IEEE Trans Cybern. 2019 Dec;49(12):4129-4139. doi: 10.1109/TCYB.2018.2859171. Epub 2018 Sep 10.
Decomposition-based evolutionary algorithms have shown great potential in many-objective optimization. However, the lack of theoretical studies on decomposition methods has hindered their further development and application. In this paper, we first theoretically prove that weight sum, Tchebycheff, and penalty boundary intersection decomposition methods are essentially interconnected. Inspired by this, we further show that highly customized dominance relationship can be derived from decomposition for any given decomposition vector. A new evolutionary algorithm is then proposed by applying the customized dominance relationship with adaptive strategy to each subpopulation of multiobjective to multiobjective framework. Experiments are conducted to compare the proposed algorithm with five state-of-the-art decomposition-based evolutionary algorithms on a set of well-known scaled many-objective test problems with 5 to 15 objectives. Simulation results have shown that the proposed algorithm can make better use of the decomposition vectors to achieve better performance. Further investigations on unscaled many-objective test problems verify the robust and generality of the proposed algorithm.
基于分解的进化算法在多目标优化中显示出巨大的潜力。然而，分解方法缺乏理论研究阻碍了它们的进一步发展和应用。在本文中，我们首先从理论上证明了权重和、切比雪夫和罚边界交叉分解方法本质上是相互关联的。受此启发，我们进一步表明，对于任何给定的分解向量，都可以从分解中导出高度定制的支配关系。然后，通过在多目标到多目标框架的每个子种群中应用定制的支配关系和自适应策略，提出了一种新的进化算法。在一组具有 5 到 15 个目标的著名规模多目标测试问题上，将所提出的算法与五种最先进的基于分解的进化算法进行了比较。仿真结果表明，所提出的算法可以更好地利用分解向量来获得更好的性能。对非规模多目标测试问题的进一步研究验证了所提出算法的稳健性和通用性。
