We consider a multiobjective optimization problem with a feasible set defined by inequality and equality constraints and a set constraint, where the objective and constraint functions are locally Lipschitz. Several co...
详细信息
We consider a multiobjective optimization problem with a feasible set defined by inequality and equality constraints and a set constraint, where the objective and constraint functions are locally Lipschitz. Several constraint qualifications are given in such a way that they generalize the classical ones, when the functions are differentiable. The relationships between them are analyzed. Then, we establish strong Kuhn-Tucker necessary optimality conditions in terms of the Clarke subdifferentials such that the multipliers of the objective function are all positive. Furthermore, sufficient optimality conditions under generalized convexity assumptions are derived. Moreover, the concept of efficiency is used to formulate duality for nonsmooth multiobjective problems. Wolf and Mond-Weir type dual problems are formulated. We also establish the weak and strong duality theorems.
In this work, we established a converse duality theorem for higher-order Mond-Weir type multiob- jective programming involving cones. This fills some gap in recently work of Kim et al. [Kim D S, Kang H S, Lee Y J, et ...
详细信息
In this work, we established a converse duality theorem for higher-order Mond-Weir type multiob- jective programming involving cones. This fills some gap in recently work of Kim et al. [Kim D S, Kang H S, Lee Y J, et al. Higher order duality in inultiobjective programming with cone constraints. Optimization, 2010, 59： 29-43].
In this paper, we unify recent optimality results under directional derivatives by the introduction of new pseudoinvex classes of functions, in relation to the study of Pareto and weak Pareto solutions for nondifferen...
详细信息
In this paper, we unify recent optimality results under directional derivatives by the introduction of new pseudoinvex classes of functions, in relation to the study of Pareto and weak Pareto solutions for nondifferentiable multiobjective programming problems. We prove that in order for feasible solutions satisfying Fritz John conditions to be Pareto or weak Pareto solutions, it is necessary and sufficient that the nondifferentiable multiobjective problem functions belong to these classes of functions, which is illustrated by an example. We also study the dual problem and establish weak, strong, and converse duality results.
The purpose of this paper is to establish characterizations for efficient solutions to multiobjective programming problems. We extend the concept of G-Karush-Kuhn-Tucker problems to the multiobjective programming case...
详细信息
ISBN:
(纸本)9781467347143
The purpose of this paper is to establish characterizations for efficient solutions to multiobjective programming problems. We extend the concept of G-Karush-Kuhn-Tucker problems to the multiobjective programming case and introduce a new class of multiobjective programming problems, which is called G-KKT-pseudoinvex multiobjective programming problems. We show that the G-Karush-Kuhn-Tucker points to be efficient solutions, if and only if the multiobjective programming problem is G-KKT-pseudoinvex. Similarly, we also propose characterizations for efficient solutions by using G-Fritz-John optimality conditions. We establish an example in support of our investigation.
An interval-valued hesitant fuzzy set (IVHFS) is a best tool to address uncertainty and hesitation of a production planning problem (PPP) which appears in engineering, agriculture, and industrial sectors. Often, a PPP...
详细信息
An interval-valued hesitant fuzzy set (IVHFS) is a best tool to address uncertainty and hesitation of a production planning problem (PPP) which appears in engineering, agriculture, and industrial sectors. Often, a PPP is formulated as a multiobjective linear programming problem (MOLPP) and therefore, it is very necessary to develop a suitable and realistic method to deal MOLPP with uncertainty and hesitation. In this paper, we define a set of possible interval-valued hesitant fuzzy degrees for all objectives, and using this, a MOLPP is converted into a interval-valued hesitant fuzzy linear programming (IVHFLPP). Further, we introduce a new optimization technique based on a new operation of IVHFS, and later it is implemented in a computational method to search a Pareto optimal solution of the considered problem. Further, a PPP is solved by using the proposed method and the result shows the superiority of the proposed computational method over the existing methods.
In this paper, we propose a new credibility function for a fuzzy variable that can accommodate the attitude of the investor (pessimistic, optimistic, or neutral) along with capturing the return expectations. We use an...
