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Solving a mathematical model integrating unequal-area facilities layout and part scheduling in a cellular manufacturing system by a genetic algorithm

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SPRINGERPLUS 2016年第1期5卷 1页

作者： Ebrahimi, Ahmad Kia, Reza Komijan, Alireza Rashidi Islamic Azad Univ Firoozkooh Branch Dept Ind Engn Firoozkooh Iran

In this article, a novel integrated mixed-integer nonlinear programming model is presented for designing a cellular manufacturing system (CMS) considering machine layout and part scheduling problems simultaneously as interrelated decisions. The integrated CMS model is formulated to incorporate several design features including part due date, material handling time, operation sequence, processing time, an intra-cell layout of unequal-area facilities, and part scheduling. The objective function is to minimize makespan, tardiness penalties, and material handling costs of inter-cell and intra-cell movements. Two numerical examples are solved by the Lingo software to illustrate the results obtained by the incorporated features. In order to assess the effects and importance of integration of machine layout and part scheduling in designing a CMS, two approaches, sequentially and concurrent are investigated and the improvement resulted from a concurrent approach is revealed. Also, due to the NP-hardness of the integrated model, an efficient genetic algorithm is designed. As a consequence, computational results of this study indicate that the best solutions found by GA are better than the solutions found by B&B in much less time for both sequential and concurrent approaches. Moreover, the comparisons between the objective function values (OFVs) obtained by sequential and concurrent approaches demonstrate that the OFV improvement is averagely around 17 % by GA and 14 % by B&B.

关键词： Cellular manufacturing system Machine layout Part scheduling mixed-integer nonlinear programming Genetic algorithm

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Constraint qualification failure in action

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OPERATIONS RESEARCH LETTERS 2016年第4期44卷 503-506页

作者： Hijazi, Hassan Liberti, Leo Australian Natl Univ CSIRO Data61 Canberra ACT 2601 Australia Ecole Polytech CNRS LIX F-91128 Palaiseau France

This note presents a theoretical analysis of disjunctive constraints featuring unbounded variables. In this framework, classical modeling techniques, including big-M approaches, are not applicable. We introduce a lifted second-order cone formulation of such on/off constraints and discuss related constraint qualification issues. A solution is proposed to avoid solvers' failure. (C) 2016 Elsevier B.V. All rights reserved.

关键词： mixed-integer nonlinear programming Disjunctive programming Second-order cone programming On/off constraints Constraint qualification

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A superstructure-based framework for simultaneous process synthesis, heat integration, and utility plant design

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COMPUTERS & CHEMICAL ENGINEERING 2016年 91卷 68-84页

作者： Kong, Lingxun Sen, S. Murat Henao, Carlos A. Dumesic, James A. Maravelias, Christos T. Univ Wisconsin Dept Chem & Biol Engn Madison WI 53706 USA

We propose a superstructure optimization framework for process synthesis with simultaneous heat integration and utility plant design. Processing units in the chemical plant can be modeled using rigorous unit models or surrogate models generated from experimental results or off-line calculations. The utility plant subsystem includes multiple steam types with variable temperature and pressure. For the heat integration subsystem, we consider variable heat loads of process streams as well as variable intervals for the utilities. To enhance the solution of the resulting mixed-integer nonlinear programming models, we develop (1) new methods for the calculation of steam properties, (2) algorithms for variable bound calculation, and (3) systematic methods for the generation of redundant constraints. The applicability of our framework is illustrated through a biofuel case study which includes a novel non-enzymatic hydrolysis technology and new separation technologies, both of which are modeled based on experimental results. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Chemical process design mixed-integer nonlinear programming Global optimization Biofuels

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A Superstructure Representation, Generation, and Modeling Framework for Chemical Process Synthesis

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AICHE JOURNAL 2016年第9期62卷 3199-3214页

作者： Wu, WenZhao Henao, Carlos A. Maravelias, Christos T. Univ Wisconsin Dept Chem & Biol Engn Madison WI 53706 USA Univ Wisconsin DOE Great Lakes Bioenergy Res Ctr Madison WI 53706 USA

We present a framework for the efficient representation, generation, and modeling of superstructures for process synthesis. First, we develop a new representation based on three basic elements: units, ports, and conditioning streams. Second, we present four rules based on "minimal" and "feasible" component sets for the generation of simple superstructures containing all feasible embedded processes. Third, in terms of modeling, we develop a modular approach, and formulate models for each basic element. We also present a canonical form of element models using input/output variables and constrained/free variables. The proposed methods provide a coherent framework for superstructure-based process synthesis, allowing efficient model generation and modification. (C) 2016 American Institute of Chemical Engineers

关键词： optimization mixed-integer nonlinear programming

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Solving Chance-Constrained Optimization Problems with Stochastic Quadratic Inequalities

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OPERATIONS RESEARCH 2016年第4期64卷 939-957页

作者： Lejeune, Miguel A. Margot, Francois George Washington Univ Washington DC 20052 USA Carnegie Mellon Univ Tepper Sch Business Pittsburgh PA 15213 USA

