Generalized decomposition and cross entropy methods for many-objective optimization
Generalized decomposition and cross entropy methods for many-objective optimization
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DOI：
10.1016/j.ins.2014.05.045
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发表时间：
2014-10
期刊：
影响因子：
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通讯作者：
I. Giagkiozis;R. Purshouse;P. Fleming
中科院分区：
文献类型：
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作者：
I. Giagkiozis;R. Purshouse;P. Fleming
在过去的十年中，基于分解的多目标优化问题算法越来越受欢迎。尽管此类算法收敛到帕累托最优前沿（PF）的能力通常优于基于帕累托的替代方案，但在高维空间中有效分布帕累托最优解的问题尚未得到解决。在这项工作中，我们引入了一个新的概念，称为广义分解。广义分解提供了一个框架，决策者 (DM) 可以利用该框架将基础搜索算法引导至特定的感兴趣区域或整个 Pareto 前沿，并具有 Pareto 最优解的所需分布。该方法通过将后验多目标优化器的三个性能目标（收敛到 PF、均匀分布的 Pareto 最优解和覆盖整个前端）统一为一个，即收敛，从而简化了多目标问题。创建了一个建立在广义分解和基于低阶统计的分布估计算法（EDA）（即交叉熵方法）的框架，以说明所提出的概念对于多目标问题的好处。该算法 - MACE-gD - 与现有的同类最佳的基于分解的算法 (MOEA/D) 和更精细的 EDA 方法 (RM-MEDA) 相比具有很强的竞争力。
Decomposition-based algorithms for multi-objective optimization problems have increased in popularity in the past decade. Although convergence to the Pareto optimal front (PF) for such algorithms can often be superior to that of Pareto-based alternatives, the problem of effectively distributing Pareto optimal solutions in a high-dimensional space has not been solved. In this work, we introduce a novel concept which we callgeneralizeddecomposition. Generalized decomposition provides a framework with which the decision maker (DM) can guide the underlying search algorithm toward specific regions of interest, or the entire Pareto front, with the desired distribution of Pareto optimal solutions. The method simplifies many-objective problems by unifying the three performance objectives of ana posteriorimulti-objective optimizer – convergence to the PF, evenly distributed Pareto optimal solutions and coverage of the entire front – to only one, that of convergence. A framework, established on generalized decomposition, and an estimation of distribution algorithm (EDA) based on low-order statistics, namely the cross-entropy method, is created to illustrate the benefits of the proposed concept for many-objective problems. The algorithm – MACE-gD – is shown to be highly competitive with the existing best-in-class decomposition-based algorithm (MOEA/D) and a more elaborate EDA method (RM-MEDA).