In this work on the management of water quality in a river basin by means of multiobjective programming, the programming model consists of three objectives that include simultaneously both economic and environmental f...
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In this work on the management of water quality in a river basin by means of multiobjective programming, the programming model consists of three objectives that include simultaneously both economic and environmental factors. These objectives are the water quality of the rivers, the cost of wastewater treatment and the assimilative capacity of the rivers. In particular, this research is the first to take into account the last objective. For practical application, this paper proposes two methods of multiobjective programming, the constraint method and the step method. Furthermore, to illustrate the application of these techniques to water quality management problems, we use the basin of Tzeng-Wen River, Taiwan, as a case study. The results show that these methods work satisfactorily to improve the water quality, to ascertain the economic cost of wastewater treatment, and to allocate allowable loading in a manner of equality from non-inferior solutions. Alternatively, these methods provide important information for regulatory agencies to implement pollution control of river water. (C) 1996 Academic Press Limited
Recently, sufficient optimality theorems for (weak) Pareto-optimal solutions of a multiobjective optimization problem (MOP) were stated in Theorems 3.1 and 3.3 of Ref. 1. In this note, we give a counterexample showing...
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Recently, sufficient optimality theorems for (weak) Pareto-optimal solutions of a multiobjective optimization problem (MOP) were stated in Theorems 3.1 and 3.3 of Ref. 1. In this note, we give a counterexample showing that the theorems of Ref. 1 are not true. Then, by modifying the assumptions of these theorems, we establish two new sufficient optimality theorems for (weak) Pareto-optimal solutions of (MOP);moreover, we give generalized sufficient optimality theorems for (MOP).
In this paper, a new version of the min-max method for solving multiobjective optimization problems is proposed. Using the new version, unlike the min-max method, we can prove results on (proper) efficiency of optimal...
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In this paper, a new version of the min-max method for solving multiobjective optimization problems is proposed. Using the new version, unlike the min-max method, we can prove results on (proper) efficiency of optimal solutions. Moreover, a special case of the model with flexible constraints is also studied. By considering approximate solutions, some relationships between epsilon 1-(weakly, properly) efficient solutions of a general multiobjective optimization problem and is an element of-optimal solutions of the introduced model are achieved. (C) 2020 Elsevier B.V. All rights reserved.
The concept of equitability in multiobjective programming is generalized within a framework of convex cones. Two models are presented. First, more general polyhedral cones are assumed so determine the equitable prefer...
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The concept of equitability in multiobjective programming is generalized within a framework of convex cones. Two models are presented. First, more general polyhedral cones are assumed so determine the equitable preference. Second, the Pareto cone appearing in the monotonicity axiom of equitability is replaced with a permutation-invariant polyhedral cone. The conditions under which the new models are related and satisfy original and modified axioms of the equitable preference are developed. Relationships between generalized equitability and relative importance of criteria and stochastic dominance are revealed. (C) 2011 Elsevier B.V. All rights reserved.
In this paper. we describe an interactive procedural algorithm for convex multiobjective programming based upon the Tchebycheff method, Wierzbicki's reference point approach, and the procedure of Michalowski and S...
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In this paper. we describe an interactive procedural algorithm for convex multiobjective programming based upon the Tchebycheff method, Wierzbicki's reference point approach, and the procedure of Michalowski and Szapiro. At each iteration, the decision maker (DM) has the option of expressing his or her objective-function aspirations in the form of a reference criterion vector. Also, the DM has the option of expressing minimally acceptable values for each of the objectives in the form of a reservation vector. Based upon this information, a certain region is defined for examination. In addition, a special set of weights is constructed. Then with the weights, the algorithm of this paper is able to generate a group of efficient solutions that provides for an overall view of the current iteration's certain region. By modification of the reference and reservation vectors, one can "steer" the algorithm at each iteration. From a theoretical point of view, we prove that none of the efficient solutions obtained using this scheme impair any reservation value for convex problems. The behavior of the algorithm is illustrated by means of graphical representations and an illustrative numerical example. (C) 2009 Elsevier B.V. All rights reserved.
