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Extended cross decomposition for mixed-integer linear programs with strong and weak linking constraints

COMPUTERS & CHEMICAL ENGINEERING 2018年 119卷 237-257页

作者： Ogbe, Emmanuel Li, Xiang Queens Univ Dept Chem Engn 19 Div St Kingston ON K7L 3N6 Canada

Large-scale mixed-integer linear programming (MILP) problems, such as those from two-stage stochastic programming, usually have a decomposable structure that can be exploited to design efficient optimization methods. Classical Benders decomposition can solve MILPs with weak linking constraints (which are decomposable when linking variables are fixed) but not strong linking constraints (which are not decomposable even when linking variables are fixed). In this paper, we first propose a new rigorous bilevel decomposition strategy for solving MILPs with strong and weak linking constraints, then extend a recently developed cross decomposition method based on this strategy. We also show how to apply the extended cross decomposition method to two-stage stochastic programming problems with conditional-value-at-risk (CVaR) constraints. In the case studies, we demonstrate the significant computational advantage of the proposed extended cross decomposition method as well as the benefit of including CVaR constraints in stochastic programming. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Cross decomposition Benders decomposition Dantzig-Wolfe decomposition Risk-averse stochastic programming mixed-integer linear programming

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Cyclic jobshop hoist scheduling with multi-capacity reentrant tanks and time-window constraints

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COMPUTERS & INDUSTRIAL ENGINEERING 2018年 120卷 382-391页

作者： Feng, Jianguang Chu, Chengbin Che, Ada Northwestern Polytech Univ Sch Management Xian 710072 Shaanxi Peoples R China Univ Paris Est ESIEE Paris 2 Blvd Blaise PascalCite Descartes BP 99 F-93162 Noisy Le Grand France Univ Paris Saciay Cent Supelec Lab Genie Ind 3 Rue Joliot Curie F-91190 Gif Sur Yvette France

This paper studies the cyclic jobshop hoist scheduling with multi-capacity reentrant tanks and time-window constraints. Parts of different types are processed in a series of tanks with bounded processing times. Multi capacity tanks are used to handle stages with long processing times. Tanks can be reentrant so that a part visits them more than once. A hoist is responsible for the transportation of parts between tanks. We consider the cyclic scheduling where multiple parts enter and leave the production line during a cycle. The difficulty to deal with the problem lies in how to effectively handle the constraints related to multi-capacity reentrant tanks and their relations with time windows. To this end, a mixed-integer linear programming model is developed by addressing the time-window constraints and tank capacity constraints in a novel way. Computational experiments are conducted to demonstrate the effectiveness of the proposed model.

关键词： Cyclic jobshop scheduling Hoist scheduling Multi-capacity reentrant tanks mixed-integer linear programming

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Multiobjective optimal setting for UFLS relays considering voltage deviation

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INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS 2019年第3期29卷 e2770.1-e2770.14页

作者： Alizadeh, Mohammad Jafari-Nokandi, Meysam Amraee, Turaj Babol Noshirvani Univ Technol Dept Elect & Comp Engn Babol Sar Iran KN Toosi Univ Dept Elect & Comp Engn Tehran Iran

The postdisturbance power imbalance causes the power system frequency to drop. For preventing the frequency drop below the safe range, under frequency load shedding (UFLS) plan should be used by applying UFLS relays. In this paper, the conventional multistage UFLS plan is promoted via a linearized AC power flow model. A multiobjective mixed-integer linear program is solved in order to minimize the load shedding amount and voltage deviation simultaneously. The proposed method simultaneously benefits from individual UFLS and under voltage LS (UVLS) features which may operate in the power system without coordination. The proposed method has been implemented in IEEE 39-bus test system, and the results are presented under different scenarios. The results show that the proposed model for locating UFLS relays and their optimal setting can maintain both the system frequency and bus voltages in the secure operating limits.

关键词： frequency stability mixed-integer linear programming under frequency load shedding voltage deviation

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ReLU networks as surrogate models in mixed-integer linear programs

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COMPUTERS & CHEMICAL ENGINEERING 2019年 131卷 106580-000页

作者： Grimstad, Bjarne Andersson, Henrik Solut Seeker AS Gaustadalleen 21 N-0349 Oslo Norway Norwegian Univ Sci & Technol Dept Ind Econ & Technol Management NO-7491 Trondheim Norway

We consider the embedding of piecewise-linear deep neural networks (ReLU networks) as surrogate models in mixed-integer linear programming (MILP) problems. A MILP formulation of ReLU networks has recently been applied by many authors to probe for various model properties subject to input bounds. The formulation is obtained by programming each ReLU operator with a binary variable and applying the big-M method. The efficiency of the formulation hinges on the tightness of the bounds defined by the big-M values. When ReLU networks are embedded in a larger optimization problem, the presence of output bounds can be exploited in bound tightening. To this end, we devise and study several bound tightening procedures that consider both input and output bounds. Our numerical results show that bound tightening may reduce solution times considerably, and that small-sized ReLU networks are suitable as surrogate models in mixed-integer linear programs. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Deep neural networks ReLU networks mixed-integer linear programming Surrogate modeling Regression

