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Enhancing cut selection through reinforcement learning

Science China Mathematics 2024年第6期67卷 1377-1394页

作者： Shengchao Wang Liang Chen Lingfeng Niu Yu-Hong Dai Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing100190China Research Center on Fictitious Economy and Data Science Chinese Academy of SciencesBeijing100190China

With the rapid development of artificial intelligence in recent years,applying various learning techniques to solve mixed-integer linear programming(MILP)problems has emerged as a burgeoning research domain.Apart from constructing end-to-end models directly,integrating learning approaches with some modules in the traditional methods for solving MILPs is also a promising direction.The cutting plane method is one of the fundamental algorithms used in modern MILP solvers,and the selection of appropriate cuts from the candidate cuts subset is crucial for enhancing efficiency.Due to the reliance on expert knowledge and problem-specific heuristics,classical cut selection methods are not always transferable and often limit the scalability and generalizability of the cutting plane method.To provide a more efficient and generalizable strategy,we propose a reinforcement learning(RL)framework to enhance cut selection in the solving process of MILPs.Firstly,we design feature vectors to incorporate the inherent properties of MILP and computational information from the solver and represent MILP instances as bipartite graphs.Secondly,we choose the weighted metrics to approximate the proximity of feasible solutions to the convex hull and utilize the learning method to determine the weights assigned to each metric.Thirdly,a graph convolutional neural network is adopted with a self-attention mechanism to predict the value of weighting factors.Finally,we transform the cut selection process into a Markov decision process and utilize RL method to train the model.Extensive experiments are conducted based on a leading open-source MILP solver SCIP.Results on both general and specific datasets validate the effectiveness and efficiency of our proposed approach.

关键词： reinforcement learning mixed-integer linear programming cutting plane method cut selection

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Short-term Transmission Maintenance Scheduling Considering Network Topology Optimization

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Journal of Modern Power Systems and Clean Energy 2022年第4期10卷 883-893页

作者： Weixin Zhang Bo Hu Kaigui Xie Changzheng Shao Tao Niu Jiahao Yan Lvbin Peng Maosen Cao Yue Sun State Key Laboratory of Power Transmission Equipment&System Security and New Technology at Chongqing University Chongqing 400044China

With the increasing penetration of renewable energy sources,transmission maintenance scheduling(TMS)will have a larger impact on the accommodation of wind power.Meanwhile,the more flexible transmission network topology owing to the network topology optimization(NTO)technique can ensure the secure and economic operation of power systems.This paper proposes a TMS model considering NTO to decrease the wind curtailment without adding control devices.The problem is formulated as a two-stage stochastic mixed-integer programming model.The first stage arranges the maintenance periods of transmission lines.The second stage optimizes the transmission network topology to minimize the maintenance cost and system operation in different wind speed scenarios.The proposed model cannot be solved efficiently with off-theshelf solvers due to the binary variables in both stages.Therefore,the progressive hedging algorithm is applied.The results on the modified IEEE RTS-79 system show that the proposed method can reduce the negative impact of transmission maintenance on wind accommodation by 65.49%,which proves its effectiveness.

关键词： mixed-integer linear programming network topology optimization progressive hedging algorithm stochastic optimization transmission maintenance scheduling wind curtailment

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Three-scale integrated optimization model of furnace simulation,cyclic scheduling,and supply chain of ethylene plants

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Chinese Journal of Chemical Engineering 2022年第4期35卷 29-40页

作者： Kexin Bi Mingyu Yan Shuyuan Zhang Tong Qiu Department of Chemical Engineering Tsinghua UniversityBeijing 100084China Beijing Key Laboratory of Industrial Big Data System and Application Beijing 100084China Fushun Petrochemical Company PetroChinaFushun 113008China

In order to explore the potential of profit margin improvement,a novel three-scale integrated optimization model of furnace simulation,cyclic scheduling,and supply chain of ethylene plants is proposed and evaluated.A decoupling strategy is proposed for the solution of the three-scale model,which uses our previously proposed reactor scale model for operation optimization and then transfers the obtained results as a parameter table in the joint MILP optimization of plant-supply chain scale for cyclic scheduling.This optimization framework simplifies the fundamental mixed-integer nonlinear programming(MINLP)into several sub-models,and improves the interpretability and extendibility.In the evaluation of an industrial case,a profit increase at a percentage of 3.25%is attained in optimization compared to the practical operations.Further sensitivity analysis is carried out for strategy evolving study when price policy,supply chain,and production requirement parameters are varied.These results could provide useful suggestions for petrochemical enterprises on thermal cracking production.

