This paper integrates an estimation of distribution (EoD)-based update operator into decomposition-based multiobjective evolutionary algorithms for binary optimization. The probabilistic model in the update operator is a probability vector, which is adaptively learned from historical information of each subproblem. We show that this update operator can significantly enhance decomposition-based algorithms on a number of benchmark problems. Moreover, we apply the enhanced algorithms to the constrained optimal software product selection (OSPS) problem in the field of search-based software engineering. For this real-world problem, we give its formal definition and then develop a new repair operator based on satisfiability solvers. It is demonstrated by the experimental results that the algorithms equipped with the EoD operator are effective in dealing with this practical problem, particularly for large-scale instances. The interdisciplinary studies in this paper provide a new real-world application scenario for constrained multiobjective binary optimizers and also offer valuable techniques for software engineers in handling the OSPS problem.

中文翻译：

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通过估计约束优化软件产品选择的分布来增强基于分解的算法

本文将基于分布估计 (EoD) 的更新算子集成到基于分解的多目标进化算法中，用于二元优化。更新算子中的概率模型是一个概率向量，它是从每个子问题的历史信息中自适应学习的。我们表明，此更新算子可以显着增强基于分解的算法在许多基准问题上的性能。此外，我们将增强算法应用于基于搜索的软件工程领域中的约束最优软件产品选择（OSPS）问题。对于这个现实世界的问题，我们给出了它的正式定义，然后基于可满足性求解器开发了一个新的修复算子。实验结果表明，配备 EoD 算子的算法可以有效处理这一实际问题，尤其是对于大规模实例。本文中的跨学科研究为受约束的多目标二元优化器提供了一个新的实际应用场景，也为软件工程师处理 OSPS 问题提供了有价值的技术。