While traditional Pareto-based evolutionary multi-objective optimization (EMO) algorithms have shown an excellent balance between convergence and diversity on a wide range of practical problems with two or three objectives in real applications, the decision maker (DM) is interested in a unique set of solutions rather than the whole population on Pareto optimal front (POF). In addition, Pareto-based EMO algorithms have some shortcomings in dealing with many-objective problems because of insufficient selection pressure toward trade-off solutions. Due to the above, it is crucial to incorporate DM preference information into EMO and seek a representative subset of Pareto optimal solutions with an increase in the number of objectives. This paper proposes a new dominance relationship, called Ra-dominance, which can improve diversity among the Pareto-equivalent solutions increase the selection pressure in evolutionary process. It has the ability to guide the population toward areas more responsive to the needs of the DM according to a reference point and preference angle. We use the new dominance relationship in the NSGA-II algorithm, and the efficacy and usefulness of the modified procedure are assessed through two- to ten-objective problems. Experimental results show that the algorithm applying this new dominance relationship is highly competitive when compared with four state-of-the-art preference-based EMO methods.

传统的基于Pareto的进化多目标优化（EMO）算法在实际应用中具有两个或三个目标的各种实际问题中，已经显示出收敛性和多样性之间的出色平衡，而决策者（DM）对独特解决方案集，而不是整个帕累托最优阵线（POF）上的总体。此外，基于Pareto的EMO算法由于对权衡解决方案的选择压力不足，在处理多目标问题方面也存在一些缺陷。由于上述原因，至关重要的是将DM偏好信息合并到EMO中，并在目标数量增加的情况下寻求Pareto最优解的代表性子集。本文提出了一种新的主​​导关系，称为Ra-dominance，它可以改善帕累托等效解之间的多样性，从而增加了进化过程中的选择压力。它具有根据参考点和偏好角度将人口引导至更符合DM需求的区域的能力。我们在NSGA-II算法中使用了新的优势关系，并通过2到10个目标问题评估了改进程序的有效性和实用性。实验结果表明，与四种最新的基于首选项的EMO方法相比，应用此新优势关系的算法具有很高的竞争力。我们在NSGA-II算法中使用了新的优势关系，并通过2到10个目标问题评估了改进程序的有效性和实用性。实验结果表明，与四种最新的基于首选项的EMO方法相比，应用这种新的优势关系的算法具有很高的竞争力。我们在NSGA-II算法中使用了新的优势关系，并通过2到10个目标问题评估了改进程序的有效性和实用性。实验结果表明，与四种最新的基于首选项的EMO方法相比，应用此新优势关系的算法具有很高的竞争力。