This paper introduces a new class of optimization problems, called Mixed Pareto-Lexicographic Multi-objective Optimization Problems (MPL-MOPs), to provide a suitable model for scenarios where some objectives have priority over some others. Specifically, this work focuses on a relevant subclass of MPL-MOPs, namely problems involving Pareto optimization of two or more priority chains. A priority chain (PC) is a sequence of objectives lexicographically ordered by importance. After examining the main features of those problems, named PC-MPL-MOPs, we propose an innovative approach to deal with them, built upon the Grossone Methodology, a recent theory which enables handling the priority in an elegant and powerful way. The most interesting aspect of this technique is the possibility to seamlessly embed it in any existing evolutionary algorithm, without altering its logical structure. In order to provide concrete examples, we implemented it on top of the well-known NSGA-II and MOEA/D algorithms, calling these new generalized versions PC-NSGA-II and PC-MOEA/D, respectively. In the second part of this article, we test the strength of our strategy in solving multi- and even many-objective problems with priority chains, comparing it against the results achieved by standard priority-based and non-priority-based approaches. Experiments show that our algorithms are generally able to produce more solutions and of higher quality.

本文介绍了一类新的优化问题，称为混合帕累托-词典词典多目标优化问题（MPL-MOP），为某些目标优先于其他目标的情况提供了合适的模型。具体来说，这项工作着重于MPL-MOP的相关子类，即涉及两个或多个优先级链的帕累托优化的问题。。优先级链（PC）是按重要性按字典顺序排序的一系列目标。在检查了这些问题的主要特征（称为PC-MPL-MOP）之后，我们提出了一种创新的方法来解决它们，该方法以格罗斯松方法论为基础，格罗斯松方法论是一种最新的理论，能够以一种优雅而强大的方式处理优先级。该技术最有趣的方面是可以将其无缝嵌入任何现有的进化算法中，而无需更改其逻辑结构。为了提供具体示例，我们在著名的NSGA-II和MOEA / D算法的基础上实现了该算法，将这些新的通用版本称为PC-NSGA-II和PC-MOEA / D， 分别。在本文的第二部分中，我们将测试我们的策略在解决具有优先级链的多目标甚至多目标问题中的实力，并将其与标准基于优先级和基于非优先级的方法所获得的结果进行比较。实验表明，我们的算法通常能够产生更多的解决方案和更高的质量。