In this papert the theory of major efficiency for multiobjective programmingis established.The major-efficient solutions and weakly major-efficient solutions of multiobjective programming given here are Pareto efficie...In this papert the theory of major efficiency for multiobjective programmingis established.The major-efficient solutions and weakly major-efficient solutions of multiobjective programming given here are Pareto efficient solutions of the same multiobjectiveprogramming problem, but the converse is not true. In a ceratin sense , these solutionsare in fact better than any other Pareto efficient solutions. Some basic theorems whichcharacterize major-efficient solutions and weakly major-efficient solutions of multiobjective programming are stated and proved. Furthermore,the existence and some geometricproperties of these solutions are studied.展开更多
New classes of functions namely (V, ρ)_(h,φ)-type I, quasi (V, ρ)_(h,φ)-type I and pseudo (V, ρ)_(h,φ)-type I functions are defined for multiobjective programming problem by using BenTal's generalized algebr...New classes of functions namely (V, ρ)_(h,φ)-type I, quasi (V, ρ)_(h,φ)-type I and pseudo (V, ρ)_(h,φ)-type I functions are defined for multiobjective programming problem by using BenTal's generalized algebraic operation. The examples of (V, ρ)_(h,φ)-type I functions are given. The sufficient optimality conditions are obtained for multi-objective programming problem involving above new generalized convexity.展开更多
As we know, the Pareto efficient (optimal) solution or in other words, thenoninferior solution, is a basic concept in multiobjective programming. In thesense of this kind of solution, much theoretical and application ...As we know, the Pareto efficient (optimal) solution or in other words, thenoninferior solution, is a basic concept in multiobjective programming. In thesense of this kind of solution, much theoretical and application work has been doneon solutions in multiobjective programming since the 1950s. However, because thePareto efficient solution is only a solution with respect to a vector objective beingnoinnferior, as for a given multiobjective programming problem, its set is large whenthe number of objectives is great. This is an inevitable flaw caused by definingPareto efficient solution with the partial order induced by a positive cone. Yu intro-duced the nondominated solution on the basis of a general convex cone or展开更多
In this paper, we introduce the comparison number for one feasible solutioncompared with another. With the help of it the comparison-number method for find-ing the major optimal solutions aud major efficient solutions...In this paper, we introduce the comparison number for one feasible solutioncompared with another. With the help of it the comparison-number method for find-ing the major optimal solutions aud major efficient solutions to discrete multiobjectiveprogramming is given.展开更多
文摘In this papert the theory of major efficiency for multiobjective programmingis established.The major-efficient solutions and weakly major-efficient solutions of multiobjective programming given here are Pareto efficient solutions of the same multiobjectiveprogramming problem, but the converse is not true. In a ceratin sense , these solutionsare in fact better than any other Pareto efficient solutions. Some basic theorems whichcharacterize major-efficient solutions and weakly major-efficient solutions of multiobjective programming are stated and proved. Furthermore,the existence and some geometricproperties of these solutions are studied.
基金Supported by the NSF of Shaanxi Provincial Educational Department(06JK152)
文摘New classes of functions namely (V, ρ)_(h,φ)-type I, quasi (V, ρ)_(h,φ)-type I and pseudo (V, ρ)_(h,φ)-type I functions are defined for multiobjective programming problem by using BenTal's generalized algebraic operation. The examples of (V, ρ)_(h,φ)-type I functions are given. The sufficient optimality conditions are obtained for multi-objective programming problem involving above new generalized convexity.
文摘As we know, the Pareto efficient (optimal) solution or in other words, thenoninferior solution, is a basic concept in multiobjective programming. In thesense of this kind of solution, much theoretical and application work has been doneon solutions in multiobjective programming since the 1950s. However, because thePareto efficient solution is only a solution with respect to a vector objective beingnoinnferior, as for a given multiobjective programming problem, its set is large whenthe number of objectives is great. This is an inevitable flaw caused by definingPareto efficient solution with the partial order induced by a positive cone. Yu intro-duced the nondominated solution on the basis of a general convex cone or
基金Research supported by the National Natural Science Foundation of China.
文摘In this paper, we introduce the comparison number for one feasible solutioncompared with another. With the help of it the comparison-number method for find-ing the major optimal solutions aud major efficient solutions to discrete multiobjectiveprogramming is given.
基金The project was supported by National Natural Science Foundation of China with grant 72072021 was supported by grant No.NX05LJ07 from Zhejiang Provincial Philosophical&Social Science Foundation.
