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Branch-and-cut for complementarity-constrained optimization

MATHEMATICAL programming COMPUTATION 2014年第4期6卷 365-403页

作者： de Farias, I. R., Jr. Kozyreff, E. Zhao, M. Texas Tech Lubbock TX 79409 USA SAS Cary NC USA

We report and analyze the results of our computational testing of branch-and-cut for the complementarity-constrained optimization problem (CCOP). Besides the MIP cuts commonly present in commercial optimization software, we used inequalities that explore complementarity constraints. To do so, we generalized two families of cuts proposed earlier by de Farias, Johnson, and Nemhauser that had never been tested computationally. Our test problems consisted of linear, binary, and general integer programs with complementarity constraints. Our results on the use of complementarity cuts within a major commercial optimization solver show that they are of critical importance to tackling difficult CCOP instances, typically reducing the computational time required to solve them tremendously.

关键词： Complementarity Multiple-choice Special ordered set mixed-integer programming Knapsack set Polyhedral method Branch-and-cut

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Cost Minimization for Fading Channels With Energy Harvesting and Conventional Energy

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2014年第8期13卷 4586-4598页

作者： Kang, Xin Chia, Yeow-Khiang Ho, Chin Keong Sun, Sumei Inst Infocomm Res Singapore 138632 Singapore

In this paper, we investigate resource allocation strategies for a point-to-point wireless communications system with hybrid energy sources consisting of an energy harvester and a conventional energy source. In particular, as an incentive to promote the use of renewable energy, we assume that the renewable energy has a lower cost than the conventional energy. Then, by assuming that the non-causal information of the energy arrivals and the channel power gains are available, we minimize the total energy cost of such a system over N fading slots under a proposed outage constraint together with the energy harvesting constraints. The outage constraint requires a minimum fixed number of slots to be reliably decoded, and thus leads to a mixed-integer programming formulation for the optimization problem. This constraint is useful, for example, if an outer code is used to recover all the data bits. Optimal linear time algorithms are obtained for two extreme cases, i.e., the number of outage slot is 1 or N - 1. For the general case, a lower bound based on the linear programming relaxation, and two suboptimal algorithms are proposed. It is shown that the proposed suboptimal algorithms exhibit only a small gap from the lower bound. We then extend the proposed algorithms to the multi-cycle scenario in which the outage constraint is imposed for each cycle separately. Finally, we investigate the resource allocation strategies when only causal information on the energy arrivals and only channel statistics is available. It is shown that the greedy energy allocation is optimal for this scenario.

关键词： Energy harvesting hybrid power supply green wireless communications block fading channels optimal resource allocation non-convex optimization mixed-integer programming

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Building Master Surgery Schedules with Leveled Bed Occupancy and Nurse Workloads

Building Master Surgery Schedules with Leveled Bed Occupancy...

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IEEE International Conference on Industrial Engineering and Engineering Management

作者： Yahia, Z. Harraz, N. Eltawil, Amr B. Egypt Japan Univ Sci & Technol Dept Ind Engn & Syst Management Alexandria Egypt Alexandria Univ Fac Engn Prod Engn Dept Alexandria Egypt

ISBN: (纸本)9781479964109

The master surgery scheduling problem involves the development of a master surgical schedule, a cyclic timetable that determines the patient category associated with each block of operating room time. A myriad of variants of the problem has been addressed in literature. Here we focus on two major variants, arising during cooperation with Karmoze hospital, a non-profit hospital located in Alexandria, Egypt. The first variant asks for balancing both beds and nurses daily requirements, whereas the second for considering surgeons preferences. To cope with these problems we introduce a new mixed integer formulation. The objective function minimizes the weighted sum of peaks in the daily bed occupancy and nurse daily workloads. The results show that our model provides a more leveled daily bed occupancy and nurse requirements. Furthermore, our model reduces both the daily bed occupancy and nurse workloads.