We propose a new and systematic reformulation and algorithmic approach to solve a complex class of stochastic programming problems involving a joint chance constraint with random technology matrix and stochastic quadratic inequalities. The method is general enough to apply to nonconvex as well as nonseparable quadratic terms. We derive two new reformulations and give sufficient conditions under which the reformulated problem is equivalent. The second reformulation provides a much sparser representation of the feasible set of the chance constraint and offers tremendous computational advantages. This new reformulation method can be used for linear stochastic inequalities and will also significantly improve the solution of such joint chance-constrained problems. We provide general and easily identifiable conditions under which the base reformulations can be linearized. We show that the size of the reformulated problems, in particular, their number of binary variables and quadratic mixed-integer terms, does not grow linearly with the number of scenarios used to represent uncertainty. We propose two new nonlinear branch-and-bound algorithms for the nonconvex quadratic integer reformulations. We present detailed empirical results, comparing the various reformulations and several algorithmic ideas that improve the performance of the mixed-integer nonlinear solver Couenne for solving these problems. Guidelines on how to tune the solver and to select reformulations are presented. The test instances are epidemiology and disaster management facility location models and cover the three types of stochastic quadratic inequalities, namely, product of two decision variables that are both binary, binary and continuous, or both continuous.

关键词： stochastic programming mixed-integer nonlinear programming Boolean programming nonlinear branch-and-bound algorithm quadratic stochastic inequality joint probabilistic constraint random technology matrix epidemiology facility location

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Normalized multiparametric disaggregation: an efficient relaxation for mixed-integer bilinear problems

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JOURNAL OF GLOBAL OPTIMIZATION 2016年第4期64卷 765-784页

作者： Castro, Pedro M. Univ Lisbon Fac Ciencias CMAF CIO P-1749016 Lisbon Portugal

A key element for the global optimization of non-convex mixed-integer bilinear problems is the computation of a tight lower bound for the objective function being minimized. Multiparametric disaggregation is a technique for generating a mixed-integer linear relaxation of a bilinear problem that works by discretizing the domain of one of the variables in every bilinear term according to a numeric representation system. This can be done up to a certain accuracy level that can be different for each discretized variable so as to adjust the number of significant digits to their range of values and give all variables the same importance. We now propose a normalized formulation (NMDT) that achieves the same goal using a common setting for all variables, which is equivalent to the number of uniform partitions in a closely related, piecewise McCormick (PCM) approach. Through the solution of several benchmark problems from the literature involving four distinct problem classes, we show that the computational performance of NMDT is already better than PCM for ten partitions, with the difference rising quickly due to the logarithmic versus linear growth in the number of binary variables with the number of partitions. The results also show that a global optimization solver based on the proposed relaxation compares favorably with commercial solvers BARON and GloMIQO.

关键词： mixed-integer nonlinear programming Quadratic optimization Disjunctive programming Algorithm Process networks

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A specialized branch-and-bound algorithm for the Euclidean Steiner tree problem in n-space

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2016年第1期65卷 47-71页

作者： Fampa, Marcia Lee, Jon Melo, Wendel Univ Fed Rio de Janeiro Inst Matemt Rio De Janeiro Brazil Univ Fed Rio de Janeiro COPPE PESC Rio De Janeiro Brazil Univ Michigan Ann Arbor MI 48109 USA

We present a specialized branch-and-bound (b&b) algorithm for the Euclidean Steiner tree problem (ESTP) in and apply it to a convex mixed-integer nonlinear programming (MINLP) formulation of the problem, presented by Fampa and Maculan. The algorithm contains procedures to avoid difficulties observed when applying a b&b algorithm for general MINLP problems to solve the ESTP. Our main emphasis is on isomorphism pruning, in order to prevent solving several equivalent subproblems corresponding to isomorphic Steiner trees. We introduce the concept of representative Steiner trees, which allows the pruning of these subproblems, as well as the implementation of procedures to fix variables and add valid inequalities. We also propose more general procedures to improve the efficiency of the b&b algorithm, which may be extended to the solution of other MINLP problems. Computational results demonstrate substantial gains compared to the standard b&b for convex MINLP.

关键词： Euclidean Steiner tree problem mixed-integer nonlinear programming Branch-and-bound Isomorphism pruning

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Arbitrage strategy of virtual power plants in energy, spinning reserve and reactive power markets

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IET GENERATION TRANSMISSION & DISTRIBUTION 2016年第3期10卷 750-763页

作者： Nezamabadi, Hossein Nazar, Mehrdad Setayesh Shahid Beheshti Univ Fac Elect Engn AC Tehran Iran

Virtual power plant (VPP) concept was developed to integrate distributed energy resources (DERs) into the grid in order that they are seen as a single power plant by the market and power system operator. Therefore, VPPs are faced with optimal bidding, and identifying arbitrage opportunities in a market environment. In this study, the authors present an arbitrage strategy for VPPs by participating in energy and ancillary service (i.e. spinning reserve and reactive power services) markets. On the basis of a security-constrained price-based unit commitment, their proposed model maximises VPP's profit (revenue minus costs) considering arbitrage opportunities. The supply-demand balancing, transmission network topology and security constraints are considered to ensure reliable operation of VPP. The mathematical model is a mixed-integer non-linear optimisation problem with inter-temporal constraints, and solved by mixed-integer non-linear programming. The result is a single optimal bidding profile and a schedule for managing active and reactive power under participating in the markets. These profile and schedule consider the DERs and network constraints simultaneously, and explore arbitrage opportunities of VPP. Results pertaining to an illustrative example and a case study are discussed.

