In many real-world applications, the Pareto Set (PS) of a continuous multiobjective optimization problem can be a piecewise continuous manifold. A decision maker may want to find a solution set that approximates a small part of the PS and requires the solutions in this set share some similarities. This paper makes a first attempt to address this issue. We first develop a performance metric that considers both optimality and variable sharing. Then we design an algorithm for finding the model that minimizes the metric to meet the user's requirements. Experimental results illustrate that we can obtain a linear model that approximates the mapping from the preference vectors to solutions in a local area well.

翻译：在许多实际应用中，连续多目标优化问题的Pareto最优解集（PS）可呈现为分段连续流形。决策者可能希望找到能够逼近Pareto最优解集局部小片段、且其中解具有某些相似性的解集。本文首次尝试解决该问题。我们首先构建了一个同时考虑最优性与变量共享性的性能指标，进而设计了一种算法来寻找最小化该指标的模型，以满足用户需求。实验结果表明，我们能够获得一个线性模型，该模型能较好地在局部区域逼近从偏好向量到解的映射关系。