This paper presents a reference point-based interactive algorithm, which has been specifically designed to deal with stochastic multiobjective programming problems. This algorithm combines the classical information us...
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This paper presents a reference point-based interactive algorithm, which has been specifically designed to deal with stochastic multiobjective programming problems. This algorithm combines the classical information used in this kind of methods, i.e. values that the decision maker regards as desirable for each objective, with information about the probabilities the decision maker wishes to accept. This novel aspect allows the method to fully take into account the randomness of the final outcome throughout the whole solution process. These two pieces of information have been introduced in an adapted achievement-scalarizing function, which assures each solution obtained to be probability efficient.
We consider the nonlinear multiobjective programming problems involving cone constraints. For this program, we construct higher order dual problems and establish weak, strong and converse duality theorems for an effic...
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We consider the nonlinear multiobjective programming problems involving cone constraints. For this program, we construct higher order dual problems and establish weak, strong and converse duality theorems for an efficient solution by using higher order generalized invexity conditions due to Zhang (Higher order convexity and duality in multiobjective programming, in oProgress in Optimizationo, Contributions from Australasia, Applied Optimization, Vol. 30, eds. A. Eberhard, R. Hill, D. Ralph and B.M. Glover, Kluwer Academic Publishers, Dordrecht, 1999, 101-116). As special cases of our duality relations, we give some known duality results.
A pair of Mond-Weir type second-order symmetric dual multiobjective programs over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under pseudoinvexity/K-F-convexity assumption...
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A pair of Mond-Weir type second-order symmetric dual multiobjective programs over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under pseudoinvexity/K-F-convexity assumptions. (C) 2009 Elsevier Ltd. All rights reserved.
Following the classical exponential penalty function method of mathematical programming, the exponential penalty function method of multiobjective programming problems (MOPP) is constructed and its convergence is prov...
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Following the classical exponential penalty function method of mathematical programming, the exponential penalty function method of multiobjective programming problems (MOPP) is constructed and its convergence is proved. In addition, the approach is applied to solving a finite min-max MOPP.
Following the classical exponential penalty function method of mathematical programming, the exponential penalty function method of multiobjective programming problems (MOPP) is constructed and its convergence is prov...
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Following the classical exponential penalty function method of mathematical programming, the exponential penalty function method of multiobjective programming problems (MOPP) is constructed and its convergence is proved. In addition, the approach is applied to solving a finite min-max MOPP.
Em diversas áreas de trabalho, da Engenharia à Economia, os problemas se apresentam como sendo multiobjetivos, característica que torna complexa a tomada de decisão. Geralmente, estes objetivos s&#...
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Em diversas áreas de trabalho, da Engenharia à Economia, os problemas se apresentam como sendo multiobjetivos, característica que torna complexa a tomada de decisão. Geralmente, estes objetivos são conflitantes e faz-se necessário o uso de técnicas de otimização para a obtenção de melhores resultados. Na presente dissertação serão estudados alguns métodos para a resolução destes problemas, com o objetivo de aplicar métodos de aglutinação em problemas de projetos de experimentos com múltiplas respostas. Deste modo, inicialmente foi realizada uma análise bibliométrica sobre os diferentes métodos utilizados para a resolução destes problemas. A partir disto, foi desenvolvida uma nova abordagem, utilizando a Programação por Compromisso (Compromise programming – CP) e a Programação por Metas (Goal programming – GP), bem como diferentes algoritmos (Gradiente Reduzido Generalizado – GRG e a metaheurística do software Optquest) que são usualmente adotados, com comparação de resultados e análise. De modo geral, esta nova proposta apresentou resultados melhores em relação à abordagem tradicional (desirability), qualificando este procedimento como uma alternativa na otimização de múltiplas *** many areas, from Engineering to Economics, problems present themselves as multiobjective, which makes a decision-making process complex. Generally, these are conflicting objectives, and optimization techniques are necessary to achieve better results. This paper applies agglutination methods in classical problems of design of experiments with multiple responses. A bibliometric analysis was made, and a new approach was developed, using Compromise programming – CP and Goal programming – GP, as well as two different algorithms (Generalized Reduced Gradient – GRG and Optquest’s software metaheuristics) with results comparison and analysis. The new proposal presented better results when compared to the traditional approach (desirability), qualifying this procedure as an alternative in
In this paper we are focused to study the nondiferentiable multiobjective programming problem. We start from the invexity proposed by H. Slimani and M.S. Radjef. They consider the invexity for a differentiable vector ...