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Comparing Spatial and Scenario Decomposition for Stochastic Hydrothermal Unit Commitment Problems

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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 2018年第3期9卷 1307-1317页

作者： Scuzziato, Murilo Reolon Finardi, Erlon Cristian Frangioni, Antonio Inst Fed Santa Catarina Dept Acad Electrotecn BR-88020300 Florianopolis SC Brazil Univ Fed Santa Catarina Dept Engn Eletr BR-88040900 Florianopolis SC Brazil Univ Pisa Dipartimento Informat I-56126 Pisa Italy

Solving very-large-scale optimization problems frequently require to decompose them in smaller subproblems, which are iteratively solved to produce useful information. One such approach is the Lagrangian relaxation (LR), a general technique that leads to many different decomposition schemes. The LR produces a lower bound of the objective function and useful information for heuristics aimed at constructing feasible primal solutions. In this paper, we compare the main LR strategies used so far for stochastic hydrothermal unit commitment problems, where uncertainty mainly concerns water availability in reservoirs and demand (weather conditions). The problem is customarily modeled as a two-stage mixed-integer optimization problem. We compare different decomposition strategies (unit and scenario schemes) in terms of quality of produced lower bound and running time. The schemes are assessed with various hydrothermal systems, considering different configuration of power plants, in terms of capacity and number of units.

关键词： Lagrangian relaxation mixed-integer linear programming hydrothermal stochastic unit commitment

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Robust supply chain network design with multi-products for a company in the food sector

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APPLIED MATHEMATICAL MODELLING 2018年 60卷 526-539页

作者： Aras, Necati Bilge, Umit Bogazici Univ Dept Ind Engn Istanbul Turkey

The paper aims to solve a problem faced by a company competing in the snacks market in Turkey. In line with the growth in this market, the company needs to make important decisions over the next few years about the timing and location of a new plant, its initial capacity, the timing and amount of additional capacity to be installed at the new and existing plants, the assignment of demand points to plants and the amount of raw materials to be shipped from suppliers to the plants in each period. The objective is to minimize the total cost of various components. The problem is formulated as a multi-period supply chain network design model with multi products. The resulting mixed-integer linear programming model is solved by the commercial solver CPLEX. This model enables us to carry out all analyses requested by the company in an efficient way. After this deterministic model is solved on the basis of a 9% annual increase in demand, it is extended to a minimax regret model to deal with uncertainty in demand quantities. The results suggest that opening the new plant in the city of Izmir is indeed a robust solution that is unaffected in different scenarios that are based on three distinct demand increase rates. Even though the location of the new plant remains unchanged with respect to scenarios, the optimal robust solution differs from the optimal solution of each scenario in terms of the capacity expansion decisions. After all obtained results had been communicated to the company managers and executives, the new plant construction was started in 2016 very close to the city that the mathematical model had determined. The new plant is expected to start operating in 2018. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Supply chain network design mixed-integer linear programming Demand uncertainty Robust optimization Facility location-allocation

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A multi-timescale hybrid stochastic/deterministic generation scheduling framework with flexiramp and cycliramp costs

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2018年第Jul.期99卷 585-593页

作者： Shaaban, Mohamed Tan, Wen-Shan Abdullah, Md. Pauzi Univ Malaysia Sarawak Fac Engn Dept Elect & Elect Engn Kota Samarahan 94300 Sarawak Malaysia Port Said Univ Fac Engn Dept Elect Engn Port Fouad 42526 Port Said Egypt Univ Teknol Malaysia Inst Future Energy Ctr Elect Energy Syst Johor Baharu 81310 Malaysia

Flexible ramping products (flexiramp), provided by entitled resources to meet net demand forecast error, are the underpinning for the accommodation of the substantial uncertainties associated with variable wind power. This paper proposes an enhanced flexiramp modeling approach, cast in a hybrid stochastic/deterministic multi-timescale framework. The framework employs a chance-constrained day-ahead scheduling method, as well as deterministic scheduling on intra-hourly basis (real-time scheduling), to allow optimal procurement planning of the flexiramp products in both timescales. A stepwise and piecewise demand price curve is also proposed to calculate the flexiramp surplus procurement price. Non-generation resource (NGR), referring to energy storage, is implemented to provide extra flexibility. Additionally, cycling ramping cost (cycliramp), introduced to model operational and maintenance costs and reduce the wear and tear of generators, is also included as a penalty. Numerical tests are conducted on 6-bus and 118-bus systems. Results demonstrate the merits of the proposed scheduling model as well as the effects of flexiramp and cycliramp costs in the multi-timescale scheduling.