关键词： Three-scale integrated optimization Cyclic scheduling Supply chain mixed-integer linear programming Thermal cracking

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Solving vehicle routing problem with time windows using metaheuristic approaches

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International Journal of Intelligent Computing and Cybernetics 2023年第1期16卷 121-138页

作者： Zeynep Aydınalp DoganÖzgen Yıldız Technical University IstanbulTurkey

Purpose-Drugs are strategic products with essential functions in human health.An optimum design of the pharmaceutical supply chain is critical to avoid economic damage and adverse effects on human health.The vehicle-routing problem,focused on finding the lowest-cost routes with available vehicles and constraints,such as time constraints and road length,is an important aspect of this.In this paper,the vehicle routing problem(VRP)for a pharmaceutical company in Turkey is discussed.Design/methodology/approach-A mixed-integer programming(MIP)model based on the vehicle routing problem with time windows(VRPTW)is presented,aiming to minimize the total route cost with certain constraints.As the model provides an optimum solution for small problem sizes with the GUROBI®solver,for large problem sizes,metaheuristic methods that simulate annealing and adaptive large neighborhood search algorithms are proposed.A real dataset was used to analyze the effectiveness of the metaheuristic algorithms.The proposed simulated annealing(SA)and adaptive large neighborhood search(ALNS)were evaluated and compared against GUROBI®and each other through a set of real problem instances.Findings-The model is solved optimally for a small-sized dataset with exact algorithms;for solving a larger dataset,however,metaheuristic algorithms require significantly lesser time.For the problem addressed in this study,while the metaheuristic algorithms obtained the optimum solution in less than one minute,the solution in the GUROBI®solver was limited to one hour and three hours,and no solution could be obtained in this time interval.Originality/value-The VRPTW problem presented in this paper is a real-life problem.The vehicle fleet owned by the factory cannot be transported between certain suppliers,which complicates the solution of the problem.

关键词： Pharmaceutical supply chain Network design mixed-integer linear programming Vehicle routing problem Simulated annealing Adaptive large neighborhood search

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Battery electric buses charging schedule optimization considering time-of-use electricity price

Journal of Intelligent and Connected Vehicles

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Journal of Intelligent and Connected Vehicles 2022年第2期5卷 138-145页

作者： Jia He Na Yan Jian Zhang Yang Yu Tao Wang Beijing Key Laboratory of Traffic Engineering Beijing University of TechnologyBeijingChina Transport for New South Wales SydneyAustralia School of Vehicle and Mobility Tsinghua UniversityBeijingChina

Purpose–This paper aims to optimize the charging schedule for battery electric buses(BEBs)to minimize the charging cost considering the time-ofuse electricity price.Design/methodology/approach–The BEBs charging schedule optimization problem is formulated as a mixed-integer linear programming model.The objective is to minimize the total charging cost of the BEB fleet.The charge decision of each BEB at the end of each trip is to be determined.Two types of constraints are adopted to ensure that the charging schedule meets the operational requirements of the BEB fleet and that the number of charging piles can meet the demand of the charging schedule.Findings–This paper conducts numerical cases to validate the effect of the proposed model based on the actual timetable and charging data of a bus line.The results show that the total charge cost with the optimized charging schedule is 15.56%lower than the actual total charge cost under given conditions.The results also suggest that increasing the number of charging piles can reduce the charging cost to some extent,which can provide a reference for planning the number of charging piles.Originality/value–Considering time-of-use electricity price in the BEBs charging schedule will not only reduce the operation cost of electric transit but also make the best use of electricity resources.

关键词： Battery electric bus Charging schedule mixed-integer linear programming Time-of-use electricity price

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Optimization operation model of electricity market considering renewable energy accommodation and flexibility requirement

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Global Energy Interconnection 2021年第3期4卷 227-238页

作者： Jinye Yang Chunyang Liu Yuanze Mi Hengxu Zhang Vladimir Terzija Key Laboratory of Power System Intelligent Dispatch and Control of Ministry of Education(Shandong University) Jinan 250061ShandongP.R.China The Center for Energy Science and Technology Skolkovo Institute of Science and TechnologyMoscowRussia

The renewable portfolio standard has been promoted in parallel with the reform of the electricity market,and the flexibility requirement of the power system has rapidly increased.To promote renewable energy consumption and improve power system flexibility,a bi-level optimal operation model of the electricity market is proposed.A probabilistic model of the flexibility requirement is established,considering the correlation between wind power,photovoltaic power,and load.A bi-level optimization model is established for the multi-markets;the upper and lower models represent the intra-provincial market and inter-provincial market models,respectively.To efficiently solve the model,it is transformed into a mixed-integer linear programming model using the Karush–Kuhn–Tucker condition and Lagrangian duality theory.The economy and flexibility of the model are verified using a provincial power grid as an example.

关键词： Renewable energy accommodation Renewable portfolio standards Flexibility requirement Optimization operation mixed-integer linear programming

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Big-M based MILP method for SCUC considering allowable wind power output interval and its adjustable conservativeness

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Global Energy Interconnection 2021年第2期4卷 193-203页

作者： Liudong Zhang Qibing Zhang Haifeng Fan Haiwei Wu Chunlei Xu State Grid Jiangsu Electric Power Company LTD.Nanjing 210024P.R.China

In contrast to most existing works on robust unit commitment(UC),this study proposes a novel big-M-based mixed-integer linear programming(MILP)method to solve security-constrained UC problems considering the allowable wind power output interval and its adjustable conservativeness.The wind power accommodation capability is usually limited by spinning reserve requirements and transmission line capacity in power systems with large-scale wind power integration.Therefore,by employing the big-M method and adding auxiliary 0-1 binary variables to describe the allowable wind power output interval,a bilinear programming problem meeting the security constraints of system operation is presented.Furthermore,an adjustable confidence level was introduced into the proposed robust optimization model to decrease the level of conservatism of the robust solutions.This can establish a trade-off between economy and security.To develop an MILP problem that can be solved by commercial solvers such as CPLEX,the big-M method is utilized again to represent the bilinear formulation as a series of linear inequality constraints and approximately address the nonlinear formulation caused by the adjustable conservativeness.Simulation studies on a modified IEEE 26-generator reliability test system connected to wind farms were performed to confirm the effectiveness and advantages of the proposed method.

