The total unimodularity property of the constraint matrix of bi-objective integer programs is not in general a sufficient condition for identifying their efficient solution sets through the solution of equivalent bi-o...
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The total unimodularity property of the constraint matrix of bi-objective integer programs is not in general a sufficient condition for identifying their efficient solution sets through the solution of equivalent bi-objective linear programs. However, in this paper we identify special classes of bi-objective linear and concave integer programs that can be easily solved when their constraint matrices are totally unimodular.
Rural energy planning is characterized by matching, as far as possible, the available local energy supply with various energy end-uses. For this matching, decision-makers have to consider several issues, such as cost,...
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Rural energy planning is characterized by matching, as far as possible, the available local energy supply with various energy end-uses. For this matching, decision-makers have to consider several issues, such as cost, technology, sustainability and equity. These objectives are conflicting and, therefore, it is difficult to find an optimized solution. Therefore, such problems should be analysed by an alternative method, such as multiobjective programming, by which more than one objective can be analysed simultaneously. This paper reviews rural energy planning and illustrates the use of a multiobjective method in rural energy analysis. The method is applied to study energy problem of a rural area in Nepal. The preliminary results, which can be taken as a guideline in the formulation of energy policy, are also presented.
In this paper, we tackle the aircraft conflict resolution problem under uncertainties. We consider errors due to the wind effect, the imprecision of aircraft speed prediction, and the delay in the execution of maneuve...
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In this paper, we tackle the aircraft conflict resolution problem under uncertainties. We consider errors due to the wind effect, the imprecision of aircraft speed prediction, and the delay in the execution of maneuvers. Using a geometrical approach, we derive an analytical expression for the minimum distance between aircraft, along with the corresponding probability of conflict. These expressions are incorporated into an existing deterministic model for conflict resolution. This model solves the problem as a maximum clique of minimum weight in a graph whose vertices represent possible maneuvers and where edges link conflict-free maneuvers of different aircraft. We then present a solution procedure focusing on two criteria, namely, fuel efficiency and the probability of reissuing maneuvers in the future: we iteratively generate Pareto front solutions to provide the controller with a set of possible solutions where she can choose the one corresponding the most to her preferences. Intensive Monte Carlo simulations validate the expressions derived for the minimum distance and the probability of conflict. Computational results highlight that up to 10 different solutions for instances involving up to 35 aircraft are generated within 3 minutes.
A new model for practical decision problems is presented. It allows one to consider lexicographic preference structures by introducing the new class of piecewise lexicographic functions which impose a total order in t...
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A new model for practical decision problems is presented. It allows one to consider lexicographic preference structures by introducing the new class of piecewise lexicographic functions which impose a total order in the objective-and-constraint space. In this way, the concepts of objective and constraints are merged into a new unified notion of coobjective. Moreover, the lexicographic preference structure may be applied not only among different coobjectives, but also among different ranges of the same decision variable. The main merits of this model appear to be its versatility (it is able to deal with different types of multiobjective optimization situations without requiring user interaction) and its compactness (it does not require one to increase the original number of decision variables and constraints). A linear version of the model is investigated in more detail.
The concept of symmetric duality for multiobjective fractional problems has been extended to the class of multiobjective variational problems. Weak, strong and converse duality theorems are proved under generalized in...
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The concept of symmetric duality for multiobjective fractional problems has been extended to the class of multiobjective variational problems. Weak, strong and converse duality theorems are proved under generalized invexity assumptions. A close relationship between these problems and multiobjective fractional symmetric dual problems is also presented. (C) 2005 Elsevier Inc. All rights reserved.
The modern quest for sustainable cities increasingly relies on using distributed energy resources (DERs), which requires new planning practices. This paper proposes an optimisation strategy to solve the fast charging ...
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The modern quest for sustainable cities increasingly relies on using distributed energy resources (DERs), which requires new planning practices. This paper proposes an optimisation strategy to solve the fast charging station (FCS) allocation of electric vehicles (EVs). A mixed-integer programming (MIP) model minimises investment and operation costs, considering the building of FCSs with photovoltaic (PV) systems over carports and battery energy storage systems (BESSs) as planning alternatives. The embedded set covering problem has special aspects that allow the development of a novel approach to evaluate candidate sites to accommodate FCSs. A preprocessing strategy is developed to fine-tune the entire solution space. A multiobjective approach is used to obtain an optimal compromise solution for the MIP model when it is required to serve the maximum number of EV owners at the lowest possible cost. The combined strategies reduce the computational burden, allowing full-scale studies of EV charging system planning. The results of studies using a real-world Brazilian case certify the benefits of the proposed strategy in the FCS allocation problem and in optimising the operation when considering renewable alternatives.
Biofuel production from agricultural waste has been identified as a promising strategy in the field of renewable energy. This topic involves complex mathematical modeling tasks such as feedstock characteristics, biore...
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Biofuel production from agricultural waste has been identified as a promising strategy in the field of renewable energy. This topic involves complex mathematical modeling tasks such as feedstock characteristics, biorefinery location, capacity strategy and material flows. This paper proposes a Multiple Objective Mixed Integer Linear programming model (MOMILP) for the design of a sustainable supply chain using multiple agricultural residues. The proposed comprehensive model is utilized in a case study in Colombia, using coffee crop residues. Computational results show the model's robustness as a decision-making tool, which allows the projection of a flexible supply chain structure in the long term.
In this paper, we study the necessary optimality conditions for local Pareto and local weak Pareto solutions of multiobjective problems (MOPs) involving inequality and equality constraints. In this regard, the approxi...
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In this paper, we study the necessary optimality conditions for local Pareto and local weak Pareto solutions of multiobjective problems (MOPs) involving inequality and equality constraints. In this regard, the approximate Karush-Kuhn-Tucker conditions for MOPs are introduced and several constraint qualifications are also presented. Moreover, some illustrative examples are provided to clarify our results.
This paper presents the solution procedure of multiobjective nonlinear transportation problem (MNOTP) where the cost coefficients of the objective functions, and the supply and the unknown demand parameters have been ...
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This paper presents the solution procedure of multiobjective nonlinear transportation problem (MNOTP) where the cost coefficients of the objective functions, and the supply and the unknown demand parameters have been formulated as interval numbers by the decision maker. This problem has been converted into a conventional MNOTP where to minimize the interval nonlinear objective functions, the order relations that define the choice between intervals have been determined by the interval arithmetic. Also, the constraints with interval supply and unknown demand parameters have been transformed into its deterministic forms. Then the deterministic problems have been solved by two compromise programming methods. Finally, a numerical example is presented to illustrate the efficiency of the proposed procedure as well.
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.
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