In this paper, I carry out an extension of the MICA method (modified interactive chebyshev algorithm) for non-convex multiobjective programming. This method is based on the Tchebychev method and in the reference point...
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In this paper, I carry out an extension of the MICA method (modified interactive chebyshev algorithm) for non-convex multiobjective programming. This method is based on the Tchebychev method and in the reference point approach. At each iteration, the decision maker (DM) can provide aspiration levels (desirable values for the objective functions) and also, if the DM wishes, reservation levels (level under which the objective function is not considered acceptable). On the basis of this preferential information, a region of the nondominated objective set is defined. In the convex case, considering the aspiration vector as a reference point in an achievement scalarizing function and taking a set of weight vectors, the efficient solutions generated satisfy the reservation levels. In this work, I analyze the non-convex case. The main result of MICA is verified and demonstrated for the non-convex bi-objective case. The MICA method is not verified in general for multiobjective problems with three or more objective functions, which is demonstrated with a counterexample.
We suggest the second-order symmetric and self dual programs in multiobjective nonlinear programming. For these second-order symmetric dual programs, we prove the weak, strong, and converse duality theorems under conv...
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We suggest the second-order symmetric and self dual programs in multiobjective nonlinear programming. For these second-order symmetric dual programs, we prove the weak, strong, and converse duality theorems under convexity and concavity conditions. Also, we prove the self duality theorem for these second-order self dual programs and illustrate its example.
A multiobjective binary integer programming model for R&D project portfolio selection with competing objectives is developed when problem coefficients in both objective functions and constraints are uncertain. Rob...
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A multiobjective binary integer programming model for R&D project portfolio selection with competing objectives is developed when problem coefficients in both objective functions and constraints are uncertain. Robust optimization is used in dealing with uncertainty while an interactive procedure is used in making tradeoffs among the multiple objectives. Robust nondominated solutions are generated by solving the linearized counterpart of the robust augmented weighted Tchebycheff programs. A decision maker's most preferred solution is identified in the interactive robust weighted Tchebycheff procedure by progressively eliciting and incorporating the decision maker's preference information into the solution process. An example is presented to illustrate the solution approach and performance. The developed approach can also be applied to general multiobjective mixed integer programming problems. (C) 2014 Elsevier B.V. All rights reserved.
In this paper, we concentrate on reference point based methods in multiobjective programming to demonstrate, as main contribution, that the solution to a multiobjective optimization problem stays unchanged if the refe...
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In this paper, we concentrate on reference point based methods in multiobjective programming to demonstrate, as main contribution, that the solution to a multiobjective optimization problem stays unchanged if the reference point is changed to any point on a set defined by means of the original reference point, the nondominated objective solution and some parameters of the ASF. Concretely, this new set of "equivalent reference points" is the convex linear combination of two straight lines, one containing the original reference point and the other a nondominated objective solution, where the slope of both straight lines is given by the inverses of the weights of the ASF. An illustrative example is used to show the results obtained and an empirical model (application with real data) allows us to highlight possible implications. (C) 2014 Elsevier Ltd. All rights reserved.
In this paper, a generalization of convexity, namely G-invexity, is considered in the case of nonlinear multiobjective programming problems where the functions constituting vector optimization problems are differentia...
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In this paper, a generalization of convexity, namely G-invexity, is considered in the case of nonlinear multiobjective programming problems where the functions constituting vector optimization problems are differentiable. The modified Karush-Kuhn-Tucker necessary optimality conditions for a certain class of multiobjective programming problems are established. To prove this result, the Kuhn-Tucker constraint qualification and the definition of the Bouligand tangent cone for a set are used. The assumptions on (weak) Pareto optimal solutions are relaxed by means of vector-valued G-invex functions.
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