According to the definition of the approximation solution of multiobjective optimization problem, the nature of the multiobjective optimization problem is discussed, and the approximate solution of multiobjective 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 multiobjective 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 multiobjective optimization problems.
LIU Jia-xing, ZHANG Qi. A Class of Combinatorial Scalarization Methods for Approximate Solutions of Multiobjective Optimization Problems[J]. Journal of Chongqing Technology and Business University(Natural Science Edition）,2020,37(4):34-38