(I broken vertical bar, rho)-invexity and (I broken vertical bar, rho) (w) -invexity generalize known invexity type properties and have been introduced with the intent of extending most of theoretical results in mathe...
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(I broken vertical bar, rho)-invexity and (I broken vertical bar, rho) (w) -invexity generalize known invexity type properties and have been introduced with the intent of extending most of theoretical results in mathematical programming. Here, we push this approach further, to obtain authentic extensions of previously known optimality and duality results in multiobjective programming.
We generalize known concepts (those introduced by Ishihuchi and Tanaka [1] and Rommelfanger et al. [2]) of the solution of the linear programming problem with interval coefficients in the objective function based an p...
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We generalize known concepts (those introduced by Ishihuchi and Tanaka [1] and Rommelfanger et al. [2]) of the solution of the linear programming problem with interval coefficients in the objective function based an preference relations between intervals, We unify all the discussed concepts as well as the corresponding solution methods into one general framework.
In this paper, a generalization of convexity is considered in the case of nonlinear multiobjective programming problem where the functions involved are nondifferentiable. By considering the concept of Pareto optimal s...
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In this paper, a generalization of convexity is considered in the case of nonlinear multiobjective programming problem where the functions involved are nondifferentiable. By considering the concept of Pareto optimal solution and substituting d-invexity for convexity, the Fritz John type and Karush-Kuhn-Tucker type necessary optimality conditions and duality in the sense of Mond-Weir and Wolfe for nondifferentiable multiobjective programming are given. (C) 2002 Elsevier Science B.V. All rights reserved.
This paper discusses the need for and the applicability of multiobjective programming methodology in solving various power system problems. The advantages of a multiobjective optimization approach over the conventiona...
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This paper discusses the need for and the applicability of multiobjective programming methodology in solving various power system problems. The advantages of a multiobjective optimization approach over the conventional single-objective approach are demonstrated in the case of thermal generating units maintenance scheduling. The proposed optimization model is based on the original multiobjective branch and bound algorithm. The following objectives: power system reliability maximization, fuel costs minimization, and minimization of constraints violations are simultaneously considered. A realistic example of annual maintenance scheduling of 21 thermal generating units illustrates the proposed methodology.
The notion of Pareto-optimality is one of the major approaches to multiobjective programming. While it is desirable to find more Pareto-optimal solutions, it is also desirable to find the ones scattered uniformly over...
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The notion of Pareto-optimality is one of the major approaches to multiobjective programming. While it is desirable to find more Pareto-optimal solutions, it is also desirable to find the ones scattered uniformly over the Pareto frontier in order to provide a variety of compromise solutions to the decision maker. In this paper, we design a genetic algorithm for this purpose. We compose multiple fitness functions to guide the search, where each fitness function is equal to a weighted sum of the normalized objective functions and we apply an experimental design method called uniform design to select the weights. As a result, the search directions guided by these fitness functions are scattered uniformly toward the Pareto frontier in the objective space. With multiple fitness functions, we design a selection scheme to maintain a good and diverse population. In addition, we apply the uniform design to generate a good initial population and design a new crossover operator for searching the Pareto-optimal solutions. The numerical results demonstrate that the proposed algorithm can find the Pareto-optimal solutions scattered uniformly over the Pareto frontier.
In this paper, nonsmooth univex, nonsmooth quasiunivex, and nonsmooth pseudounivex functions are introduced. By utilizing these new concepts, sufficient optimality conditions for a weakly efficient solution of the non...
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In this paper, nonsmooth univex, nonsmooth quasiunivex, and nonsmooth pseudounivex functions are introduced. By utilizing these new concepts, sufficient optimality conditions for a weakly efficient solution of the nonsmooth multiobjective programming problem are established. Weak and strong duality theorems axe also derived for Mond-Weir type multiobjective dual programs.
In this paper, (generalized) G-type I functions are defined for a nonlinear multiobjective programming problem where the functions involved are assumed to be locally Lipschitz. This new class of functions is a general...
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In this paper, (generalized) G-type I functions are defined for a nonlinear multiobjective programming problem where the functions involved are assumed to be locally Lipschitz. This new class of functions is a generalization of G-invex functions defined in Kang et al. (2012) [20]. Examples are given to show the existence of these functions. G-type Kuhn-Tucker necessary conditions are established for a nondifferentiable multiobjective programming problem (GMP). By using suitable G-type I functions, sufficient optimality conditions are derived for the problem (GMP). Further a Mond-Weir type dual (GMWD) is formulated and using these newly defined functions various duality results are established. (C) 2014 Elsevier Inc. All rights reserved.
In this paper, we are concerned with the multiobjective programming problem with inequality constraints. We introduce new classes of generalized alpha-univex type I vector valued functions. A number of Kuhn-Tucker typ...
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In this paper, we are concerned with the multiobjective programming problem with inequality constraints. We introduce new classes of generalized alpha-univex type I vector valued functions. A number of Kuhn-Tucker type sufficient optimality conditions are obtained for a feasible solution to be an efficient solution. The Mond-Weir type duality results are also presented.
In the held of process synthesis, heat integration methodologies have been matured considerably during the past two decades. Today, these techniques are widely accepted as effective tools for improving chemical proces...
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In the held of process synthesis, heat integration methodologies have been matured considerably during the past two decades. Today, these techniques are widely accepted as effective tools for improving chemical processes in terms of capital investment and energy consumption. However, as the problems of environmental pollution have become more and more serious in recent years, the development of process integration methods for waste reduction is now recognized as an area of urgent research. Tn this paper, mathematical programming models, which take into account both economical incentives and environmental penalties, are formulated for the design of ''best'' utility systems. The pollution problem associated with a utility system can be mainly attributed to gas emissions (e.g. COx, NOx and SOx()) caused by burning fuels for generating power and/or heating utilities. In some cases, in order to satisfy the additional demand for power, electricity is imported from a central power plant which may also consume fuels. This demand for external electricity should therefore be considered as a hidden source of emission indirectly caused by running the utility plant. To address these environmental concerns, an improved version of the traditional MILP model for utility network design is proposed in this work. Not only the problem of cost minimization can be handled efficiently with an elaborate heat recovery scheme embedded in the modified superstructure, but also the concept of global emission can be incorporated in the model formulation. By making use of the goal programming techniques, appropriate designs of the the utility networks can be obtained according to the decision maker's priority. From the experiences we have gathered so far in solving the improved MILP model, it can be concluded that the proposed techniques are applicable for a wide variety of processes having extremely different utility demands and, also, it is a sensible design approach for establishing a compromi
In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce new concepts of d(l)-invexity and generalized d(l)-invexity in which each component...
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In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce new concepts of d(l)-invexity and generalized d(l)-invexity in which each component of the objective and constraint functions is directionally differentiable in its own direction d(l) New Fritz-John type necessary and Karush-Kuhn-Tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be weakly efficient, efficient or properly efficient. Moreover, we prove weak, strong, converse and strict duality results for a Mond-Weir type dual under various types of generalized d(l)-invexity assumptions. (C) 2009 Elsevier B.V. All rights reserved.
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