基于非拥挤超体积的基因库最优混合多目标优化
Uncrowded Hypervolume-based Multi-objective Optimization with Gene-pool Optimal Mixing
摘要：
基于支配的多目标（MO）进化算法（EA）是目前最常用的MOEA类型。然而，当大多数人口成为非支配时，这些方法就会停滞，从而阻止收敛到帕累托集。基于超体积的MO优化已经显示出有希望的结果来克服这一点。然而，直接使用超体积导致没有选择压力的优势解决方案。最近推出的Sofomore框架克服了这一点，通过解决多个交错的单目标动态问题，迭代地提高一个单一的近似集，基于不拥挤的超体积改进（UHVI）。然而，它因此失去了基于群体的MO优化的许多优点，例如处理多模态。在这里，我们将UHVI重新表述为近似集的质量度量，称为非拥挤超体积（UHV），可用于直接用单目标优化器解决MO优化问题。我们使用最先进的基因库最优混合进化算法（GOMEA），能够有效地利用这个问题的内在可用的灰箱属性。由此产生的算法，UHV-GOMEA，相比Sofomore配备GOMEA，和基于支配的MO-GOMEA。在这样做时，我们调查在哪些情况下，无论是基于支配或基于超卷的方法是首选。最后，我们构建了一个简单的混合方法，结合MO-GOMEA与UHV-GOMEA和优于两者。
英文摘要：
Domination-based multi-objective (MO) evolutionary algorithms (EAs) are today arguably the most frequently used type of MOEA. These methods however stagnate when the majority of the population becomes non-dominated, preventing convergence to the Pareto set. Hypervolume-based MO optimization has shown promising results to overcome this. Direct use of the hypervolume however results in no selection pressure for dominated solutions. The recently introduced Sofomore framework overcomes this by solving multiple interleaved single-objective dynamic problems that iteratively improve a single approximation set, based on the uncrowded hypervolume improvement (UHVI). It thereby however loses many advantages of population-based MO optimization, such as handling multimodality. Here, we reformulate the UHVI as a quality measure for approximation sets, called the uncrowded hypervolume (UHV), which can be used to directly solve MO optimization problems with a single-objective optimizer. We use the state-of-the-art gene-pool optimal mixing evolutionary algorithm (GOMEA) that is capable of efficiently exploiting the intrinsically available grey-box properties of this problem. The resulting algorithm, UHV-GOMEA, is compared to Sofomore equipped with GOMEA, and the domination-based MO-GOMEA. In doing so, we investigate in which scenarios either domination-based or hypervolume-based methods are preferred. Finally, we construct a simple hybrid approach that combines MO-GOMEA with UHV-GOMEA and outperforms both.
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