Most interactive methods developed for solving multiobjective optimization problems sequentially generate Pareto optimal or nondominated vectors and the decision maker must always allow impairment in at least one obje...
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Most interactive methods developed for solving multiobjective optimization problems sequentially generate Pareto optimal or nondominated vectors and the decision maker must always allow impairment in at least one objective function to get a new solution. The NAUTILUS method proposed is based on the assumptions that past experiences affect decision makers' hopes and that people do not react symmetrically to gains and losses. Therefore, some decision makers may prefer to start from the worst possible objective values and to improve every objective step by step according to their preferences. In NAUTILUS, starting from the nadir point, a solution is obtained at each iteration which dominates the previous one. Although only the last solution will be Pareto optimal, the decision maker never looses sight of the Pareto optimal set, and the search is oriented so that (s)he progressively focusses on the preferred part of the Pareto optimal set. Each new solution is obtained by minimizing an achievement scalarizing function including preferences about desired improvements in objective function values. NAUTILUS is specially suitable for avoiding undesired anchoring effects, for example in negotiation support problems, or just as a means of finding an initial Pareto optimal solution for any interactive procedure. An illustrative example demonstrates how this new method iterates. (C) 2010 Elsevier B.V. All rights reserved.
In this note we address the problem of determining selection probabilities for multipurpose surveys, when the aim is the simultaneous minimization of variances for each variable under study. A characterization of the ...
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In this note we address the problem of determining selection probabilities for multipurpose surveys, when the aim is the simultaneous minimization of variances for each variable under study. A characterization of the set of Pareto-optimal designs is given for designs with replacement and also for a class of designs without replacement, namely, Poisson designs. As an application, we describe a problem encountered in Auditing, where both the fraction of misstatements, and the average amount of such misstatements are of interest. (C) 2009 Elsevier B.V. All rights reserved.
The bi-objective set packing problem is a multi-objective combinatorial optimization problem similar to the well-known set covering/partitioning problems. To our knowledge and surprise, this problem has not yet been s...
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The bi-objective set packing problem is a multi-objective combinatorial optimization problem similar to the well-known set covering/partitioning problems. To our knowledge and surprise, this problem has not yet been studied whereas several applications have been reported. Unfortunately, solving the problem exactly in a reasonable time using a generic solver is only possible for small instances. We designed three alternative procedures for approximating solutions to this problem. The first is derived from the original 'Strength Pareto Evolutionary Algorithm', which is a population-based metaheuristic. The second is an adaptation of the 'Greedy Randomized Adaptative Search Procedure', which is a constructive metaheuristic. As underlined in the overview of the literature summarized here, almost all the recent, effective procedures designed for approximating optimal solutions to multi-objective combinatorial optimization problems are based on a blend of techniques, called hybrid metaheuristics. Thus, the third alternative, which is the primary subject of this paper, is an original hybridization of the previous two metaheuristics. The algorithmic aspects, which differ from the original definition of these metaheuristics, are described, so that our results can be reproduced. The performance of our procedures is reported and the computational results for 120 numerical instances are discussed. (C) 2009 Elsevier B.V. All rights reserved.
We prove that in order for the Kuhn-Tucker or Fritz John points to be efficient solutions, it is necessary and sufficient that the non-differentiable multiobjective problem functions belong to new classes of functions...
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We prove that in order for the Kuhn-Tucker or Fritz John points to be efficient solutions, it is necessary and sufficient that the non-differentiable multiobjective problem functions belong to new classes of functions that we introduce here: KT-pseudoinvex-II or FJ-pseudoinvex-II, respectively. We illustrate it by examples. These characterizations generalize recent results given for the differentiable case. We study the dual problem and establish weak, strong and converse duality results. (C) 2010 Elsevier Ltd. All rights reserved.
This paper presents a multiple reference point approach for multi-objective optimization problems of discrete and combinatorial nature. When approximating the Pareto Frontier, multiple reference points can be used ins...
