Many-objective optimization problems with degenerate Pareto fronts are hard to solve for most existing many-objective evolutionary algorithms. This is particularly true when the shape of the degenerate Pareto front is very narrow, and there are many dominated solutions near the Pareto front. To solve this particular class of many-objective optimization problems, a new evolutionary algorithm is proposed in this paper. In this algorithm, a set of reference vectors is generated to locate the potential Pareto front and then generate a set of location vectors. With the help of the location vectors, the solutions near the Pareto front are mapped to the hyperplane and clustered to generate more reference vectors pointing to Pareto front. This way, the location vectors are able to efficiently guide the population to converge towards the Pareto front. The effectiveness of the proposed algorithm is examined on two typical test problems with degenerate Pareto fronts, namely DTLZ5 and DTLZ6 with 5–40 objectives. Our experimental results show that the proposed algorithm has a clear advantage in dealing with this class of many-objective optimization problems. In addition, the proposed algorithm has also been successfully applied to optimization of process parameters of polyester fiber filament melt-transportation.

对于大多数现有的多目标进化算法，具有退化的Pareto前沿的多目标优化问题很难解决。当退化的帕累托锋面的形状非常狭窄，并且在帕累托锋面附近有许多主导解时，尤其如此。为了解决这类特殊的多目标优化问题，本文提出了一种新的进化算法。在该算法中，将生成一组参考向量以定位潜在的帕累托前沿，然后生成一组位置向量。借助位置矢量，将帕累托前沿附近的解映射到超平面并聚类以生成更多指向帕累托前沿的参考向量。这样，位置矢量能够有效地引导人口向帕累托前沿收敛。在退化的Pareto前沿的两个典型测试问题（即具有5-40个目标的DTLZ5和DTLZ6）上，对所提出算法的有效性进行了检验。我们的实验结果表明，该算法在处理这类多目标优化问题时具有明显的优势。此外，该算法也已成功地应用于聚酯纤维长丝熔体输送工艺参数的优化。