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Achieving MILP feasibility quickly using general disjunctions

COMPUTERS & OPERATIONS RESEARCH 2013年第8期40卷 2094-2102页

作者： Mahmoud, Hanan Chinneck, John W. Carleton Univ Ottawa ON K1S 5B6 Canada

Branch and bound algorithms for mixed-integer linear programming (MILP) almost universally branch on a single variable to create disjunctions. General linear expressions involving multiple variables are another option for branching disjunctions, but are not used for two main reasons: (i) descendent LPs tend to solve more slowly because of the added constraints, so the overall solution time is increased, and (ii) it is difficult to quickly find an effective general disjunction. We study the use of general disjunctions to reach the first MILP-feasible solution quickly, showing for the first time that general disjunctions can provide speed improvements for hard MILP models. The speed-up is due to new and efficient ways to (i) trigger the inclusion of a general disjunction only when it is likely to be beneficial, and (ii) construct effective general disjunctions very quickly. Our empirical results show performance improvements versus a state of the art commercial MILP solver. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： mixed integer linear programming General disjunctions Branching

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Designing and planning a multi-echelon multi-period multi-product closed-loop supply chain utilizing genetic algorithm

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2013年第1-4期68卷 917-931页

作者： Soleimani, Hamed Seyyed-Esfahani, Mirmehdi Shirazi, Mohsen Akbarpour Amirkabir Univ Technol Dept Ind Engn & Management Syst Tehran Polytech Tehran Iran

Designing and planning a closed-loop supply chain in a comprehensive structure is vital for its applicability. To cope with the design and planning issue of a comprehensive closed-loop supply chain network, this paper develops an extended model, which is multi-echelon, multi-product, and multi-period in a mixed integer linear programming framework. The word "comprehensive," in our mathematical approach, in designing and planning a closed-loop supply chain problem, can be analyzed from two complementary angles: including all possible entities (facilities) of a real condition and considering minimum limitations on possible flows between entities. In our proposed model, customers can be supplied via manufacturers, warehouses, and distributors, as an example. The proposed model is solved by CPLEX optimization software and by a developed genetic algorithm. During this computational analysis, we compare results of proposed pretuned genetic algorithm with a global optimum of CPLEX solver. Then, a sufficient number of large-size instances are generated and solved by the proposed genetic algorithm. To the best of our knowledge, there has been no similar multi-period multi-product closed-loop supply chain design and planning problem utilizing any kind of meta-heuristics let alone genetic algorithms. Therefore, in this issue, it is an original research, and results prove the acceptable performances of the developed genetic algorithm.

关键词： Closed-loop supplychain Design and planning Genetic algorithm mixed integer linear programming

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Optimization model for sustainable materials selection using objective and subjective factors

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MATERIALS & DESIGN 2013年 46卷 310-321页

作者： Florez, Laura Castro-Lacouture, Daniel Georgia Inst Technol Sch Bldg Construct Atlanta GA 30332 USA

Materials selection is an area where designers can have a significant impact on the sustainable performance of a building. Objective factors such as cost constraints, design considerations, and environmental requirements can play a role in the selection of materials. However, there may be subjective factors that could also impact the selection and affect the achievement of sustainability goals. In order to help decision makers with the selection of appropriate materials, this study proposes a mixed integer optimization model that considers objective and subjective factors. Design, budget, and the number of points achieved under the Leadership in Energy and Environmental Design (LEED) account for objective factors while subjective factors comprehend user-based perceptions. An instrument further validated through a factor analysis approach is developed to measure perceptions of product sustainability in an attempt to capture subjective factors. To illustrate how objective and subjective factors influence decision making, this paper presents two cases of a building in which materials are selected using the optimization model proposed. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Selection for material properties Environmental performance mixed integer linear programming Building design practices Sustainability perceptions

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Frequency-Regulating Reserve Constrained Unit Commitment for an Isolated Power System

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IEEE TRANSACTIONS ON POWER SYSTEMS 2013年第2期28卷 578-586页

作者： Chang, Gary W. Chuang, Ching-Sheng Lu, Tai-Ken Wu, Ching-Chung Natl Chung Cheng Univ Dept Elect Engn Chiayi 621 Taiwan Natl Taiwan Ocean Univ Dept Elect Engn Keelung Taiwan Taiwan Power Co Syst Operat Dept Taipei Taiwan

