Combined Scalarizing Method Of C(?)-Approximate Solution In Multi-objective Optimization Problems

Multi-objective optimization problem is an optimization problem that maximizes or minimizes several conflicting or contradictory objectives at the same time.Multi-objective optimization theory and method are applied importantly in many fields,such as economic management,engineering design,environmental protection and intelligent transportation.How to introduce new mathematical tools and put forward the unified solution definition of multi-objective optimization problem and study its properties under the unified framework is an important research direction in the field of multi-objective optimization.Scalar quantification method is a kind of basic method that transforms the multi-objective optimization problem into the single-objective optimization problem in a certain way,and then studies the multi-objective optimization problem with the help of the existing theory and method of the single-objective optimization problem.This paper mainly studies the combined scalarizing methods of C(?)-approximate solution for multi-objective optimization problems.Using two different types of combined scalarizing methods,some scalarization results of the C(?)-(weak)effective solution and E-(weak)effective solution of the multi-objective optimization problem are established under the assumption of no convexity for any objective function.The main research contents of this paper can be summarized as follows:In the first chapter,the research background and significance of multi-objective op-timization problems,the development history of various solutions of the multi-objective optimization problem and the research progress of some scalarizing methods are briefly described,including some related concepts and basic tools needed for the research work in this paper.In the second chapter,some scalarization results of exact and approximate solution are generalized by adjusting the range of parameters in the scalarization model in the absence of any convexity assumption of the objective function based on the idea of the Epsilon-constraint method and a kind of combined scalar method proposed by Ehrgott and Ruzika.Some scalarization results of C(?)-effective solution,C(?)-weak effective solution,E-effective solution and E-weak effective solution defined based on the co-radiant sets and improvement sets are established.Some examples are given to explain the main results.In the third chapter,we use another kind of combined scalarization method proposed by Ehrgott and Ruzika,that is,the improved Epsilon-constrained scalarization method with slack and surplus variables.In the absence of any convexity assumption of the objective function,some scalarization results of the C(?)-(weak)effective solution are defined based on the co-radiant sets and the E-(weak)effective solution defined based on the improvement sets are obtained by adjusting the parameter range.Some examples are also provided to explain the main results.