On Theory, Method And Innovation Of Subset Selection And Optimization Problem

Subset selection problem can be described as: There is a set including limited amount of projects, which have two features, consuming a certain amount of resources and output a certain amount of outcome in given objects. Then how to determine a optimal portfolio of projects, which can maximize the utility of decision-maker, within a given resource constraints. Various fields, including economics management, project construction, industry production, etc., are involving with subset selection problem. For instance, the investment portfolio design in the field of investment decision making, the plan design in the field of information system construction, budgeting problem in the field of public finance and projects optimization in the field of project construction are only a part of the applications of subset selection theory. Nevertheless, the researches on subset selection theory are considerable deficient, and most of them are limited to linear programming form. These researches cannot meet the demand of solving practical problems. Aiming at these weaknesses, the study on non-linear subset selection problem, subset selection problem with interdependence, the non-parametric method for subset selection problem and subset selection problem with ordinal criteria is addressed in this dissertation, based on the analysis and summarizing the general theory framework of subset selection problem.The conception, definition, general mathematic form, and programming form of subset selection problem are addressed in the first chapter of the dissertation. Then, according to the feature of objective function and the constraints, the classification system of the subset selection problem is constructed. The overall theory framework of subset selection theory is introduced. In accordance with the weakness of the researches on the subset selection problem, the purpose, content, outline and innovation of the dissertation is given. Then, based on the analysis of the non-linear feature of the investment portfolio selection problem, a dynamic programming model is formulated. After that, an exterior point heuristic algorithm is constructed to solve the model. The surrogate model to determine original point and advanced greedy search algorithm to obtain optimal point are discussed, and the whole processes of the algorithm are addressed. In the third chapter, the crucial effect of the interdependence among the projects is discussed. And a group of definitions and theorems is given to build a definition and measurement system of interdependence phenomena. After that, a non-linear programming model of subset selection problem with interdependence is formulated, and the linearization method for the non-linear model is given. Finally, an application of the model is given.In the fourth chapter, two methods for solving multi-objective subset selection problem: parametric and nonparametric are compared, and the shortcoming of parametric method is analyzed. Based on these, the general idea of the DEA model to solve multi-objective subset selection problem is proposed and corresponding model is constructed. After that, utilizing the outcome of the chapter three, a DEA model to solve subset selection problem with interdependence is formulated. Ordinal criteria are often used in many practical subset selection problems. There are scarce effective methods to solving this kind of problems. Aiming at this, an idea to solve the problems is proposed. That is transforming the subset selection problem with ordinal criteria to the problem with cardinal criteria and then solving the problem. Finally the concrete model and an application are given. Some theoretical study is give hereinbefore. After that, one feature of the subset selection problem, which is that the number of feasible solutions of the subset selection problem will exponentially increase with the increase of the number original projects for selection. So, the most effective way to decrease the computer complexity of the subset selection problem is eliminating the origin...