LIU Jia-xing，ZHANG Qi.A Class of Combinatorial Scalarization Methods for Approximate Solutions of Multi objective Optimization Problems[J].Journal of Chongqing Technology and Business University(Natural Science Edition）,2020,37(4):34-38

A Class of Combinatorial Scalarization Methods for Approximate Solutions of Multi objective Optimization Problems

DOI：

 作者 单位 刘佳星，张琦 重庆师范大学 数学科学学院，重庆 401331

根据多目标优化问题近似解的定义，对它的性质进行讨论；借助Ehrgott和Ruzika基于传统的标量化方法结合剩余变量提出的一类改进的ε-约束法组合标量化模型对多目标优化问题的近似解性质进行了研究；建立了多目标优化问题的近似有效解与标量化问题的最优解之间的关系，得到了近似真有效解与对应标量优化问题最优解的等价关系，并提出反例对部分结论进行了解释说明，指出若不满足所给定的条件，其结论不一定成立；所提出的主要结果是对一些已有标量化结果的改进与推广，为设计和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。

According to the definition of the approximation solution of multi objective optimization problem, the nature of the multi objective optimization problem is discussed, and the approximate solution of multi objective optimization problem is studied by Ehrgott and Ruzika based on the traditional standardization method combining the remaining variables. The relationship between the approximate effective solution of multi objective optimization problem and the optimal solution of the calibration problem is established, and in particular, the equivalent relationship between the approximately effective solution and the optimal solution of the corresponding scale optimization problem is obtained. Some of the conclusions are explained by the counterexample, and the conclusions are not necessarily valid if the given conditions are not met, and the main results presented are the improvement and promotion of some existing quantitative results, which provide the theoretical and methodological basis for the optimal algorithm for designing and solving the approximation of multi objective optimization problems.