Study On Scalarization And Genetic Algorithm Of Multiobjective Optimization Problem

In recent years,with the continuous development of multiobjective optimization theories and methods,scalarization properties of solutions of multi-objective optimization problems,solution methods for multiobjective optimization problems,and applications of multi-objective optimization models to carry out relevant researches have quite momentous theoretical significance and applied value.Related researches on multiobjective optimiza-tion problems have achieved a large number of basic and significant research results,mainly including various types of the concepts of effective solutions and approximate solutions of multi-objective optimization problems,the linear and nonlinear scalarization properties of various solutions,as well as the algorithm design to solve these problems.This paper mainly uses the theoretical basis of nonlinear programming,convex analysis and other disciplines,and the relevant conclusions of the heuristic algorithm to further explore scalarization methods and the improved multiobjective genetic algorithm.Specifically it includes scalarization properties of approximate G-proper efficient solutions of an extended generalized Tchebyshev norm,ideal point scalarization method for efficient solution and its algorithm design,as well as the improved multiobjective genetic algorithm for the selection operator.Chapter 1 mainly gives the research background of multiobjective optimization problems,solution properties of multiobjective optimization problems,the scalarization methods as well as some major progresses in multiobjective genetic algorithm researches and some basic concepts.Chapter 2 chiefly presents scalarization properties of approximate G-weak(proper)efficient solutions for multiobjective optimization problems.A class of scalarization methods of an extended generalized Tchebyshev norm are used to establish some nonlinear scalarization results of the ?-weak efficient solution and the ?-proper efficient solution for multiobjective optimization problems.And some nonlinear scalarization results of the precise solution are extended to the approximate solution in multiobjective optimization.Chapter 3 mainly studies the algorithm design of a nonlinear scalarization method.Based on the ideal point method,the algorithm of nonlinear scalarization method is designed to calculate Pareto frontier of the nonconvex multiobjective optimization problem at one time.The method is effective by numerical experiments.Chapter 4 focuses on the multiobjective genetic algorithm.The selection operator for genetic algorithms has been improved in terms of diversity of reservation points and reduction of computational complexity.An improved multiobjective genetic algorithm is given.In view of the dynamic programming of Pareto frontier classification,this method defines density index rendering to characterize the density of effective points on the frontier surface,making the selected points more different and closer to the frontier surface.Numerical experiments show that the method is effective.