关键词： Health-care optimization Master surgery scheduling mixed-integer programming Operating room planning Scheduling

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New Product Introduction Against a Predator: A Bilevel mixed-integer programming Approach

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NAVAL RESEARCH LOGISTICS 2009年第8期56卷 714-729页

作者： Smith, J. Cole Lim, Churlzu Alptekinoglu, Aydin Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA Univ N Carolina Syst Engn & Engn Management Program Charlotte NC 28223 USA So Methodist Univ Edwin L Cox Sch Business Dallas TX 75275 USA

We consider a scenario with two firms determining which products to develop and introduce to the market. In this problem, there exists a finite set of potential products and market segments. Each market segment has a preference list of products and will buy its most preferred product among those available. The firms play a Stackelberg game in which the leader firm first introduces a set of products, and the follower responds with its own set of products. The leader's goal is to maximize its profit subject to a product introduction budget, assuming that the follower will attempt to minimize the leader's profit using a budget of its own. We formulate this problem as a multistage integer program amenable to decomposition techniques. Using this formulation, we develop three variations of an exact mathematical programming method for solving the multistage problem, along with a family of heuristic procedures for estimating the follower solution. The efficacy of our approaches is demonstrated on randomly generated test instances. This article contributes to the operations research literature a multistage algorithm that directly addresses difficulties posed by degeneracy, and contributes to the product variety literature an exact optimization algorithm for a novel competitive product introduction problem. (C) 2009 Wiley Periodicals, Inc. Naval Research Logistics 56: 714-729, 2009

关键词： mixed-integer programming product introduction Stackelberg game

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Application of Multiple Equilibrium Point Search in Gradient Systems to mixed-integer programming

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ELECTRONICS AND COMMUNICATIONS IN JAPAN 2009年第8期92卷 53-63页

作者： Masuda, Kazuaki Kurihara, Kenzo Kanagawa Univ Kanagawa Japan

This paper proposes a solution to mixed-integer programming by using a gradient system and searching for multiple equilibrium points in the system. The method is available when the objective function of a problem is continuous and differentiable. In order to find feasible Solutions of a mixed-integer programming problem by gradient systems, discrete decision variables are treated as continuous ones. We demonstrate a systematic way to build the kind of gradient systems in which equilibrium points are embedded at feasible solutions of a mixed-integer problem. For numerical computation, the multiple equilibrium points search method we have already proposed is available and its adjustments to improve efficiency and certainly for mixed-integer programming are also proposed in this paper. Results for some problems show the effectiveness of our method: high ability of thorough search and high quality of derived solutions. (C) 2009 Wiley Periodicals, Inc. Electron Comm Jpn, 92(8): 53-63, 2009;Published online in Wiley InterScience (***). DOI 10.1002/ecj.10037

关键词： mixed-integer programming global optimization gradient system multiple equilibrium points search

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Elastic Rerouting - models and resolution methods 6

Elastic Rerouting - models and resolution methods

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6th International Workshop on Reliable Networks Design and Modeling

作者： Fouquet, Yoann Nace, Dritan Pioro, Michal Poss, Michael Zotkiewicz, Mateusz Univ Technol Compiegne Lab Heudiasyc UMR CNRS 7253 Compiegne France Warsaw Univ Technol Dept Elect & Informat Technol PL-00661 Warsaw Poland Lund Univ Dept Elect & Informat Technol S-22100 Lund Sweden

ISBN: (纸本)9781479970407

This study is concerned with an original traffic restoration strategy for wide-area communication networks called Elastic Rerouting (ER). ER aims at alleviating the trade-off between the network cost and traffic restoration complexity observed in existing solutions. We present the strategy, provide a mathematical formulation for the ER related optimization problem, and discuss an approach to its resolution. We also report results of a numerical illustrating effectiveness of ER in terms of the link capacity cost.

关键词： survivability traffic restoration mixed-integer programming branch-and-bound

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Optimal Transmission Switching Based on Auxiliary Induce Function

Optimal Transmission Switching Based on Auxiliary Induce Fun...

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IEEE PES General Meeting

作者： Yang, Zhifang Zhong, Haiwang Xia, Qing Tsinghua Univ Dept Elect Engn State Key Lab Power Syst Beijing 100084 Peoples R China

ISBN: (纸本)9781479964154

Optimal transmission switching (OTS) has become a research focus in recent years as a new operational method for power systems. OTS is modeled as a mixed-integer programming (MIP) problem and it is difficult to solve it within short time horizon. Current acceleration heuristics cannot guarantee both the computational accuracy and efficiency. In this paper, a new concept called auxiliary induce function (AIF) is proposed. Based on the result of the relaxation problem, the coefficients of integer variables are strategically decided in AIF. Then the AIF algorithm is proposed, which properly adds the AIF function into the objective function of the OTS model. AIF algorithm is able to speed up the solving process for OTS while achieving exactly the same optimal solution. Case study on the IEEE 118-bus system shows that the AIF algorithm can improve 5 times as much the computation speed while obtaining the same optimal solution. Another case study on the IEEE 662-bus system indicates that the AIF algorithm is also capable of further improving the computational efficiency of current acceleration heuristics.