关键词： Big-M method Security-constrained unit commitment Robust optimization mixed-integer linear programming Allowable wind power output interval Adjustable conservativeness

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A new approach for scheduling of multipurpose batch processes with unlimited intermediate storage policy

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Frontiers of Chemical Science and Engineering 2019年第4期13卷 784-802页

作者： Nikolaos Rakovitis Nan Zhang Jie Li Liping Zhang Centre for Process Integration School of Chemical Engineering and Analytical ScienceThe University of ManchesterManchesterM139PLUK Department of Industrial Engineering School of Machinery and AutomationWuhan University of Science and TechnologyWuhan 430081China

The increasing demand of goods,the high competitiveness in the global marketplace as well as the need to minimize the ecological footprint lead multipurpose batch process industries to seek ways to maximize their productivity with a simultaneous reduction of raw materials and utility consumption and efficient use of processing units.Optimal scheduling of their processes can lead facilities towards this direction.Although a great number of mathematical models have been developed for such scheduling,they may still lead to large model sizes and computational time.In this work,we develop two novel mathematical models using the unit-specific eventbased modelling approach in which consumption and production tasks related to the same states are allowed to take place at the same event points.The computational results demonstrate that both proposed mathematical models reduce the number of event points required.The proposed unit-specific event-based model is the most efficient since it both requires a smaller number of event points and significantly less computational time in most cases especially for those examples which are computationally expensive from existing models.

关键词： scheduling multipurpose batch processes simultaneous transfer mixed-integer linear programming

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A Model Predictive Control for Microgrids Considering Battery Aging

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Journal of Modern Power Systems and Clean Energy 2020年第2期8卷 296-304页

作者： Ugur Can Yilmaz Mustafa Erdem Sezgin Murat Gol Department of Electrical and Electronics Engineering Middle East Technical UniversityAnkaraTurkey

The increasing number of distributed energy resources(DERs),advancing communication and computation technologies,and reliability concerns of the customers have caused an intense interest in the concept of microgrid.Although DERs are the biggest motivation of the microgrids due to their intermittent generation characteristics,they constitute a risk for system reliability.Battery storage systems(BSSs)stand as one of the most effective solutions for this reliability problem.However,the inappropriate use of BSS creates other operational problems in power systems.In order to deal with these concerns explicitly in microgrids,an optimized microgrid central controller(MGCC)is the key factor,which controls the realtime operation of a microgrid.This work proposes a model predictive control(MPC)based MGCC that will provide optimal control of the microgrid,considering economic and operational constraints.The proposed system will minimize the energy cost of the microgrid by utilizing mixed-integer linear programming(MILP)assuming the presence of DERs and BSS as well as the bi-directional grid connection.Moreover,the aging effect of BSS will be considered in the proposed optimization problem which will provide an up-to-date system model.The proposed method is evaluated using real load and photovoltaic(PV)generation data.

关键词： Microgrid optimization battery storage model predictive control mixed-integer linear programming

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Heuristic solution of a joint electric control reserve and wholesale market model

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International Journal of Modeling, Simulation, and Scientific Computing 2019年第2期10卷 1-20页

作者： Timo Breithaupt Thomas Leveringhaus Lutz Hofmann Institute of Electric Power Systems Leibniz Universit¨at Hannover Welfengarten 1 30167 HanoverGermany

A mixed integer linear programming(MILP)approach for the joint simulation of electric control reserve and electricity wholesale markets is presented.This generation dispatch model extends an existing integrated grid and electricity market(IGEM)model covering the Continental European electric power system.By explicitly incorporating the markets for primary and secondary control reserves(PCR and SCR),the model can reproduce the decisions of generating unit operators on which markets get involved.Besides,the introduction of the integrality conditions allows considering start-up costs and the calculus of generating units to pass through the economically unattractive periods with low or even negative prices in order to avoid another start-up.Since this model is too large to be solved with common MILP solvers for the intended simulation time of one year,temporal and geographical interdependencies are used to solve it heuristically.The heuristic therefore splits the model into various sub-problems so that on the one hand,the number of variables,especially of integer variables,per sub-problem is reduced significantly and on the other hand,the relevant interdependencies remain considered.The heuristic is evaluated in terms of accuracy and computation time by means of two case studies.Both case studies show satisfactory accuracy and significant advantages in computation time.

关键词： mixed-integer linear programming unit commitment rolling horizon heuristic

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