法比基于IGDX,PSP和IGD在内的已建立指标的上述算法表现出明显更好的性能。我们希望这项研究能够鼓励设计简单,高效和普遍的算法,以改善其用于实际应用的吸收。

In solving multi-modal, multi-objective optimization problems (MMOPs), the objective is not only to find a good representation of the Pareto-optimal front (PF) in the objective space but also to find all equivalent Pareto-optimal subsets (PSS) in the variable space. Such problems are practically relevant when a decision maker (DM) is interested in identifying alternative designs with similar performance. There has been significant research interest in recent years to develop efficient algorithms to deal with MMOPs. However, the existing algorithms still require prohibitive number of function evaluations (often in several thousands) to deal with problems involving as low as two objectives and two variables. The algorithms are typically embedded with sophisticated, customized mechanisms that require additional parameters to manage the diversity and convergence in the variable and the objective spaces. In this letter, we introduce a steady-state evolutionary algorithm for solving MMOPs, with a simple design and no additional userdefined parameters that need tuning compared to a standard EA. We report its performance on 21 MMOPs from various test suites that are widely used for benchmarking using a low computational budget of 1000 function evaluations. The performance of the proposed algorithm is compared with six state-of-the-art algorithms (MO Ring PSO SCD, DN-NSGAII, TriMOEA-TA&R, CPDEA, MMOEA/DC and MMEA-WI). The proposed algorithm exhibits significantly better performance than the above algorithms based on the established metrics including IGDX, PSP and IGD. We hope this study would encourage design of simple, efficient and generalized algorithms to improve its uptake for practical applications.

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