Study On Scalarization Properties And Application Of Multi-objective Optimization

The theory and method of multi-objective optimization have very significant ap-plications in many practical fields,such as economic management,engineering design,transportation,signal control,performance evaluation,optimal scheme design of moderate scale operation and so on.In addition,the study of approximate solutions and their properties of multi-objective optimization problems also has very important theoretical significance and application value,which has became an vital direction in the research of multi-objective optimization.Firstly,the combined scalar results of e-efficient solution are established by using a class of combined scalarization methods for general multi-objective optimization problems in this paper.Furthermore,some combined scalar results of(C,?)-approximate solution and E-approximate solution based on co-radiant sets and improved sets for multi-objective optimization problems are also established.These results provide bases for the algorithm design to solve multi-objective optimization problems.For the problem of appropriate scale management of idle land resources,which the state attaches great importance to,this paper uses distance function to deal with parameters and introduces positive and negative deviation variable linearization to deal with relevant parameters of planting a certain crop.The land with similar nature in idle land resources is classified into the same category and obtains l kinds of land by using the method of k-means clustering analysis.With the help of batch processing thinking,regarding the same kind of idle land resources with similar nature as the same idle land resources and selecting arbitrarily an idle land resource to construct a multi-objective optimization model,then use Matlab programming to solve the modle.In the first chapter,the research background of multi-objective optimization problems,solution definitions and solution properties of multi-objective optimization problems,the scalarization methods and related researches,idle land resource problem as well as some major progresses are given,besides some basic concepts and tools are needed in this paper.In Chapter 2,a class of combined scalar methods proposed by Rastegar and Khorram are used to study multi-objective optimization problems.Necessity conditions of ?-efficient solution for multi-objective optimization problems are established.Further,we set up the combined scalar results of multi-objective optimization problems between(C,?)-effective solution,E-effective solution,(C,?)-weak effective solution and E-weak effective solution,which are established by using co-radiant sets and improved sets,of multi-objective optimization problems.Chapter 3 mainly studies about the optimal crop planting scheme of moderate scale management of idle land resources by using multi-objective methods.A double-objective optimization model that aiming at maximizing the benefit of planting and solving employees as many as possible is established.The properties of the model are studied and numerical experiments are carried out on the model.