多目标优化问题近似解的组合标量化

Combined Scalarizations for Approximate Solutions of Multi-Objective Optimization Problems

【目的】研究多目标优化问题近似解的标量化性质。【方法】利用一类组合标量化方法、co-radiant集和改进集等建立多目标优化问题近似解的组合标量化。【结果】得到了多目标优化问题ε-有效解、(C,ε)-有效解、E-有效解、(C,ε)-弱有效解、E-弱有效解的组合标量化结果。【结论】得到的标量化结果为设计多目标优化问题近似解的求解算法提供了理论基础。

[Purposes]The scalarization properties of approximate solutions for multi-objective optimization problems is studied here.[Methods]Co-radiant sets and improved sets are used to establish approximate solutions of multi-objective optimization problems by a kind of combined scalarization method.[Findings]The combined scalarization results ofε-effective solution,(C,ε)-efficient solutions,E-efficient solutions,(C,ε)-weakly efficient solutions and E-weakly efficient solutions of the multi-objective optimization problem are obtained.[Conclusions]These combined scalarization results provide a theoretical basis for designing approximate solutions of multi-objective optimization problems.