关键词： distributed power generation power distribution economics power transmission economics power markets power system management power system security integer programming nonlinear programming power generation scheduling reactive power management active power management mixed-integer nonlinear programming intertemporal constraints mixed-integer nonlinear optimisation problem mathematical model transmission network security constraint transmission network topology constraint supply-demand balancing security-constrained price-based unit commitment VPP profit maximization ancillary service market energy service market single optimal bidding profile power system operator distributed energy resource integration reactive power markets spinning reserve virtual power plants arbitrage strategy

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Assessing solution quality and computational performance in the hydro unit commitment problem considering different mathematical programming approaches

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ELECTRIC POWER SYSTEMS RESEARCH 2016年 136卷 212-222页

作者： Finardi, E. C. Takigawa, F. Y. K. Brito, B. H. Univ Fed Santa Catarina Elect Syst Planning Res Lab BR-88040900 Florianopolis SC Brazil Fed Inst Santa Catarina BR-88020300 Florianopolis SC Brazil Fed Inst Tocantins BR-77020450 Palmas Brazil

This paper presents a comparative analysis of different mathematical programming approaches for optimizing the hydro unit commitment (HUC) problem with cascaded plants, multiple generating units, and a head-dependent hydropower model. Regarding the HUC problem related to this paper, the objective is to minimize the cascade outflow while satisfying all constraints, including a power target for each plant, in a day-ahead planning horizon. The decision variables are the on/off status of the units and the respective generation levels. Rigorously, the HUC is a mixed-integer nonlinear programming (MINLP) problem, and several strategies can be used to compute near-optimal solutions. In this paper, we are interested in accessing the solution quality, as well as the computational performance when the HUC problem is solved using the following mathematical programming approaches: (i) the Lagrangian relaxation that represents a decomposition technique that exploits the HUC modeling structure, (ii) a MINLP solver that can handle the size and the non-concavity of the problem, and (iii) a mixed-integer linear programming (MILP) approach obtained by means of the hydropower model linearization. To perform the proposed analysis, numerical results are presented related to a real hydro system with eight cascaded reservoirs and 29 generating units. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Hydro unit commitment Lagrangian relaxation mixed-integer nonlinear programming mixed-integer linear programming Hydropower model

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Simultaneous Model Selection and Parameter Estimation for Lithium-Ion Batteries: A Sequential MINLP Solution Approach

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AICHE JOURNAL 2016年第1期62卷 78-89页

作者： Shen, Jia-Ni He, Yi-Jun Ma, Zi-Feng Shanghai Jiao Tong Univ Dept Chem Engn Shanghai Electrochem Energy Devices Res Ctr Shanghai 200240 Peoples R China

Equivalent circuit model (ECM) is a practical and commonly used tool not only in state of charge (SOC) estimation but also in state of health (SOH) monitoring for lithium-ion batteries (LIBs). The functional forms of circuit parameters with respect to SOC in ECM are usually empirical determined, which cannot guarantee to obtain a compact and simple model. A systematical solution framework for simultaneous functional form selection and parameter estimation is proposed. A bi-objective mixed-integer nonlinear programming (MINLP) model is first constructed. Two solution approaches, namely the explicit and implicit methods, are then developed to balance model accuracy and model complexity. The former explicitly treats the model complexity as a constraint and the latter implicitly embeds the model complexity into the objective as a penalty. Both approaches require sequential solution of the transformed MINLP model and an ideal and nadir ideal solutions-based criterion is utilized to terminate the solution procedure for determining the optimal functional forms, in which ideal solution and nadir ideal solution represent the best and worst of each objective, respectively. Both explicit and implicit approaches are thoroughly evaluated and compared through experimental pulse current discharge test and hybrid pulse power characterization test of a commercial LIB. The fitting and prediction results illustrate that the proposed methods can effectively construct an optimal ECM with minimum complexity and prescribed precision requirement. It is thus indicated that the proposed MINLP-based solution framework, which could automatically guide the optimal ECM construction procedure, can be greatly helpful to both SOC estimation and SOH monitoring for LIBs. (C) 2015 American Institute of Chemical Engineers

关键词： lithium-ion batteries state of charge equivalent circuit model functional forms selection parameter estimation mixed-integer nonlinear programming

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