This paper proposes a goal programming methodology to ensure that a mix of balance and optimisation is achieved across a hierarchical decision network. The extended goal programming principle is used for this purpose....
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This paper proposes a goal programming methodology to ensure that a mix of balance and optimisation is achieved across a hierarchical decision network. The extended goal programming principle is used for this purpose. A model is constructed that provides consideration of balance and efficiency of multipleobjectives and stakeholders at each network node level. A goal programming formulation to provide the decision that best meets the goals of the network is given. The proposed model is controlled by three key parameters that represent the level of non-compensation between objectives, level of non-compensation between stakeholders, and level of centralisation in the network. The methodology is demonstrated on an example pertaining to regional renewable energy generation and the results are discussed. Conclusions are drawn as to the effect of different attitudes towards compensatory behaviour between objectives and stakeholders in the network. (C) 2016 Elsevier B.V. All rights reserved.
In this paper, we consider the problem of planning inspections and other operations within a software development (SD) project with respect to the objectives quality (no. of defects), project makespan, and costs. The ...
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In this paper, we consider the problem of planning inspections and other operations within a software development (SD) project with respect to the objectives quality (no. of defects), project makespan, and costs. The considered model of SD processes comprises the phases coding, inspection, test, and rework and includes the assignment of operations to persons and the generation of a project schedule. Based on this model we discuss a multiobjective optimization problem. For solving the problem (i.e. finding an approximation of the efficient set) we develop a multiobjective evolutionary algorithm. Details of the algorithm are discussed as well as results of its application to sample problems. (C) 2004 Elsevier B.V. All rights reserved.
Given a finite set N of feasible points of a multi-objective optimization (MOO) problem, the search region corresponds to the part of the objective space containing all the points that are not dominated by any point o...
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Given a finite set N of feasible points of a multi-objective optimization (MOO) problem, the search region corresponds to the part of the objective space containing all the points that are not dominated by any point of N, i.e. the part of the objective space which may contain further nondominated points. In this paper, we consider a representation of the search region by a set of tight local upper bounds (in the minimization case) that can be derived from the points of N. Local upper bounds play an important role in methods for generating or approximating the nondominated set of an MOO problem, yet few works in the field of MOO address their efficient incremental determination. We relate this issue to the state of the art in computational geometry and provide several equivalent definitions of local upper bounds that are meaningful in MOO. We discuss the complexity of this representation in arbitrary dimension, which yields an improved upper bound on the number of solver calls in epsilon-constraint-like methods to generate the nondominated set of a discrete MOO problem. We analyze and enhance a first incremental approach which operates by eliminating redundancies among local upper bounds. We also study some properties of local upper bounds, especially concerning the issue of redundant local upper bounds, that give rise to a new incremental approach which avoids such redundancies. Finally, the complexities of the incremental approaches are compared from the theoretical and empirical points of view. (C) 2015 Elsevier B.V. All rights reserved.
Shippers are daily users of the French gas grid. Differences between planned and effective gas demand unbalance the grid. To restore the balance, GRTgaz computes every day amounts of gas transiting on the grid. Amount...
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Shippers are daily users of the French gas grid. Differences between planned and effective gas demand unbalance the grid. To restore the balance, GRTgaz computes every day amounts of gas transiting on the grid. Amounts injected or withdrawn from the storages, balancing tolerances use rates are also computed. Finally, if the grid is still unbalanced, amounts of gas (associated with penalties) bought or sold to shippers are computed too. To minimize billed penalties to shippers, GRTgaz uses all these balancing facilities in a certain order. We solve a four stages lexicographical (or hierarchical) optimization program. The cost function to be minimized at each stage is convex quadratic. Lagrange multipliers are interpreted as pressures;flows try to balance pressures over the network. In the subset of nodes with zero pressure, a careful formulation of the previous stages problems is necessary in order to guarantee the robustness of computations. A numerical illustration is given.
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 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 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.
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.
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.
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