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Fast Non-Parametric Learning to Accelerate mixed-integer programming for Hybrid Model Predictive Control ⁎

IFAC-PapersOnLine 2020年第2期53卷 5239-5245页

作者： Jia-Jie Zhu Georg Martius Empirical Inference Department Max Planck Institute for Intelligent Systems Tübingen Germany Autonomous Learning Group Max Planck Institute for Intelligent Systems Tübingen Germany

Today’s fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated that exact optimal control law can be computed, e.g., by mixed-integer programming (MIP) under piecewise-affine (PWA) system models. Despite the elegant theory, online solving hybrid MPC is still out of reach for many applications. We aim to speed up MIP by combining geometric insights from hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start techniques. Following a line of work in approximate explicit MPC, the proposed learning-control algorithm, LNMS, gains computational advantage over MIP at little cost and is straightforward for practitioners to implement.

关键词： Model Predictive Control of Hybrid System Machine Learning Learning for Control Nonparametric learning mixed-integer programming

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Reinforcement learning and mixed-integer programming for power plant scheduling in low carbon systems: Comparison and hybridisation

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APPLIED ENERGY 2023年第1期349卷

作者： O'Malley, Cormac de Mars, Patrick Badesa, Luis Strbac, Goran Imperial Coll London London SW7 2AZ England UCL Gower St London WC1E 6BT England Tech Univ Madrid UPM Ronda Valencia 3 Madrid 28012 Spain

Decarbonisation is driving dramatic growth in renewable power generation. This increases uncertainty in the load to be served by power plants and makes their efficient scheduling, known as the unit commitment (UC) problem, more difficult. UC is solved in practice by mixed-integer programming (MIP) methods;however, there is growing interest in emerging data-driven methods including reinforcement learning (RL). In this paper, we extensively test two MIP (deterministic and stochastic) and two RL (model-free and with lookahead) scheduling methods over a large set of test days and problem sizes, for the first time comparing the state-of-the-art of these two approaches on a level playing field. We find that deterministic and stochastic MIP consistently produce lower-cost UC schedules than RL, exhibiting better reliability and scalability with problem size. Average operating costs of RL are more than 2 times larger than stochastic MIP for a 50-generator test case, while the cost is 13 times larger in the worst instance. However, the key strength of RL is the ability to produce solutions practically instantly, irrespective of problem size. We leverage this advantage to produce various initial solutions for warm starting concurrent stochastic MIP solves. By producing several near-optimal solutions simultaneously and then evaluating them using Monte Carlo methods, the differences between the true cost function and the discrete approximation required to formulate the MIP are exploited. The resulting hybrid technique outperforms both the RL and MIP methods individually, reducing total operating costs by 0.3% on average.

关键词： Unit commitment Reinforcement learning mixed-integer programming Renewable power uncertainty

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A general mixed-integer programming framework for efficient modeling, integration and optimization of thermodynamic cycle-based energy systems

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ENERGY CONVERSION AND MANAGEMENT 2021年 250卷 114905-114905页

作者： Liang, Yingzong Hui, Chi Wai Luo, Xianglong Chen, Jianyong Yang, Zhi Chen, Ying Guangdong Univ Technol Sch Mat & Energy Guangzhou Peoples R China Guangdong Univ Technol Guangdong Prov Key Lab Funct Soft Matter Guangzhou Peoples R China Hong Kong Univ Sci & Technol Dept Chem & Biol Engn Clear Water Bay Hong Kong Peoples R China

Thermodynamic cycles are imperative systems for energy conversion, and optimization has been an important tool to improve their thermo-economic benefits. However, off-the-shelf software is often limited by long computational time, inflexibility for modeling and numerical difficulties. Here, we present an equation-based optimization framework featuring: (1) an inclusive modeling structure applicable to various thermodynamic cycles design problems;(2) versatile thermodynamic properties estimation for different working fluids;(3) capability of working fluids optimization with complex composition;(4) an efficient formulation method to model potential phase change of streams in simple/complicated heat exchangers;(5) a systematic optimization strategy to improve solution efficiency. The framework is formulated as mixed-integer nonlinear programming models, and its performance is demonstrated by two thermodynamic cycle optimization problems and one system design problem, including a supercritical CO2 Brayton cycle, cryogenic cycle (PRICO), and concentrated solar power (CSP) system. The Brayton cycle case serves as an illustrative example to show thermodynamic cycle design combining the consideration of stream properties calculation, unit operations, and flowsheet optimization. The PRICO example shows the efficacy of the proposed framework in simultaneously optimizing flowsheet and working fluids composition with complex heat exchangers and stream phase unknown a priori. The CSP case demonstrates that the framework can be extended to system optimization problems with high accuracy multiparameter equation of state. Results prove that the framework is efficient and effective in solving thermodynamic cycle and related energy systems optimization problems.

