Studies On The Efficient Solution Theory For Stochastic Multiobjective Programming

The various kinds of efficient solutions to stochastic multiobjective programming are defined from different aspects and their properties are analyzed based on the determinate multiobjective programming efficient solution theory and its concept. The relations among the relative efficient solutions are obtained. Meanwhile, the methods of searching some efficient solution are discussed tentatively. This paper is divided in seven sections, the contents is as follows:Chapter 1 is an introduction to the development process of stochastic programming and stochastic multiobjective programming ,This part is also meant to present the propose and significance of the paper.Chapter 2 is an introduction to general knowledge of determinate multiobjective programming and stochastic programming.Chapter 3 deals with five kinds of efficient solutions to multiobjective stochastic programming, Such as expected-value efficient solution, minimum-variance efficient solution, expected-value standard-deviation efficient solution, β - efficient solution, minimum-risk efficient solutions.Stress is laid on the relations among the first three kinds of efficient solutions,the relations between β- efficient solution and expected- value standard-deviation efficient solution and the relations between minimum-risk efficient solution and expected-value standard-deviation efficient solution. And a kind of new efficient solution- α - expected-value standard-deviation efficient solution is defined and its properties are given.Chapter 4 gives a kind of method of comparing with two solutions. A kind of new efficient solution-probability efficient solution is defined and discussed.Chapter 5 discusses the utility set distributional efficient solution when the utility function is unknown and probability distribution is known. U -admissible efficient solution, U -unanimous efficient solution U-advocated efficient solution are defined and their properties are discussed respectively. The relations among them are discussed also.Chapter 6 presents the utility set pointwise efficient solution when both the utility functionand the probability distribution are unknown. (P,U1) - unanimous efficient solution, (P.U1) -admissible efficient solution, (P,U1) - extreme advocated efficient solution (P,U1)-S admissible efficient solution, (P,U1) - S unanimous efficient solution, (P,U1) - I admissible efficient solution and (P,U1) - I unanimous efficient solution are defined respectively and their properties are discussed respectively. The relations among them are discussed and the approach to every efficient solution is given.Chapter 7 discusses the efficient rate of stochastic multiobjective programming tentatively.