Several Results In Group Decision-Making, Multi-objective Optimization And Global Optimization

Group Decision making,multiobject optimization, and global optimization are important research areas in operations research. The theories and methods derived from have found wide applications in industrial manufacturing, financial investment, transportation, environment protection, and military strategies. This paper explores theories and methods of group decision making,multiobjective optimization and global optimization, and obtains several meaningful results. In the area of group decision making ,we prove that cardinal group deviation measure method has several extended rational properties, and we also give two classes of methods in ordinal group decision making with stochastic preference. In multiobjective optimization, We obtain the existence of G-properly efficient solution and connectedness of G-properle efficient solution set,and prove several properties of joint efficient preference method in group multiobjective optimization. In global optimization, we construe a new algorithm for solving global optimal solution of the problem.Chapter 1 is an introduce to group decision making,multiobjective optimization and global optimization, specifically, it expatiates problem and developments related to our study.Chapter 2,3 and 4 concentrate on group decision making. Some extended rational are given with regard to cardinal group decision measure method in Chapter 2,and the method checked to satisfy these conditions . Ordinal methods with stochastic preference for group decision making are studied in Chapter 3 and 4. In Chapter 3, a stochastic major method using major stochastic preference number for ordering alternatives and it is further extended to a stochasticαmajor method with parameter are given. In Chapter 4, a stochastic Borda-number method for group decision making is given.In Chapter 5 and 6, we study a few theoretical problems in multiobjective optimization. In Chapter 5, we prove the existence of G-properly efficient solution of multiobjective optimization problems when the constrained set is nonempty compact convex and the vector objective function is like-convex. And based on this result, we also prove the connectedness of G-properly efficient solution set when the vector objected function is both like-convex and quasi-convex. Moreover, we obtain the connectedness of Pareto efficient solution set. In Chapter 6,we introduce some fundamental rational conditions in group multiobjective optimization, and show that joint efficient preference method , which can order all alterntives for group preference, satisfies all these conditions.Global optimization problem is studies in Chapter 7, the last chapter. Combining the advantages of filled function algorithm and tunneling function algorithm, we introduce a filled modified tunneling function algorithm for nonlinear global optimization . This algorithm depends less on the parameters than ordinary filled function algorithm and tractable as shown by numerical tests.