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This paper presents a multiple reference point approach for multi-objective optimization problems of discrete and combinatorial nature. When approximating the Pareto Frontier, multiple reference points can be used instead of traditional techniques. These multiple reference points can easily be implemented in a parallel algorithmic framework. The reference points can be uniformly distributed within a region that covers the Pareto Frontier. An evolutionary algorithm is based on an achievement scalarizing function that does not impose any restrictions with respect to the location of the reference points in the objective space. Computational experiments are performed on a bi-objective flow-shop scheduling problem. Results, quality measures as well as a statistical analysis are reported in the paper. (C) 2010 Elsevier B.V. All rights reserved.
Industry planning is a complex decision making problem involving various criteria under dynamic situations. This paper studies the natural gas industry planning where natural gas is used to produce chemical products i...
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Industry planning is a complex decision making problem involving various criteria under dynamic situations. This paper studies the natural gas industry planning where natural gas is used to produce chemical products in the upper course of the Yangtze River in China. We identify the main uncertainty factors that affecting planning, and then model and analyze them using rough set, dynamic system and multiple objective programming theories. Thus, we develop system dynamic-rough multiple objective programming (SD-RMOP) models to plan and develop natural gas industry operations in this region. We then carry out a simulation experiment using optimized parameters from SD-RMOP. We compare performance from different models and show how decision-making is improved by the insight the model provides. (C) 2009 Published by Elsevier Ltd.
Real-world applications of multi-objective optimization often involve numerous objective functions. But while such problems are in general computationally intractable, it is seldom necessary to determine the Pareto op...
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Real-world applications of multi-objective optimization often involve numerous objective functions. But while such problems are in general computationally intractable, it is seldom necessary to determine the Pareto optimal set exactly. A significantly smaller computational burden thus motivates the loss of precision lithe size of the loss can be estimated. We describe a method for finding an optimal reduction of the set of objectives yielding a smaller problem whose Pareto optimal set w.r.t. a discrete subset of the decision space is as close as possible to that of the original set of objectives. Utilizing a new characterization of Pareto optimality and presuming a Finite decision space, we derive a program whose solution represents an optimal reduction. We also propose an approximate, computationally less demanding formulation which utilizes correlations between the objectives and separates into two parts. Numerical results from an industrial instance concerning the configuration of heavy-duty trucks are also reported. demonstrating the usefulness of the method developed. The results show that multi-objective optimization problems can be significantly simplified with an induced error which can be measured. (C) 2010 Elsevier B.V. All rights reserved.
This paper deals with a class of multipleobjective linear programs (MOLP) called lexicographic multipleobjective linear programs (LMOLP). In this paper, by providing an efficient algorithm which employs the precedin...
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This paper deals with a class of multipleobjective linear programs (MOLP) called lexicographic multipleobjective linear programs (LMOLP). In this paper, by providing an efficient algorithm which employs the preceding computations as well, it is shown how we can solve the LMOLP problem if the priority of the objective functions is changed. In fact, the proposed algorithm is a kind of sensitivity analysis on the priority of the objective functions in the LMOLP problems. (C) 2010 Elsevier B.V. All rights reserved.
In this paper, we develop a hybrid immune multiobjective optimization algorithm (HIMO) based on clonal selection principle. In HIMO, a hybrid mutation operator is proposed with the combination of Gaussian and polynomi...
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In this paper, we develop a hybrid immune multiobjective optimization algorithm (HIMO) based on clonal selection principle. In HIMO, a hybrid mutation operator is proposed with the combination of Gaussian and polynomial mutations (GP-HM operator). The GP-HM operator adopts an adaptive switching parameter to control the mutation process, which uses relative large steps in high probability for boundary individuals and less-crowded individuals. With the generation running, the probability to perform relative large steps is reduced gradually. By this means, the exploratory capabilities are enhanced by keeping a desirable balance between global search and local search, so as to accelerate the convergence speed to the true Pareto-optimal front in the global space with many local Pareto-optimal fronts. When comparing HIMO with various state-of-the-art multiobjective optimization algorithms developed recently, simulation results show that HIMO performs better evidently. (C) 2009 Elsevier B.V. All rights reserved.
The effective management of natural resources is a critical issue that concerns many people with differing interests. This paper examines aspects of overcapacity and optimal capacity within fisheries by accounting for...
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