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Multi-Objectivising Combinatorial Optimisation Problems byMeans of Elementary Landscape Decompositions

机译：基于基本景观分解的多目标组合优化问题

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摘要

In the last decade, many works in combinatorial optimisation have shown that, due to the advances in multi-objective optimisation, the algorithms from this field could be used for solving single-objective problems as well. In this sense, a number of papers have proposed multi-objectivising single-objective problems in order to use multi-objective algorithms in their optimisation. In this article, we follow up this idea by presenting a methodology for multi-objectivising combinatorial optimisation problems based on elementary landscape decompositions of their objective function. Under this framework, each of the elementary landscapes obtained from the decomposition is considered as an independent objective function to optimise. In order to illustrate this general methodology, we consider four problems from different domains: the quadratic assignment problem and the linear ordering problem (permutation domain), the 0-1 unconstrained quadratic optimisation problem (binary domain), and the frequency assignment problem (integer domain). We implemented two widely known multi-objective algorithms, NSGA-II and SPEA2, and compared their performance with that of a single-objective GA. The experiments conducted on a large benchmark of instances of the four problems show that the multi-objective algorithms clearly outperform the single-objective approaches. Furthermore, a discussion on the results suggests that the multi-objective space generated by this decomposition enhances the exploration ability, thus permitting NSGA-II and SPEA2 to obtain better results in the majority of the tested instances.
机译：在过去的十年中，组合优化的许多工作表明，由于多目标优化的进步，该领域的算法也可以用于解决单目标问题。从这个意义上讲，许多论文提出了多目标的单目标问题，以便在其优化中使用多目标算法。在本文中，我们通过提出一种基于目标功能的基本景观分解的多目标组合优化问题的方法，来遵循这一思想。在此框架下，从分解中获得的每个基本景观均被视为优化的独立目标函数。为了说明这种通用方法，我们考虑了来自不同域的四个问题：二次分配问题和线性排序问题（置换域），0-1无约束二次优化问题（二进制域）和频率分配问题（整数域）。我们实施了两种广为人知的多目标算法NSGA-II和SPEA2，并将它们的性能与单目标GA的性能进行了比较。在四个问题的实例的大型基准上进行的实验表明，多目标算法明显优于单目标方法。此外，对结果的讨论表明，这种分解生成的多目标空间增强了探索能力，从而使NSGA-II和SPEA2在大多数测试实例中都能获得更好的结果。

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