In the field of preference-based evolutionary multiobjective optimization, optimization algorithms are required to search for the Pareto optimal solutions preferred by the decision-maker (DM). The reference point is a type of techniques that effectively describe the preferences of DM. So far, the reference point is either static or interactive with the evolutionary process. However, the existing reference point techniques do not cover all application scenarios. A novel case, i.e., the reference point changes over time due to the environment change, has not been considered. This paper focuses on the multiobjective optimization problems with dynamic preferences of the DM. First, we propose a change model of the reference point to simulate the change of the preference by the DM over time. Then, a dynamic preference-based multiobjective evolutionary algorithm framework with a clonal selection algorithm (ĝa-NSCSA) and a genetic algorithm (ĝa-NSGA-II) is designed to solve such kind of optimization problems. In addition, in terms of practical applications, the experiments on the portfolio optimization problems with the dynamic reference point model are tested. Experimental results on the benchmark problems and the practical applications show that ĝa-NSCSA exhibits better performance among the compared optimization algorithms.

在基于偏好的进化多目标优化领域，需要优化算法来搜索决策者（DM）偏好的帕累托最优解。参考点是一种有效描述 DM 偏好的技术。到目前为止，参考点要么是静态的，要么是与进化过程交互的。然而，现有的参考点技术并不能涵盖所有的应用场景。未考虑新情况，即参考点因环境变化而随时间变化。本文重点研究具有 DM 动态偏好的多目标优化问题。首先，我们提出了一个参考点的变化模型来模拟 DM 的偏好随时间的变化。然后，设计了一个基于动态偏好的多目标进化算法框架，包括克隆选择算法（ĝa-NSCSA）和遗传算法（ĝa-NSGA-II）来解决此类优化问题。此外，在实际应用方面，对动态参考点模型的投资组合优化问题进行了实验。基准问题和实际应用的实验结果表明，在比较的优化算法中，ĝa-NSCSA 表现出更好的性能。