In many real decision situations more than one objective has to be considered and different kinds of uncertainty must be handled. The uncertainty is generally of two natures: stochastic uncertainty related to environm...
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In many real decision situations more than one objective has to be considered and different kinds of uncertainty must be handled. The uncertainty is generally of two natures: stochastic uncertainty related to environmental data and fuzzy uncertainty related to expert judgement. This paper proposes a fuzzy chance constrained approach to solve mathematical programs integrating fuzzy and stochastic parameters with multiple objective aspects. Our approach is applied to determine reservoirs releases in the Echkeul basin in Tunisia.
A variety of approaches exist for the determination of a weighting scheme from a pairwise comparison matrix describing a scale-relation between objectives or alternatives. The most common context for such an algorithm...
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A variety of approaches exist for the determination of a weighting scheme from a pairwise comparison matrix describing a scale-relation between objectives or alternatives. The most common context for such an algorithm is that of the analytic hierarchy process (AHP), although uses in other areas of the field of multicriteria decision making (MCDM) can also be found. Typically, the eigenvalue method is the standard method employed in the AHP to determine weights, as in the ExpertChoice software. However, another class of techniques are the distance-metric-based approaches, which are frequently proposed as alternatives to the eigenvalue method. This paper evaluates such distance-metric-based approaches comparing their effectiveness, using the eigenvalue method as a benchmark. A common framework is introduced to establish an efficient frontier for method comparison. Journal of the Operational Research Society (2004).
We compare several ways to model a habitat reserve site selection problem in which an upper bound on the total area of the selected sites is included. The models are cast as optimization coverage models drawn from the...
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We compare several ways to model a habitat reserve site selection problem in which an upper bound on the total area of the selected sites is included. The models are cast as optimization coverage models drawn from the location science literature. Classic covering problems typically include a constraint on the number of sites that can be selected. If potential reserve sites vary in terms of area, acquisition cost or land value, then sites need to be differentiated by these characteristics in the selection process. To address this within the optimization model, the constraint on the number of selected sites can either be replaced by one limiting the total area of the selected sites or area minimization can be incorporated as a second objective. We show that for our dataset and choice of optimization solver average solution time improves considerably when an area-constrained reserve site selection problem is modeled as a two objective rather than a single objective problem with a constraint limiting the total area of the selected sites. Computational experience is reported using a large dataset from Australia. Published by Elsevier Ltd.
multiobjective methods for group decision situations that are proposed in the literature do not generally model power and influence. On the other hand, papers dealing with influence and power in group decision support...
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multiobjective methods for group decision situations that are proposed in the literature do not generally model power and influence. On the other hand, papers dealing with influence and power in group decision support system (GDSS) are looking for the effects of GDSS on the distribution of power among the group members. This paper proposes an interactive method for group decision aid in multiobjective context integrating he concept of power and influence within the multiperson-multicriteria aspect. The method is designed to be used by a committee to solve a multiple criteria allocation problem. The method is tested on a resource allocation problem in the Municipality of Tunis.
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, we are concerned with the multiobjective programming problem with inequality constraints. We introduce new classes of generalized type I vector-valued functions. Duality theorems are proved for Mond-Wei...
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In this paper, we are concerned with the multiobjective programming problem with inequality constraints. We introduce new classes of generalized type I vector-valued functions. Duality theorems are proved for Mond-Weir and general Mond-Weir type duality under the above generalized type I assumptions.
Airline network design encompasses decisions on an airline network shape and route flight frequencies. Related investigations handle the trade-off between enhancing passengers' service levels and lowering the airl...
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Airline network design encompasses decisions on an airline network shape and route flight frequencies. Related investigations handle the trade-off between enhancing passengers' service levels and lowering the airline's operating costs by applying deterministic optimization methods. In contrast with other conventional methods, Grey theory is a feasible mathematical device capable of forecasting airline traffic with minimum data and resolving problems containing uncertainty and indetermination. In the light of these developments, this study develops a series of models capable of forecasting airline city-pair passenger traffic, designing a network of airline routes and determining Eight frequencies on individual routes by applying Grey theory and multiobjective programming. A case study demonstrates the feasibility of applying the proposed models. Results in this study not only confirm the practical nature of the preposed models, but also their ability to provide high flexibility in decision making for airlines. (C) 2000 Elsevier Science B.V. All rights reserved.
We examine new second-order necessary conditions and sufficient conditions which characterize nondominated solutions of a generalized constrained multiobjective programming problem. The vector-valued criterion functio...
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We examine new second-order necessary conditions and sufficient conditions which characterize nondominated solutions of a generalized constrained multiobjective programming problem. The vector-valued criterion function as well as constraint functions are supposed to be from the class C1,1. Second-order optimality conditions for local Pareto solutions are derived as a special case.
Multipurpose operation is adopted by most reservoirs in Taiwan in order to maximize the benefits of power generation, water supply, irrigation and recreational purposes. A multiobjective approach can be used to obtain...
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Multipurpose operation is adopted by most reservoirs in Taiwan in order to maximize the benefits of power generation, water supply, irrigation and recreational purposes. A multiobjective approach can be used to obtain trade-off curves among these multipurpose targets. The weighting method, in which different weighting factors are used for different purposes, was used in this research work. In Taiwan, most major reservoirs are operated by rule curves. Genetic algorithms with characteristics of artificial intelligence were applied to obtain the optimal rule curves of the multireservoir system under multipurpose operation in Chou-Shui River Basin in central Taiwan. The model results reveal that different shapes of rule curves under different weighting factors on targets can be efficiently obtained by genetic algorithms. Pareto optimal solutions for a trade-off between water supply and hydropower were obtained and analyzed.
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