关键词： Flexible ramping product Generation unit ramping cost Ramp market Renewable energy integration mixed-integer linear programming

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Bi-objective optimization of biochar-based carbon management networks

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JOURNAL OF CLEANER PRODUCTION 2018年 188卷 911-920页

作者： Belmonte, Beatriz A. Benjamin, Michael Francis D. Tan, Raymond R. De La Salle Univ Chem Engn Dept 2401 Taft Ave Manila 0922 Philippines Univ Santo Tomas Chem Engn Dept Espana Blvd Manila 1015 Philippines Univ Santo Tomas Res Ctr Nat & Appl Sci Espana Blvd Manila 1015 Philippines

Biochar is the carbon-rich solid product derived from thermochemical processing of biomass. Its application to soil can sequester atmospheric carbon, leading to negative net emissions, while also improving agricultural yield. Biochar-based carbon management networks thus have the potential for scalable contributions to climate change mitigation efforts. However, it is necessary to allocate biochar of suitable quality to appropriate sinks, based on contaminant tolerance limits of soil. In this work, the network is modelled as a bi-objective mixed integer linear programming model, with profit and carbon sequestration as the objective functions. The model calculates the optimum allocation of biochar such that their prescribed limits for the contaminants are met. A Philippine case study is solved under different scenarios to illustrate the practical use of the developed model. The results provide useful insights for the rational decision-maker to arrive at the most preferred solution among the Pareto optimal choices. Comparison of the two scenarios substantiate the significance of unique sequestration factor as an additional parameter in the model to account for the interactions between the soils and biochars so that the maximum sustainable potential of biochar in climate change mitigation can be properly assessed. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Biochar Negative emissions technology Bi-objective optimization Carbon management network Source-sink model mixed-integer linear programming

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Integration of Flow Temperatures in Unit Commitment Models of Future District Heating Systems

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ENERGIES 2019年第6期12卷 1061-1061页

作者： Boysen, Cynthia Kaldemeyer, Cord Hilpert, Simon Tuschy, Ilja Ctr Sustainable Energy Syst ZNES D-24943 Flensburg Germany Flensburg Univ Appl Sci Dept Energy & Biotechnol Kanzleistr 91-93 D-24943 Flensburg Germany Europa Univ Flensburg Dept Energy & Environm Management Campus 1 D-24943 Flensburg Germany

The transformation of heat supply structures towards 4th generation district heating (4GDH) involves lower supply temperatures and a shift in technology. In order to assess the economic viability of the respective systems, adequate unit commitment models are needed. However, maintaining the formal requirements, while reducing the computational efforts of these models, often includes simplifications such as the assumption of constant supply temperatures. This study investigates the effect of introducing varying supply temperatures in mixed-integer linear programming models. Based on a case study of a municipal district heating system, how the temperature integration approach affects unit commitment and technology assessment for different temperature levels and scenarios is analyzed. In particular, three supply temperature levels are investigated with both variable and constant temperatures in two scenarios. Results indicate that lower flow temperature levels in the heating network tend to favor internal combustion engines, combined cycle power plants, and heat pumps;while back pressure steam turbines, peak loads, and electric boilers show declining operating hours. Furthermore, the effect of varying versus constant temperatures at the same temperature level is rather small, at least as long as technical restrictions do not come into play. Finally, it is found that the effect of changing temperature on a technology assessment is comparably small as opposed to adaptions in the regulatory framework.

关键词： mixed-integer linear programming unit commitment district heating systems supply temperature low temperature levels

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A new formulation of the electric vehicle routing problem with time windows considering concave nonlinear charging function

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JOURNAL OF CLEANER PRODUCTION 2019年 236卷 117687-000页

作者： Zuo, Xiaorong Xiao, Yiyong You, Meng Kaku, Ikou Xu, Yuchun China Aerosp Acad Syst Sci & Engn Beijing 100854 Peoples R China Beihang Univ Sch Reliabil & Syst Engn Beijing 100191 Peoples R China Tokyo City Univ Dept Environm Management Yokohama Kanagawa 2248551 Japan Aston Univ Sch Engn & Appl Sci Birmingham B4 7ET W Midlands England

The electric vehicle routing problem with time window (EVRPTW) is an extension of the traditional vehicle routing problem with time window (VRPTW), where new features of electric vehicles are considered, such as limited battery capacities, lack of infrastructures, and long charging time. In this study, new technical formulations were presented for vehicle route selection and charging station visit, which reduces the formulation complexity without using duplicated dummy nodes or arcs. Besides, a new linearization method was developed that employs a set of secant lines to surrogate the concave nonlinear charging function with linear constraints. This method defines the charging time as a continuous variable and uses fewer variables than existing formulation in literature. A mixed-integer linear programming (MILP) model was developed for the EVRPTW and computational experiments on Solomon's VRPTW instances were conducted to verify the proposed model. The experimental results were compared with those obtained by traditional routing models, which showed that the proposed model can result in better EVs logistics schedules with higher charging time utilizations. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Electric vehicle routing problem mixed-integer linear programming Nonlinear charging function Continuous optimization

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