The purpose of unit commitment (UC) for electric utilities is to determine the optimal thermal unit on/off statuses and their MW generations over the scheduled time horizon. The UC problem is formulated to minimize the total generation cost, while the load demand, reserve requirements, and unit constraints are satisfied. Among the UC constraints, an adequate provision of reserve is important to ensure the security of the power system and the frequency-regulating reserve is essential to bring the system frequency back to acceptable level following the loss of a sizable online unit within seconds. In this paper, the authors present and solve a mixed-integer linear programming (MILP)-based UC problem including the frequency-regulating reserve (FRR) constraints to determine the optimal FRR requirements and unit MW schedules for an isolated power system. Simulation results are then compared with those obtained by Lagrangian relaxation-based approach and by the current Taipower operation practice. It is observed that favorable reserve and unit MW schedules are obtained by the proposed method while the system security is maintained.

关键词： Frequency-regulating reserve load-frequency sensitivity index mixed integer linear programming unit commitment

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Flexible disassembly planning considering product conditions

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2013年第20期51卷 6209-6228页

作者： Ullerich, Christian Buscher, Udo Tech Univ Dresden LSt BWL Fak Wirtschaftswissensch D-01062 Dresden Germany

To increase the economic benefit of product recovery at the end of life of a consumer product, the profit margins should be augmented. This can be realised by utilising the existing flexibility of today's mostly manually-conducted disassembly processes. Moreover, with increased economic benefits, the recovery becomes even more attractive, which is also beneficial to the environment. A key component of product recovery is disassembly. Allowing different disassembly states (or levels) per core (i.e. recovered product) increases flexibility in planning. This should result in higher profits, as long as the flexibility is still manageable for the companies. This study focuses on flexible disassembly planning, i.e. the integration of sequencing aspects into disassembly (process) planning. In addition, we further incorporate the condition of items in the core, item damaging, purity requirements, special treatment of hazardous items and several limitations like core availability, item, module and material distribution, disposal and labour time limit. We base our developed mixed integer linear programme on graphs, such as the disassembly state graph for sequencing, and a hypergraph to model the core condition. Lastly, our considerations are illustrated by a numerical example.

关键词： flexible disassembly planning incomplete disassembly mixed integer linear programming profit maximisation core condition material purity

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Optimal source-sink matching in carbon capture and storage systems with time, injection rate, and capacity constraints

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ENVIRONMENTAL PROGRESS & SUSTAINABLE ENERGY 2013年第2期32卷 411-416页

作者： Tan, Raymond R. Aviso, Kathleen B. Bandyopadhyay, Santanu Ng, Denny K. S. De La Salle Univ Ctr Engn & Sustainable Dev Res Dept Chem Engn Manila 1004 Philippines Indian Inst Technol Dept Energy Sci & Engn Bombay 400076 Maharashtra India

Carbon capture and storage (CCS) involves capturing relatively pure carbon dioxide (CO2) from gaseous combustion products and storing it in various reservoirs. In this work, a multiperiod mixed integer linear programming model focusing primarily on physical and temporal considerations of CO2 sourcesink matching is proposed. CO2 sources are assumed to be characterized by variable flow rates and fixed operating lives;on the other hand, CO2 sinks are characterized by finite injection rate and storage capacity limits, as well as earliest time of availability. The proposed approach takes into account important temporal issues that may be encountered in planning the CCS system, particularly when the operating lives of sources and sinks do not completely overlap. Two illustrative case studies are then solved to illustrate the use of the model to realistic CCS planning problems. (c) 2012 American Institute of Chemical Engineers Environ Prog, 32: 411-416, 2013

关键词： Carbon capture and storage sourcesink matching mixed integer linear programming

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Global optimization of bilinear programs with a multiparametric disaggregation technique

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JOURNAL OF GLOBAL OPTIMIZATION 2013年第4期57卷 1039-1063页

作者： Kolodziej, Scott Castro, Pedro M. Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA Unidade Modelacaoe Otimizacao Sistemas Lab Nacl Energia & Geol P-1649038 Lisbon Portugal

In this paper, we present the derivation of the multiparametric disaggregation technique (MDT) by Teles et al. (J. Glob. Optim., 2011) for solving nonconvex bilinear programs. Both upper and lower bounding formulations corresponding to mixed-integer linear programs are derived using disjunctive programming and exact linearizations, and incorporated into two global optimization algorithms that are used to solve bilinear programming problems. The relaxation derived using the MDT is shown to scale much more favorably than the relaxation that relies on piecewise McCormick envelopes, yielding smaller mixed-integer problems and faster solution times for similar optimality gaps. The proposed relaxation also compares well with general global optimization solvers on large problems.