关键词： Security-constrained economic dispatch mixed-integer programming optimal transmission switching auxiliary induce function relaxation solution

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A Operational Optimization Model for Wind Power and Pumped-storage Plant Based on Stochastic programming 6

A Operational Optimization Model for Wind Power and Pumped-s...

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China International Conference on Electricity Distribution (CICED)

作者： Liu, Chunhui Zhang, Liudong Liu, Wanxia Nanjing Univ Sci & Technol Sch Automat Nanjing Jiangsu Peoples R China Inner Mongolia Univ Finance & Econ Inst Stat & Math Hohhot Inner Mongolia Peoples R China

ISBN: (纸本)9781479941254

Based on the day-ahead forecast of system load and wind power output. A joint operation of pumped storage and wind power plants model is built with the purpose of minimizing the system operation cost. In order to achieve the higher system flexibility and reduce the impact of volatility of wind power, pumped-storage units are incorporated into the unit commitment (UC) problem with wind power. The UC problem of the joint operation of pumped-storage and wind power plants is formulated as the mixed integer convex program, which is optimized by Cplex. Conducted on a ten-unit system simulation, we can get the conclusion that the joint operation of pumped-storage and wind power plants is effective to reduce the impact of volatility of wind power on the power grid operation. At the same time, economic benefit is remarkable.

关键词： joint operation mixed-integer programming pumped-storage wind power wind power scenario

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Applying Robust Optimization to MISO Look-Ahead Commitment

Applying Robust Optimization to MISO Look-Ahead Commitment

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IEEE PES General Meeting

作者： Chen, Yonghong Wang, Qianfan Wang, Xing Guan, Yongpei Midcontinent Independent Syst Operator Inc MISO Carmel IN 46032 USA

ISBN: (纸本)9781479964154

Managing uncertainty has been a challenging task for market operations. This paper first reviews the current practice of managing uncertainties at MISO. A framework of using robust optimization based approach on MISO Look-Ahead commitment (LAC) is then introduced. The numerical results show that this type of approaches are promising and yet with challenges to overcome in order to be practical for real world application.

关键词： Uncertainty Look-Ahead Unit Commitment mixed-integer programming Two-Stage Robust Optimization

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Optimal Control Formulations for the Unit Commitment Problem 1

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5th International Conference on the Dynamics of Information Systems

作者： Fontes, Dalila B. M. M. Fontes, Fernando A. C. C. Roque, Luis A. C. Univ Porto LIAAD INESC TEC Rua Dr Roberto Frias P-4200464 Oporto Portugal Univ Porto Rua Dr Roberto Frias Inst Sistemas Robot Porto Fac Engn P-4200465 Porto Portugal Inst Super Engenharia Porto Dept Matemat Porto Portugal

ISBN: (数字)9783319100463

ISBN: (纸本)9783319100456

The unit commitment (UC) problem is a well-known combinatorial optimization problem arising in operations planning of power systems. It involves deciding both the scheduling of power units, when each unit should be turned on or off, and the economic dispatch problem, how much power each of the on units should produce, in order to meet power demand at minimum cost while satisfying a set of operational and technological constraints. This problem is typically formulated as nonlinear mixed-integer programming problem and has been solved in the literature by a huge variety of optimization methods, ranging from exact methods (such as dynamic programming and branch-and-bound) to heuristic methods (genetic algorithms, simulated annealing, and particle swarm). Here, we discuss how the UC problem can be formulated with an optimal control model, describe previous discrete-time optimal control models, and propose a continuous-time optimal control model. The continuous-time optimal control formulation proposed has the advantage of involving only real-valued decision variables (controls) and enables extra degrees of freedom as well as more accuracy, since it allows to consider sets of demand data that are not sampled hourly.

关键词： Unit commitment problem Power systems planning Nonlinear optimization mixed-integer programming Optimal control

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