A Class Of Scalarization Methods For Approximate Solutions Of Multi-Objective Optimization Problems

Multi-objective optimization is a very important branch in the field of mathematical optimization and optimization.The study of the properties of various explicit solutions and approximate solutions of multi-objective optimization problems is also a very important research direction in the research of multi-objective optimization theory and methods.This paper research by useing a class of improved ε-constrained scalarization model proposed by Ehrgott and Ruzika based on the classic ε-constrained scalarization method and surplus variables.Some relations between several types of approximate solutions of multi-objective optimization problems and explicit solutions of such scalarition problems are established.Including the scalarization propertise of the multi-objective optimization problem ε-weak effective solution,ε-effective solution,ε-strict effective solution,and ε-properly effective solution.Further,this paper also uses this kind of scalarization model to establish(C,ε)(weak)effective solutions based on Co-radiant sets and E-(weak)effective solutions based on improved sets Some scalarization properties.The first chapter mainly gives the research background and significance of the multiobjective optimization problem,summarizes the multi-objective optimization and some research statuses related to the main research content of this paper,and then proposes the main research content of this paper.The second chapter mainly studies some relationships between the ε-type approximate solutions of multi-objective optimization problems and the improved ε-constrained scalarization problem approximate optimal solutions.Using the improved ε-constrained scalarization model,the multi-objective optimization problem scalarization results ofε-weak effective solution,ε-effective solution and ε-strict effective solution are established without any convexity.In particular,without any convexity assumptions,the scalarization model is used to establish some sufficient and necessary conditions for the multi-objective optimization problem ε-properly efficient solution.The third chapter mainly studies some scalarization properties of multi-objective optimization problems(C,ε)-(weak)effective solutions and E-(weak)effective solutions.Using the improved ε-constrained scalarization model proposed by Ehrgott and Ruzika,without any convexity assumptions,established some sufficient and necessary conditions for multi-objective optimization problem(C,ε)-effective solutions and(C,ε)-Weak efficient solutions based on the Co-radiant set,and established some sufficient and necessary conditions for E-effective solutions and E-weak effective solutions based on improved sets.The fourth chapter summarizes the main conclusions of this paper and puts forward some questions for further study.