多目标优化问题近似解的一类标量化方法

A Class of Scalarization Methods for Approximate Solutions of Multi-Objective Optimization Problems

【目的】研究多目标优化问题近似解的一类标量化方法。【方法】利用Ehrgott和Ruzika提出的多目标优化问题的标量化模型。【结果】建立了基于co-radiant集定义的(C,ε)-近似解和改进集定义的E-近似解的一些标量化结果,并提出了一些例子对主要结果进行了解释。【结论】所得结果为设计求解多目标优化问题近似解的最优算法提供理论与方法基础。

[Purposes]To study a class of scalarization methods for approximate solutions of multi-objective optimization problems.[Methods]Using the scalarization model of multi-objective optimization problem proposed by Ehrgott and Ruzika.[Findings]Some scalarization results of(C,ε)-approximate solution defined by co-radiant set and E-approximate solution defined by improved set are established,and some examples are given to explain the main results.[Conclusions]The results provide a theoretical and methodological basis for designing the optimal algorithm for solving the approximate solution of multi-objective optimization problems.