Bilevel programming involves two optimization problems where the constraint region of the first level problem is implicitly determined by another optimization problem. In this paper we consider the bilevel linear/line...
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Bilevel programming involves two optimization problems where the constraint region of the first level problem is implicitly determined by another optimization problem. In this paper we consider the bilevel linear/linear fractional programming problem in which the objective function of the first level is linear, the objective function of the second level is linear fractional and the feasible region is a polyhedron. For this problem we prove that an optimal solution can be found which is an extreme point of the polyhedron. Moreover, taking into account the relationship between feasible solutions to the problem and bases of the technological coefficient submatrix associated to variables of the second level, an enumerative algorithm is proposed that finds a global optimum to the problem. (C) 1999 Elsevier Science B.V. All rights reserved.
In this paper we analyze different solution procedures for the two-machine flow shop scheduling problem with a common due date and weighted late work criterion, i.e. for problem F2 vertical bar d(j) = d vertical bar Y...
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In this paper we analyze different solution procedures for the two-machine flow shop scheduling problem with a common due date and weighted late work criterion, i.e. for problem F2 vertical bar d(j) = d vertical bar Y-w, which is known to be binary NP-hard. In computational experiments we compare the practical efficiency of a dynamic programming approach, an enumerative method and a heuristic list scheduling procedure. Test results show that each solution method has its advantages and none of them can be rejected from consideration a priori. (c) 2005 Elsevier Ltd. All rights reserved.
In this paper, the authors propose an algorithm using branch and bound method to search an optimal replacement scheduling of obsolete equipment in aged primary substations. The developed tool can efficiently find an o...
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ISBN:
(纸本)9781424483570
In this paper, the authors propose an algorithm using branch and bound method to search an optimal replacement scheduling of obsolete equipment in aged primary substations. The developed tool can efficiently find an optimal solution from huge combinations of replacement schedules. The objective function to be minimized is the net present value of the sum of operation and maintenance cost, replacement cost, and the reliability cost in case of CB failure for each substation during the specified time frame. To solve this problem under the constraints such as annual budget ceiling, number of replacement targets per annum, and replacement time frame for each substation, we apply the branch and bound method, which is well known as an efficient combinatorial optimization technique. The proposed algorithm is demonstrated using a small scale model (2 substations, 4-year time frame) to verify its effectiveness.
This article addresses the reduction of power losses in smart grids. Two optimization algorithms are used in this article. The first method is the enumerative method. The second method of the optimization calculation ...
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This article addresses the reduction of power losses in smart grids. Two optimization algorithms are used in this article. The first method is the enumerative method. The second method of the optimization calculation is based on the self-organizing migrating algorithm. In the first step, the network parameters are calculated based on the input data, and then the target function is determined. In this article, the target function is used to reduce the active power losses that occur during the operation of an electric network. More specifically, we attempt to determine the reactive power with the enumerative and SOMA algorithms to reduce the value of the active power losses. This article intends to illustrate the differences between the selected optimization algorithms. As observed, the optimization algorithm determines the computation time.
We define and discuss different enumerative methods to compute solutions of generalized Nash equilibrium problems with linear coupling constraints and mixed-integer variables. We propose both branch-and-bound methods ...
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We define and discuss different enumerative methods to compute solutions of generalized Nash equilibrium problems with linear coupling constraints and mixed-integer variables. We propose both branch-and-bound methods based on merit functions for the mixed-integer game, and branch-and-prune methods that exploit the concept of dominance to make effective cuts. We show that under mild assumptions the equilibrium set of the game is finite and we define an enumerative method to compute the whole of it. We show that our branch-and-prune method can be suitably modified in order to make a general equilibrium selection over the solution set of the mixed-integer game. We define an application in economics that can be modelled as a Nash game with linear coupling constraints and mixed-integer variables, and we adapt the branch-and-prune method to efficiently solve it.
Reactive powder concrete (RPC) is an ultra-high strength material based on cement composite with advanced durability and superior toughness. Firstly the failure criterion is defined according to the strength performan...
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Reactive powder concrete (RPC) is an ultra-high strength material based on cement composite with advanced durability and superior toughness. Firstly the failure criterion is defined according to the strength performance, which is very different from the conventional concrete failure criteria. And then the optimization design of the RPC simply supported beam is discussed by using the enumerative method, in which the objective function manufacturing cost, the constraint conditions are strength and displacement. Optimization design of prestressed simply supported beam is carried out using program. The polynomial curves are fitted including the span-price curve, span-quantity of reinforcement curve and span-height of beam curve, and the simplified formulas on price, quantity of reinforcement and height of beam are presented. The economical span formula is also put forward. The results indicate that the manufacturing cost of the beam of 30-60 m after the optimization will be decreased to about 29.3%.
In this paper, we focus on the bilevel linear-linear fractional programming problem (BLLFP), in which the upper level objective is linear and the lower level objective is linear fractional over a polyhedron. We provid...
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In this paper, we focus on the bilevel linear-linear fractional programming problem (BLLFP), in which the upper level objective is linear and the lower level objective is linear fractional over a polyhedron. We provided a modified enumerative searching scheme and then incorporated the Charnes-Cooper transformation for dealing with associated lower level problems, to find the global optimal solution of this nonconvex optimization problem. The numerical example shows that our algorithm achieves the global optimal solution in finite steps with less procedures than the only one existing enumerative based algorithm in literature. As a result, our version is an improved and simplified version with some computational advantage.
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