Abstract

Many optimization problems encountered in the real-world have more than two objectives. To address such optimization problems, a number of evolutionary many-objective optimization algorithms were developed recently. In this paper, we tested 18 evolutionary many-objective algorithms against well-known combinatorial optimization problems, including knapsack problem (MOKP), traveling salesman problem (MOTSP), and quadratic assignment problem (mQAP), all up to 10 objectives. Results show that some of the dominance and reference-based algorithms such as non-dominated sort genetic algorithm (NSGA-III), strength Pareto-based evolutionary algorithm based on reference direction (SPEA/R), and Grid-based evolutionary algorithm (GrEA) are promising algorithms to tackle MOKP and MOTSP with 5 and 10 while increasing the number of objectives. Also, the dominance-based algorithms such as MaOEA-DDFC as well as the indicator-based algorithms such as HypE are promising to solve mQAP with 5 and 10 objectives. In contrast, decomposition based algorithms present the best on almost problems at saving time. For example, t-DEA displayed superior performance on MOTSP for up to 10 objectives.

中文翻译：

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组合优化问题的进化多目标算法的比较研究

摘要

现实世界中遇到的许多优化问题都有两个以上的目标。为了解决这种优化问题，最近开发了许多进化的多目标优化算法。在本文中，我们针对众所周知的组合优化问题（包括背包问题（MOKP），旅行商问题（MOTSP）和二次分配问题（mQAP））测试了18种进化多目标算法，这些问题最多可达到10个目标。结果表明，一些主导和基于参考的算法，例如非主导排序遗传算法（NSGA-III），基于参考方向的基于强度帕累托的进化算法（SPEA / R）和基于网格的进化算法（GrEA） ）是有前途的算法，可以在增加目标数量的同时解决5和10的MOKP和MOTSP。也，基于优势的算法（例如MaOEA-DDFC）以及基于指标的算法（例如HypE）有望解决具有5和10个目标的mQAP。相比之下，基于分解的算法在节省时间上几乎可以解决所有问题。例如，t-DEA在MOTSP上显示出优异的性能，最多可达到10个目标。