关键词： Thermodynamic cycle Heat integration mixed-integer programming

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Learning to select cuts for efficient mixed-integer programming

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PATTERN RECOGNITION 2022年 123卷 108353-108353页

作者： Huang, Zeren Wang, Kerong Liu, Furui Zhen, Hui-Ling Zhang, Weinan Yuan, Mingxuan Hao, Jianye Yu, Yong Wang, Jun Shanghai Jiao Tong Univ Shanghai Peoples R China UCL London England Huawei Technol Noahs Ark Lab Shenzhen Peoples R China

Cutting plane methods play a significant role in modern solvers for tackling mixed-integer programming (MIP) problems. Proper selection of cuts would remove infeasible solutions in the early stage, thus largely reducing the computational burden without hurting the solution accuracy. However, the major cut selection approaches heavily rely on heuristics, which strongly depend on the specific problem at hand and thus limit their generalization capability. In this paper, we propose a data-driven and generalizable cut selection approach, named CUT RANKING , in the settings of multiple instance learning. To measure the quality of the candidate cuts, a scoring function, which takes the instance-specific cut features as inputs, is trained and applied in cut ranking and selection. In order to evaluate our method, we conduct extensive experiments on both synthetic datasets and real-world datasets. Compared with commonly used heuristics for cut selection, the learning-based policy has shown to be more effective, and is capable of generalizing over multiple problems with different properties. CUT RANKING has been deployed in an industrial solver for large-scale MIPs. In the online A/B testing of the product planning problems with more than 10 7 variables and constraints daily, CUT RANKING has achieved the average speedup ratio of 12.42% over the production solver without any accuracy loss of solution. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： mixed-integer programming Cutting plane Multiple instance learning Generalization ability

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Data Mining Approach for Feature Based Parameter Tunning for mixed-integer programming Solvers

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Procedia Computer Science 2017年 108卷 715-724页

作者： Matheus G. Vilas Boas Haroldo G. Santos Rafael de S.O. Martins Luiz H.C. Merschmann Federal University of Ouro Preto Department of Computing Ouro Preto Brazil Federal University of Ouro Preto Department of Information Systems and Computing João Monlevade Brazil Federal University of Lavras Department of Computer Science Lavras Brazil

integer programming (IP) is the most successful technique for solving hard combinatorial optimization problems. Modern IP solvers are very complex programs composed of many different procedures whose execution is embedded in the generic Branch & Bound framework. The activation of these procedures as well the definition of exploration strategies for the search tree can be done by setting different parameters. Since the success of these procedures and strategies in improving the performance of IP solvers varies widely depending on the problem being solved, the usual approach for discovering a good set of parameters considering average results is not ideal. In this work we propose a comprehensive approach for the automatic tuning of integer programming solvers where the characteristics of instances are considered. Computational experiments in a diverse set of 308 benchmark instances using the open source COIN-OR CBC solver were performed with different parameter sets and the results were processed by data mining algorithms. The results were encouraging: when trained with a portion of the database the algorithms were able to predict better parameters for the remaining instances in 84% of the cases. The selection of a single best parameter setting would provide an improvement in only 56% of instances, showing that great improvements can be obtained with our approach.

关键词： feature based parameter tunning mixed-integer programming data mining regression algorithms coin-or branch cut

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Economical sizing and multi-azimuth layout optimization of grid-connected rooftop photovoltaic systems using mixed-integer programming

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APPLIED ENERGY 2023年第1期335卷

作者： Alharbi, Abdulaziz Awwad, Zeyad Habib, Abdulelah de Weck, Olivier MIT Ctr Complex Engn Syst KACST Riyadh Saudi Arabia MIT Dept Aeronaut & Astronaut Cambridge MA 02139 USA

