Penalty Function Methods For Constrained Multiobjective Optimization Problems And Applications

Multiobjective optimization is one of the main research fields of optimization.Multiobjective optimization theory has been applied in environmental analysis,statistics,management science,space exploration,engineering plan,traffic network and so on.Therefore,the study of multiobjective optimization has important theoretical significance and practical application value.This thesis is devoted to the research of the penalty function methods for multiobjective optimization problems and its application.There are five chapters in this thesis.In the first chapter,the research background and significance of multiobjective optimization problems are briefly introduced,and the latest research and development of multiobjective optimization algorithms at home and abroad is summarized.Then,the main research content of this thesis is introduced.In the second chapter,the basic definitions and symbols of multiobjective optimization are provided.The classic mixed interior-exterior penalty method and augmented Lagrangian penalty method of nonlinear optimization are briefly introduced,and the basic definitions and symbols of multicriteria traffic network equilibrium problems are introduced.In the third chapter,the mixed interior-exterior penalty method for multiobjective optimization problems is proposed,and the basic steps of this method are given.Under certain assumptions and conditions,the convergence of the method is established,which is proved that the generated sequence by the algorithm converges to Pareto or weak Pareto optimal solutions of the original problem.Moreover,the feasibility and effectiveness of the proposed algorithm are verified by numerical experiments.Then,the method is applied to multicriteria traffic network equilibrium problems to solve minimum cost flow.In the fourth chapter,from the classic augmented Lagrangian penalty method,the augmented Lagrangian penalty method for multiobjective optimization problems is presented.The algorithm steps are given in the ideal case where the weak Pareto optimal solution of the subproblem must be obtained in each iteration.The convergence result that the sequences generated by the algorithm converges to weak Pareto optimal solutions of the original problem is proved.Since the weak Pareto optimal solution of the subproblem is difficult to acquire in practice,the inexact version of the augmented Lagrangian penalty method for multiobjective optimization problems is proposed,and its feasibility is verified by numerical experiments.It is also applied to the multicriteria traffic network equilibrium problems to solve minimum cost flow.In the fifth chapter,the main research work of this thesis is summarized and some shortcomings of the research work and questions to be considered in the future is proposed.