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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

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

Agency: Department of Defense | Branch: Missile Defense Agency | Program: SBIR | Phase: Phase II | Award Amount: 2.55M | Year: 2010

OptTek proposes to create a new methodology and tool set, “OptDef,” to provide MDA a capability to optimize Ballistic Missile Defense systems—a capability that will enable MDA to answer credibly not only “what if?”, but also “what’s best?” and “why this and not that?” OptDef will build on proven OptTek-proprietary technologies in simulation optimization that will leverage MDA’s investment in such credible and accredited BMDS-level performance tools as SABER, CAPS, I-SIM, DE Sim and LIDS. OptDef will significantly increase the effective utility of BMDS simulation models allowing analysts to optimize more than 10,000 continuous and/or discrete system decision variables. OptDef’s technology will seamlessly integrate with MDA simulation systems without modifying or affecting the simulation systems in any way. Toward fulfillment of this SBIR’s long-term objective, the technical objectives for this proposal fall into three categories – Software Integration, Optimization Technology, and System Analyses. The Software Integration component will address the mechanics of coupling OptDef with DSA and other systems of simulations. The Optimization Technology objectives will focus on development of specific algorithms and techniques to enhance the utility of OptDef for MDA applications. Finally, the System Analyses component of this project will provide analysis support for the war-fighter using OptDef.

This Small Business Innovation Research (SBIR) Phase I project seeks to design a model and algorithmic approach and develop pilot software as a teaching tool for building proficiency in decision-making and analysis relating to economic and environmental impacts of new initiatives to support economic development planning for American Indian Reservation Communities. This work adds innovations in optimizing technologies, yielding capabilities for entrepreneurial education that do not currently exist. The software is anticipated to have widespread application for improving economic performance and quality of life on Native American Reservations.

The broader impacts of this research include the potential to: a) improve entrepreneurial education applications for economic development planning; b) support significant social and economic initiatives; c) design a more effective approach using simulation and optimization techniques to economic planning; d) develop and market commercial-grade software that may be applied to other high-risk, highly complex development environments; e) attract downstream funding from sources including private capital firms, non-government agencies, and business alliance partners as it significantly increases economic performance; f) add to the body of knowledge in education applications, economic planning, and decision sciences that may be leveraged to enable additional research and development.

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