Solar energy is expected to be a significant contributor to meet the increasing global energy demand. Rooftop photovoltaic (PV) systems account for a substantial portion of the global solar energy potential. However, optimizing the size and layout of these systems remains challenging. Existing approaches either focus on maximizing energy generation, heavily restrict the space of potential layouts, ignore inverter-type implications, or neglect practical aspects, such as minimizing self-shading. This paper presents a mixed-integer programming (MIP) model to address these limitations for PV systems installed on flat rooftops. The proposed model optimizes the net present value (NPV) and can produce multi-azimuth layouts while accounting for practical considerations, including mitigating self-shading, and ensuring rooftop walkability. The proposed model is adapted for systems that utilize micro-inverters or string-inverters. Two case studies are conducted to evaluate the performance of the proposed model. In one case study, the model is applied to a residential area. It is numerically shown that in some instances of capital costs and billing policies, the use of multi-azimuth layouts could significantly improve the NPV compared to the use of single-azimuth layouts with parallel rows of panels. The proposed model solutions are compared to an existing optimized installation in the second case study. The proposed model multi-azimuth layout solution improves the NPV by 10.17%. When restricted to single-azimuth layouts, the proposed model produces the same design as that of the existing installation in only a few seconds.

关键词： Optimization mixed-integer programming Photovoltaic system sizing optimization Photovoltaic system layout optimization

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Optimal Operational Planning of a Gas Turbine Combined Heat and Power Plant Based on the mixed-integer programming

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IFAC Proceedings Volumes 1988年第11期21卷 371-377页

作者： K. Ito R. Yokoyama S. Akagi T. Yamaguchi Y. Matsumoto Dept. of Mech. Eng. for Indu. Mach and Syst. Faculty of Eng. Osaka Univ. Suita Osaka Japan Technical Research Center. The Kansai Electric Power Co. Inc. Amagasaki Hyogo Japan

A planning method is proposed for determining the optimal operational policy of a gas turbine combined heat and power plant connected with distributed heat supply plants at several districts. For the purpose of the efficient planning, a hierarchical approach is adopted. At the first level, the optimal operational policy is determined for each heat supply plant so as to minimize the required amount of input energy. At the second level, the optimal operational policy is determined for the combined heat and power plant so as to minimize its operational cost. These optimization problems are formulated respectively as a mixed-integer quadratic programming problem and a mixed-integer linear one, and they are both solved by applying the branch and bound method. Lastly, the effectiveness of the proposed method is ascertained through a case study.

关键词： Computer-aided systet design power generation heat systems gas turbines optimization hierarchical systems district heating and cooling optimal operation mixed-integer programming

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A Survey on mixed-integer programming Techniques in Bilevel Optimization

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EURO JOURNAL ON COMPUTATIONAL OPTIMIZATION 2021年 9卷

作者： Kleinert, Thomas Labbe, Martine Ljubic, Ivana Schmidt, Martin Friedrich Alexander Univ Erlangen Nurnberg Discrete Optimizat Cauerstr 11 D-91058 Erlangen Germany Energie Campus Nurnberg Further Str 250 D-90429 Nurnberg Germany Univ Libre Bruxelles Dept Comp Sci Blvd TriompheCP212 B-1050 Brussels Belgium Inria Lille Nord Europe Parc Sci Haute Borne 40Av Halley Bat APk Plaza F-59650 Villeneuve Dascq France ESSEC Business Sch Paris F-95021 Cergy Pontoise France Trier Univ Dept Math Univ Ring 15 D-54296 Trier Germany

Bilevel optimization is a field of mathematical programming in which some variables are constrained to be the solution of another optimization problem. As a consequence, bilevel optimization is able to model hierarchical decision processes. This is appealing for modeling real-world problems, but it also makes the resulting optimization models hard to solve in theory and practice. The scientific interest in computational bilevel optimization increased a lot over the last decade and is still growing. Independent of whether the bilevel problem itself contains integer variables or not, many state-of-the-art solution approaches for bilevel optimization make use of techniques that originate from mixed-integer programming. These techniques include branch-and-bound methods, cutting planes and, thus, branch-and-cut approaches, or problem-specific decomposition methods. In this survey article, we review bilevel-tailored approaches that exploit these mixed-integer programming techniques to solve bilevel optimization problems. To this end, we first consider bilevel problems with convex or, in particular, linear lower-level problems. The discussed solution methods in this field stem from original works from the 1980's but, on the other hand, are still actively researched today. Second, we review modern algorithmic approaches to solve mixed-integer bilevel problems that contain integrality constraints in the lower level. Moreover, we also briefly discuss the area of mixed-integer nonlinear bilevel problems. Third, we devote some attention to more specific fields such as pricing or interdiction models that genuinely contain bilinear and thus nonconvex aspects. Finally, we sketch a list of open questions from the areas of algorithmic and computational bilevel optimization, which may lead to interesting future research that will further propel this fascinating and active field of research.

