This article investigates the properties of ratio and difference-based indicators under the Minkovsky distance and demonstrates that a ratio-based indicator with infinite norm is the best for solution evaluation among these indicators. Accordingly, a promising-region-based evolutionary many-objective algorithm with the ratio-based indicator is proposed. In our proposed algorithm, a promising region is identified in the objective space using the ratio-based indicator with infinite norm. Since the individuals outside the promising region are of poor quality, we can discard these solutions from the current population. To ensure the diversity of population, a strategy based on the parallel distance is introduced to select individuals in the promising region. In this strategy, all individuals in the promising region are projected vertically onto the normal plane so that crowded distances between them can be calculated. Afterward, two solutions with a smaller distance are selected from the candidate solutions each time, and the solution with the smaller indicator fitness value is removed from the current population. Empirical studies on various benchmark problems with 3–20 objectives show that the proposed algorithm performs competitively on all test problems. Compared with a number of other state-of-the-art evolutionary algorithms, the proposed algorithm is more robust on these problems with various Pareto fronts.

中文翻译：

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使用有希望的区域研究指标的属性和进化多目标算法


本文研究了明可夫斯基距离下基于比率和基于差异的指标的性质，并证明了具有无限范数的基于比率的指标是这些指标中解决方案评估的最佳选择。因此，提出了一种具有基于比率指标的基于有前景区域的进化多目标算法。在我们提出的算法中，使用具有无限范数的基于比率的指标来识别目标空间中的有希望的区域。由于有希望区域之外的个体质量较差，因此我们可以从当前种群中丢弃这些解决方案。为了保证种群的多样性，引入基于平行距离的策略来选择有希望的区域中的个体。在该策略中，有希望区域中的所有个体都垂直投影到法线平面上，以便可以计算它们之间的拥挤距离。之后，每次从候选解中选择距离较小的两个解，将指标适应度值较小的解从当前种群中剔除。对具有 3-20 个目标的各种基准问题的实证研究表明，所提出的算法在所有测试问题上都具有竞争力。与许多其他最先进的进化算法相比，所提出的算法在具有各种帕累托前沿的这些问题上更加鲁棒。