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.
Traditional focus on reducing one environmental externality may cause another externality to increase. This article examines the environmental and economic costs of abating soil loss and (or) nitrate leaching through ...
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Traditional focus on reducing one environmental externality may cause another externality to increase. This article examines the environmental and economic costs of abating soil loss and (or) nitrate leaching through alternative optimal production systems in the nonirrigated farming systems of Northeastern Oregon. Models estimating soil loss and nitrate-nitrogen leaching rates associated with current production processes, are linked to a Multi-objectiveprogramming (MOP) model. The results show that site specific conditions influence the level of abatement expenditures and optimal production strategies to reduce soil loss and leaching rates. Moreover while existing production strategies are effective in reducing soil loss at little cost, no strategies could be identified to reduce nitrate leaching rate on some soils.
We propose a polynomial-time-delay polynomial-space algorithm to enumerate all efficient extreme solutions of a multi-criteria minimum-cost spanning tree problem, while only the bi-criteria case was studied in the lit...
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We propose a polynomial-time-delay polynomial-space algorithm to enumerate all efficient extreme solutions of a multi-criteria minimum-cost spanning tree problem, while only the bi-criteria case was studied in the literature. The algorithm is based on the reverse search framework due to Avis and Fukuda. We also show that the same technique can be applied to the multi-criteria version of the minimum-cost basis problem in a (possibly degenerated) submodular system. As an ultimate generalization, we propose an algorithm to enumerate all efficient extreme solutions of a multi-criteria linear program. When the given linear program has no degeneracy, the algorithm runs in polynomial-time delay and polynomial space. To best of our knowledge, they are the first polynomial-time delay and polynomial-space algorithms for the problems. (C) 2010 Elsevier B.V. All rights reserved.
We are interested in a class of linear bilevel programs where the upper level is a linear scalar optimization problem and the lower level is a linear multi-objective optimization problem. We approach this problem via ...
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We are interested in a class of linear bilevel programs where the upper level is a linear scalar optimization problem and the lower level is a linear multi-objective optimization problem. We approach this problem via an exact penalty method. Then, we propose an algorithm illustrated by numerical examples. (C) 2008 Elsevier B.V. All rights reserved.
It is undeniably crucial for a firm to be able to make a forecast regarding the sales volume of new products. However, the current economic environments invariably have uncertain factors and rapid fluctuations where d...
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It is undeniably crucial for a firm to be able to make a forecast regarding the sales volume of new products. However, the current economic environments invariably have uncertain factors and rapid fluctuations where decision makers must draw conclusions from minimal data. Previous studies combine scenario analysis and technology substitution models to forecast the market share of multigenerational technologies. However, a technology substitution model based on a logistic curve will not always fit the S curve well. Therefore, based on historical data and the data forecast by both the Scenario and Delphi methods, a two stage fuzzy piecewise logistic growth model with multiple objective programming is proposed herein. The piecewise concept is adopted in order to reflect the market impact of a new product such that it can be possible to determine the effective length of sales forecasting intervals even when handling a large variation in data or small size data. In order to demonstrate the model's performance, two cases in the Television and Telecommunication industries are treated using the proposed method and the technology substitution model or the Norton and Bass diffusion model. A comparison of the results shows that the proposed model outperforms the technology substitution model and the Norton and Bass diffusion model. (C) 2014 Elsevier B.V. All rights reserved.
We introduce a new interactive multiobjective optimization method operating in the objective space called Nonconvex Pareto Navigator. It extends the Pareto Navigator method for nonconvex problems. An approximation of ...
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We introduce a new interactive multiobjective optimization method operating in the objective space called Nonconvex Pareto Navigator. It extends the Pareto Navigator method for nonconvex problems. An approximation of the Pareto optimal front in the objective space is first generated with the PAINT method using a relatively small set of Pareto optimal outcomes that is assumed to be given or computed prior to the interaction with the decision maker. The decision maker can then navigate on the approximation and direct the search for interesting regions in the objective space. In this way, the decision maker can conveniently learn about the interdependencies between the conflicting objectives and possibly adjust one's preferences. To facilitate the navigation, we introduce special cones that enable extrapolation beyond the given Pareto optimal outcomes. Besides handling nonconvexity, the new method contains new options for directing the navigation that have been inspired by the classification-based interactive NIMBUS method. The Nonconvex Pareto Navigator method is especially well-suited for computationally expensive problems, because the navigation on the approximation is computationally inexpensive. We demonstrate the method with an example. Besides proposing the new method, we characterize interactive navigation based methods in general and discuss desirable properties of navigation methods overall and in particular with respect to Nonconvex Pareto Navigator. (C) 2018 Elsevier B.V. All rights reserved.
We investigate a method for constructing piecewise-linear approximations of an additive (called also separable) objective function in n target variables from a few indifference points in two-dimensional planes. It is ...
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We investigate a method for constructing piecewise-linear approximations of an additive (called also separable) objective function in n target variables from a few indifference points in two-dimensional planes. It is shown that (a) the data used by the method are ordinal.. simplest, and minimal;(b) the limit ordinal preference is independent of the cardinal utility scale used in intermediate computations, since the accuracy of the approximations is estimated in the Hausdorff metric on the space of binary relations. The method is illustrated with an example of constructing an additive objective function of German economic policy in four target variables: Inflation, Unemployment, GNP Growth, and Increase in Public Debt. We provide some modifications of the model aimed at user's convenience. (C) 2003 Elsevier B.V. All rights reserved.
In this paper, we obtain necessary and sufficient second order optimality conditions for multiobjective problems using second order directional derivatives. We propose the notion of second order KT-pseudoinvex problem...
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In this paper, we obtain necessary and sufficient second order optimality conditions for multiobjective problems using second order directional derivatives. We propose the notion of second order KT-pseudoinvex problems and we prove that this class of problems has the following property: a problem is second order KT-pseudoinvex if and only if all its points that satisfy the second order necessary optimality condition are weakly efficient. Also we obtain second order sufficient conditions for efficiency. (C) 2013 Elsevier Ltd. All rights reserved.
This paper investigates two approaches for solving bi-objective constrained minimum spanning tree problems. The first seeks to minimize the tree weight, keeping the problem's additional objective as a constraint, ...
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This paper investigates two approaches for solving bi-objective constrained minimum spanning tree problems. The first seeks to minimize the tree weight, keeping the problem's additional objective as a constraint, and the second aims at minimizing the other objective while constraining the tree weight. As case studies, we propose and solve bi-objective generalizations of the Hop-Constrained Minimum Spanning Tree Problem (HCMST) and the Delay-Constrained Minimum Spanning Tree Problem (DCMST). First, we present an Integer Linear programming (ILP) formulation for the HCMST. Then, we propose a new com-pact mathematical model for the DCMST based on the well-known Miller-Tucker-Zemlin subtour elimination constraints. Next, we extend these formulations as bi-objective models and solve them using an Augmented e-constraints method. Computational experiments per-formed on classical instances from the literature evaluated two different implementations of the Augmented e-constraints method for each problem. Results indicate that the algorithm performs better when minimizing the tree weight while constraining the other objective since this implementation finds shorter running times than the one that minimizes the additional objective and constrains the tree weight.
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