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ISBN:
(纸本)9780982148938
In this paper we are focused to study the nondiferentiable multiobjective programming problem. We start from the invexity proposed by H. Slimani and M.S. Radjef. They consider the invexity for a differentiable vector function when each component of function is invex with respect to its own function eta(i). We extend this concept to a general invexity class of rho -invexity and moreover for this case we consider that the vector function is nondifferentiable. In this framework we investigate the optimality conditions and give some new theorems that state the sufficient conditions for a feasible point to be efficient.
The weighted sum of objective functions is one of the simplest fitness functions widely applied in evolutionary algorithms (EAs) for multiobjective programming. However, EAs with this fitness function cannot find unif...
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The weighted sum of objective functions is one of the simplest fitness functions widely applied in evolutionary algorithms (EAs) for multiobjective programming. However, EAs with this fitness function cannot find uniformly distributed solutions on the entire Pareto front for nonconvex and complex multiobjective programming. In this paper, a novel EA based on adaptive multiple fitness functions and adaptive objective space division is proposed to overcome this shortcoming. The objective space is divided into multiple regions of about the same size by uniform design, and one fitness function is de fined on each region by the weighted sum of objective functions to search for the nondominated solutions in this region. Once a region contains fewer nondominated solutions, it is divided into several sub-regions and one additional fitness function is de fined on each sub-region. The search will be carried out simultaneously in these sub-regions, and it is hopeful to find more nondominated solutions in such a region. As a result, the nondominated solutions in each region are changed adaptively, and eventually are uniformly distributed on the entire Pareto front. Moreover, the complexity of the proposed algorithm is analyzed. The proposed algorithm is applied to solve 13 test problems and its performance is compared with that of 10 widely used algorithms. The results show that the proposed algorithm can effectively handle nonconvex and complex problems, generate widely spread and uniformly distributed solutions on the entire Pareto front, and outperform those compared algorithms.
The concept and characterization of proper efficiency is of significant theoretical and computational interest, in multiobjective optimization and decision-making, to prevent solutions with unbounded marginal rates of...
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The concept and characterization of proper efficiency is of significant theoretical and computational interest, in multiobjective optimization and decision-making, to prevent solutions with unbounded marginal rates of substitution. In this paper, we propose a slight modification to the original definition in the sense of Geoffrion, which maintains the common characterizations of properly efficient points as solutions to weighted sums or series and augmented or modified weighted Tcheby-cheff norms, also if the number of objective functions is countably infinite. We give new proofs and counter examples which demonstrate that such results become invalid for infinitely many criteria with respect to the original definition, in general, and we address the motivation and practical relevance of our findings for possible applications in stochastic optimization and decision-making under uncertainty.
In stratified sampling when strata weights are unknown a double sampling technique may be used to estimate them. A large simple random sample from the unstratified population is drawn and units falling in each stratum...
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In stratified sampling when strata weights are unknown a double sampling technique may be used to estimate them. A large simple random sample from the unstratified population is drawn and units falling in each stratum are recorded. A stratified random sample is then selected and simple random subsamples are obtained out of the previously selected units of the strata. This procedure is called double sampling for stratification. If the problem of non-response is there, then subsamples are divided into classes of respondents and non-respondents. A second subsample is then obtained out of the non-respondents and an attempt is made to obtain the information by increasing efforts, persuasion and call backs. In this paper, the problem of obtaining a compromise allocation in multivariate stratified random sampling is discussed when strata weights are unknown and non-response is present. The problem turns out to be a multiobjective non-linear integer programming problem. An approximation of the problem to an integer linear programming problem by linearizing the non-linear objective functions at their individual optima is worked out. Chebyshev's goal programming technique is then used to solve the approximated problem. A numerical example is also presented to exhibit the practical application of the developed procedure.
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