关键词： Global optimization mixed integer linear programming mixed integer nonlinear programming Quadratic optimization Disjunctive programming

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Unique lifting of integer variables in minimal inequalities

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MATHEMATICAL programming 2013年第1-2期141卷 561-576页

作者： Basu, Amitabh Campelo, Manoel Conforti, Michele Cornuejols, Gerard Zambelli, Giacomo Univ Calif Davis Dept Math Davis CA 95616 USA Univ Fed Ceara Dept Estat & Matemat Aplicada Fortaleza Ceara Brazil Univ Padua Dipartimento Matemat Pura & Appl I-35121 Padua Italy Carnegie Mellon Univ Tepper Sch Business Pittsburgh PA 15213 USA Univ London London Sch Econ & Polit Sci London WC2A 2AE England

This paper contributes to the theory of cutting planes for mixed integer linear programs (MILPs). Minimal valid inequalities are well understood for a relaxation of an MILP in tableau form where all the nonbasic variables are continuous;they are derived using the gauge function of maximal lattice-free convex sets. In this paper we study lifting functions for the nonbasic integer variables starting from such minimal valid inequalities. We characterize precisely when the lifted coefficient is equal to the coefficient of the corresponding continuous variable in every minimal lifting (This result first appeared in the proceedings of IPCO 2010). The answer is a nonconvex region that can be obtained as a finite union of convex polyhedra. We then establish a necessary and sufficient condition for the uniqueness of the lifting function.

关键词： mixed integer linear programming Minimal valid inequality Lifting

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Minimising makespan heuristics for scheduling a single batch machine processing machine with non-identical job sizes

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2013年第12期51卷 3488-3500页

作者： Lee, Yoon Ho Lee, Young Hoon Yonsei Univ Dept Informat & Ind Engn Seoul 120749 South Korea

In this paper, the problem of minimising maximum completion time on a single batch processing machine is studied. A batch processing is performed on a machine which can simultaneously process several jobs as a batch. The processing time of a batch is determined by the longest processing time of jobs in the batch. The batch processing machine problem is encountered in many manufacturing systems such as burn-in operations in the semiconductor industry and heat treatment operations in the metalworking industries. Heuristics are developed by iterative decomposition of a mixed integer programming model, modified from the successive knapsack problem by Ghazvini and Dupont (1998, Minimising mean flow times criteria on a single batch processing machine with non-identical jobs sizes. International Journal of Production Economics 55: 273-280) and the waste of batch clustering algorithm by Chen, Du, and Huang (2011, Scheduling a batch processing machine with non-identical job sizes: a clustering perspective. International Journal of Production Research 49 (19): 5755-5778). Experimental results show that the suggested heuristics produce high-quality solutions comparable to those of previous heuristics in a reasonable computation time.

关键词： scheduling batch scheduling mixed integer linear programming

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The heterogeneous multi-factory production network scheduling with adaptive communication policy and parallel machine

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INFORMATION SCIENCES 2013年 219卷 181-196页

作者： Behnamian, J. Ghomi, S. M. T. Fatemi Amirkabir Univ Technol Dept Ind Engn Tehran *** Iran

Traditionally centralized manufacturing planning, scheduling, and control mechanisms are being found to be insufficiently flexible to respond to highly dynamic variations in the market requirements. In order to be competitive in today's rapidly changing business world, organizations have shifted from a centralized to a decentralized structure in many areas of decision making. Distributed scheduling is an approach that enables local decision makers to create schedules that consider local objectives and constraints within the boundaries of the overall system objectives. In this paper, we assumed that production takes place in several factories, which may be geographically distributed in different locations, in order to take advantage from the trend of globalization. In this approach, the factories that are available to process the jobs have different speeds in which each factory has parallel identical machine. The optimization criterion is the minimization of the maximum completion time or makespan among the factories. After proposing mixed integer linear programming model for the problem, we developed a heuristic and genetic algorithm. For the proposed genetic algorithm, at first, to represent the solutions, we suggested a new encoding scheme, and then proposed a local search based on the theorem developed in the paper. Finally, we compare the obtained solutions using the lower bound developed in this paper. The results show the proposed algorithms to be very efficient for different structures of instances. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Production network scheduling Distributed system Heterogeneous multi-factory mixed integer linear programming Lower bound Genetic algorithm

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