In preference based optimization, knee points are considered the naturally preferred trade-off solutions, especially when the decision-maker has little a priori knowledge about the problem to be solved. However, identifying all convex knee regions of a Pareto front remains extremely challenging, in particular in a high-dimensional objective space. This paper presents a new evolutionary multi-objective algorithm for locating knee regions using two localized dominance relationships. In the environmental selection, the �-dominance is applied to each subpopulation partitioned by a set of predefined reference vectors, thereby guiding the search towards different potential knee regions while removing possible dominance resistant solutions. A knee-oriented dominance measure making use of the extreme points is then proposed to detect knee solutions in convex knee regions and discard solutions in concave knee regions. Our experimental results demonstrate that the proposed algorithm outperforms the state-of-the-art knee identification algorithms on a majority of multi-objective optimization test problems having up to eight objectives and a hybrid electric vehicle controller design problem with seven objectives.

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一种使用两个局部优势关系寻找膝关节区域的多目标进化算法

在基于偏好的优化中，拐点被认为是自然首选的权衡解决方案，特别是当决策者对要​​解决的问题几乎没有先验知识时。然而，识别帕累托前沿的所有凸膝区域仍然极具挑战性，尤其是在高维目标空间中。本文提出了一种新的进化多目标算法，用于使用两个局部优势关系定位膝盖区域。在环境选择中，β-优势被应用于由一组预定义的参考向量划分的每个子群，从而引导搜索到不同的潜在膝盖区域，同时去除可能的抗优势解决方案。然后提出了一种利用极值点的面向膝盖的优势度量，以检测凸膝盖区域的膝盖解并丢弃凹膝盖区域的解。我们的实验结果表明，在大多数具有多达八个目标的多目标优化测试问题和具有七个目标的混合动力电动汽车控制器设计问题上，所提出的算法优于最先进的膝关节识别算法。