详细信息
In this paper, we propose a new credibility function for a fuzzy variable that can accommodate the attitude of the investor (pessimistic, optimistic, or neutral) along with capturing the return expectations. We use an adaptive index, which the investors can use to specify their general perception of the financial market. We extend the classic mean-variance model so that it provides greater flexibility to the investors in specifying their requirements viz., level of diversification, minimum and maximum level of investment in a particular asset, and the skewness requirement. We also replace variance with mean-absolute semideviation as a measure of quantifying risk, which is more realistic, and solve the resultant multiobjective credibility model with a real-coded genetic algorithm. Numerical examples have been provided at the end to illustrate the methodology and advantages of the model.
This paper unified Wolfe and Mond-Weir-type higher-order symmetric dual multiobjective programs over arbitrary cones. The usual duality theorems are proved for unified dual programs under the assumptions of higher-ord...
详细信息
This paper unified Wolfe and Mond-Weir-type higher-order symmetric dual multiobjective programs over arbitrary cones. The usual duality theorems are proved for unified dual programs under the assumptions of higher-order K-eta-convexity. Several known results are obtained as special cases. An example is given to show how higher-order Wolfe and Mond-Weir-type symmetric duals can be extracted from our model. An example is presented to show the existence of higher-order K-eta-convex functions.
In equitable multiobjective optimization, all of the objectives are uniformly optimized, but in some cases, the decision maker believes that some of them should be uniformly optimized. In order to solve the proposed p...
详细信息
In equitable multiobjective optimization, all of the objectives are uniformly optimized, but in some cases, the decision maker believes that some of them should be uniformly optimized. In order to solve the proposed problem, we introduce the concept of equitable A(P)-efficiency, where P={P-1,P-2,& mldr;,P-n}is a partition of the index set of objective functions and the preference matrix A(P) is the direct sum of the matrices A(1),A(2),& mldr;,A(n), in which A(k) is a preference matrix for the objective functions in the class P-k for k=1,2,& mldr;,n. We examine some theoretical and practical aspects of equitably A(P)-efficient solutions and provide the some conditions that guarantee the relation of equitable APAP-dominance is a P-equitable rational preference. Furthermore, we introduce the new problem with the preference matrix A(P ) and we decompose it into a collection of smaller subproblems. In continuation, the subproblems are solved by the concept of equitable efficiency. Finally, two models are demonstrated to coordinate equitably efficient solutions of the proposed subproblems.
A popular topic in the field of underground engineering is to find synchronous grouting materials with excellent performance and environmental protection characteristics. In this study, CO 2 -foamed synchronous grouti...
详细信息
A popular topic in the field of underground engineering is to find synchronous grouting materials with excellent performance and environmental protection characteristics. In this study, CO 2 -foamed synchronous grouting (CSG) materials are prepared with cement, water, CO 2 foams, fly ash, fine river sand and bentonite. The feasibility of the material is verified by a series of detailed tests and analyses. The properties and performance of the CSG materials are investigated. The effects of the ratios of water/binder (cement + fly ash), fly ash/cement, binder/fine river sand and bentonite/water on the response value of the synchronous grouting material performances are investigated with stepwise nonlinear regression analysis models and response plane diagrams. NSGA-II is used to solve the multiobjective problem to obtain an optimal mass ratio. The results indicate that the grout component proportion directly impacts the performance of CSG material. Under the optimal ratio conditions, the specific gravity of CSG is 19.42 % lower and the early strength is 52.46 % higher than that of traditional grouts, and other properties meet the basic performance requirements of grout. The microstructure and product analysis show that the presence of CO 2 foams causes the carbonation reaction of the hydration products in the cement mortar to form calcium carbonate and silica gel. The carbonation reaction consumes free water, decreasing the setting time. Calcium carbonate and silica gel effectively increase the mechanical properties of the material and achieve the storage of CO 2 in cement -based materials. The research strategy and optimal ratio proposed in this paper verify the effectiveness, practicality and environmental economy of CSG material as a synchronous grouting material, providing a new choice for tunnel excavation grouting.
In this paper we suggest an approach for solving a multiobjective stochastic linear programming problem with normal multivariate distributions. Our approach is a combination between a multiobjective method and a nonco...
详细信息
In this paper we suggest an approach for solving a multiobjective stochastic linear programming problem with normal multivariate distributions. Our approach is a combination between a multiobjective method and a nonconvex technique. The problem is first transformed into a deterministic multiobjective problem introducing the expected value criterion and an utility function that represents the decision makers preferences. The obtained problem is reduced to a mono-objective quadratic problem using a weighting method. This last problem is solved by DC (Difference of Convex) programming and DC algorithm. A numerical example is included for illustration.
暂无评论