关键词： Bilevel optimization mixed-integer programming Applications Branch-and-bound Branch-and-cut Survey

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Research on obstetric ward planning combining lean thinking and mixed-integer programming

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INTERNATIONAL JOURNAL FOR QUALITY IN HEALTH CARE 2021年第3期33卷 mzab101-mzab101页

作者： Mu, Dongmei Li, Hua Zhao, Danning Ju, Yuanhong Li, Yuewei Jilin Univ Sch Publ Hlth 1163 Xinmin St Changchun 130000 Jilin Peoples R China Jilin Univ First Hosp Dept Clin Res 1 Xinmin St Changchun 130000 Jilin Peoples R China Jilin Univ First Hosp Dept Abdominal Ultrasound 1 Xinmin St Changchun 130000 Jilin Peoples R China Jilin Univ Sch Nursing 965 Xinjiang St Changchun 130000 Jilin Peoples R China

Background: In recent years, there are many studies on scheduling methods of patient flow, nurse scheduling, bed allocation, operating room scheduling and other problems, but there is no report on the research methods of how to plan ward allocation from a more macroscopic perspective. Objective: Refine and stratify the obstetric ward to provide more accurate medical service for pregnant women and improve the work efficiency of obstetricians and midwives. The problem of how to allocate the number of each type of ward is modeled as a mixed integer programming problem, which maximizes the patient flow of pregnant women in obstetric hospitals. Methods: The obstetric wards are divided into observation ward, cesarean section ward and natural delivery ward according to lean thinking. CPLEX is used to solve the mixed-integer programming problem of ward allocation. In R software, multivariate Generalized Linear Models (GLM) regression model is used to analyze the influence of each factor on patient flow. Results: The maximum patient flow of each case was obtained by CPLEX, which was 19-25% higher than that of patients without refinement, stratification and planning. GLM regression analysis was carried out on the abovementioned data, and the positive and negative correlation factors were obtained. Conclusion: According to lean thinking, obstetric wards are divided into three types of wards. Obstetricians and midwives work more efficiently and get more rest time. Pregnant women also enjoy more detailed medical services. By modeling the delivery ward allocation problem as a mixed-integer programming problem, we can improve the capacity of the service in obstetric hospitals from a macro perspective. Through GLM regression model analysis, it is conducive to improve the obstetric hospital capacity from the perspective of positive and negative correlation factors.

关键词： obstetric ward planning lean thinking mixed-integer programming clinical pathway CPLEX

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Branch-and-Bound for Biobjective mixed-integer Linear programming

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INFORMS JOURNAL ON COMPUTING 2022年第2期34卷 909-933页

作者： Adelgren, Nathan Gupte, Akshay Edinboro Univ Dept Math & Comp Sci Edinboro PA 16444 USA Princeton Univ Andlinger Ctr Energy & Environm Princeton NJ 08544 USA Univ Edinburgh Sch Math Edinburgh EH9 3FD Midlothian Scotland

We present a generic branch-and-bound algorithm for finding all the Pareto solutions of a biobjective mixed-integer linear program. The main contributions are new algorithms for obtaining dual bounds at a node, checking node fathoming, presolve, and duality gap measurement. Our branch-and-bound is predominantly a decision space search method because the branching is performed on the decision variables, akin to single objective problems, although we also sometimes split gaps and branch in the objective space. The various algorithms are implemented using a data structure for storing Pareto sets. Computational experiments are carried out on literature instances and on a new set of instances that we generate using a benchmark library (MIPLIB2017) for single objective problems. We also perform comparisons against the triangle splitting method from literature, which is an objective space search algorithm. Summary of Contribution: Biobjective mixed-integer optimization problems have two linear objectives and a mixed-integer feasible region. Such problems have many applications in operations research, because many real-world optimization problems naturally comprise two conflicting objectives to optimize or can be approximated in such a manner and are even harder than single objective mixed-integer programs. Solving them exactly requires the computation of all the nondominated solutions in the objective space, whereas some applications may also require finding at least one solution in the decision space corresponding to each nondominated solution. This paper provides an exact algorithm for solving these problems using the branch-and-bound method, which works predominantly in the decision space. Of the many ingredients of this algorithm, some parts are direct extensions of the single-objective version, but the main parts are newly designed algorithms to handle the distinct challenges of optimizing over two objectives. The goal of this study is to improve solution quality and

关键词： branch-and-bound mixed-integer programming multiobjective optimization Pareto optima fathoming rules

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