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Shortle J.,George Mason University | Rebennack S.,Colorado School of Mines | Glover F.W.,OptTek Systems, Inc.
IEEE Transactions on Power Systems | Year: 2014

The objective of this paper is to determine an optimal plan for expanding the capacity of a power grid in order to minimize the likelihood of a large cascading blackout. Capacity-expansion decisions considered in this paper include the addition of new transmission lines and the addition of capacity to existing lines. We embody these interacting considerations in a simulation optimization model, where the objective is to minimize the probability of a large blackout subject to a budget constraint. The probability of a large-scale blackout is estimated via Monte Carlo simulation of a probabilistic cascading blackout model. Because the events of interest are rare, standard simulation is often intractable from a computational perspective. We apply a variance-reduction technique within the simulation to provide results in a reasonable time frame. Numerical results are given for some small test networks including an IEEE 14-bus test network. A key conclusion is that the different expansion strategies lead to different shapes of the tails of the blackout distributions. In other words, there is a tradeoff between reducing the frequency of small-scale blackouts versus reducing the frequency of large-scale blackouts. © 1969-2012 IEEE. Source


Wang H.,Texas A&M International University | Kochenberger G.,University of Colorado at Denver | Glover F.,OptTek Systems, Inc.
Computers and Operations Research | Year: 2012

The quadratic knapsack problem (QKP) has been the subject of considerable research in recent years. Despite notable advances in special purpose solution methodologies for QKP, this problem class remains very difficult to solve. With the exception of special cases, the state-of-the-art is limited to addressing problems of a few hundred variables and a single knapsack constraint. In this paper we provide a comparison of quadratic and linear representations of QKP based on test problems with multiple knapsack constraints and up to eight hundred variables. For the linear representations, three standard linearizations are investigated. Both the quadratic and linear models are solved by standard branch-and-cut optimizers available via CPLEX. Our results show that the linear models perform well on small problem instances but for larger problems the quadratic model outperforms the linear models tested both in terms of solution quality and solution time by a wide margin. Moreover, our results demonstrate that QKP instances larger than those previously addressed in the literature as well as instances with multiple constraints can be successfully and efficiently solved by branch and cut methodologies. © 2011 Elsevier Ltd. All rights reserved. Source


Glover F.,OptTek Systems, Inc. | Lu Z.,University of Angers | Hao J.-K.,University of Angers
4OR | Year: 2010

This paper describes a Diversification-Driven Tabu Search (D2TS) algorithm for solving unconstrained binary quadratic problems. D2TS is distinguished by the introduction of a perturbation-based diversification strategy guided by long-term memory. The performance of the proposed algorithm is assessed on the largest instances from the ORLIB library (up to 2500 variables) as well as still larger instances from the literature (up to 7000 variables). The computational results show that D2TS is highly competitive in terms of both solution quality and computational efficiency relative to some of the best performing heuristics in the literature. © 2010 Springer-Verlag. Source


Lu Z.,University of Angers | Hao J.-K.,University of Angers | Glover F.,OptTek Systems, Inc.
Journal of Heuristics | Year: 2011

In this paper, we present an in-depth analysis of neighborhood relations for local search algorithms. Using a curriculum-based course timetabling problem as a case study, we investigate the search capability of four neighborhoods based on three evaluation criteria: percentage of improving neighbors, improvement strength and search steps. This analysis shows clear correlations of the search performance of a neighborhood with these criteria and provides useful insights on the very nature of the neighborhood. This study helps understand why a neighborhood performs better than another one and why and how some neighborhoods can be favorably combined to increase their search power. This study reduces the existing gap between reporting experimental assessments of local search-based algorithms and understanding their behaviors. © Springer Science+Business Media, LLC 2010. Source


Wang Y.,University of Angers | Lu Z.,Huazhong University of Science and Technology | Glover F.,OptTek Systems, Inc. | Hao J.-K.,University of Angers
Computers and Operations Research | Year: 2013

This paper presents two algorithms combining GRASP and Tabu Search for solving the Unconstrained Binary Quadratic Programming (UBQP) problem. We first propose a simple GRASP-Tabu Search algorithm working with a single solution and then reinforce it by introducing a population management strategy. Both algorithms are based on a dedicated randomized greedy construction heuristic and a tabu search procedure. We show extensive computational results on two sets of 31 large random UBQP instances and one set of 54 structured instances derived from the MaxCut problem. Comparisons with state-of-the-art algorithms demonstrate the efficacy of our proposed algorithms in terms of both solution quality and computational efficiency. It is noteworthy that the reinforced GRASP-Tabu Search algorithm is able to improve the previous best known results for 19 MaxCut instances. © 2011 Elsevier Ltd. Source

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