Evolutionary methods are effective tools for obtaining high-quality results when solving hard practical problems. Linkage learning may increase their effectiveness. One of the state-of-the-art methods that employ linkage learning is the Parameter-less Population Pyramid (P3). P3 is dedicated to solving single-objective problems in discrete domains. Recent research shows that P3 is highly competitive when addressing problems with so-called overlapping blocks, which are typical for practical problems. In this paper, we consider a multi-objective industrial process planning problem that arises from practice and is NP-hard. To handle it, we propose a multi-objective version of P3. The extensive research shows that our proposition outperforms the competing methods for the considered practical problem and typical multi-objective benchmarks.

进化方法是解决棘手的实际问题时获得高质量结果的有效工具。链接学习可以提高其有效性。一种采用链接学习的最新方法是无参数人口金字塔（P3）。P3致力于解决离散域中的单目标问题。最近的研究表明，P3在解决所谓重叠块的问题时具有很高的竞争力，而重叠块是实际问题的典型代表。在本文中，我们考虑了一个多目标的工业过程计划问题，该问题是从实践中产生的，并且是NP难题。为了解决这个问题，我们提出了P3的多目标版本。广泛的研究表明，对于所考虑的实际问题和典型的多目标基准，我们的命题优于竞争方法。