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A mixed-integer linear programming model for hydro unit commitment considering operation constraint priorities

RENEWABLE ENERGY 2023年第1期204卷 507-520页

作者： Wu, Xinyu Wu, Yiyang Cheng, Xilong Cheng, Chuntian Li, Zehong Wu, Yongqi Dalian Univ Technol Inst Hydropower & Hydroinformat Dalian 116024 Peoples R China Yunhe Henan Informat Technol Co Ltd Zhengzhou 450003 Peoples R China Guizhou Qianyuan Power Co Ltd Guiyang 550002 Peoples R China

Optimizing hydro unit commitment (HUC) has the potential to improve water use efficiency, but should consider complex constraints from power grid, hydropower station and unit operation. When confronted with extreme operating conditions, conflicting constraints cannot be satisfied simultaneously, resulting in no feasible solution. To overcome this drawback, the constraint grading principle is proposed to illustrate how to convert hard constraints into soft constraints and rank them in priority levels. Soft constraints are destroyed according to priority levels from low to high to obtain a feasible solution, simultaneously minimizing the damage degree of soft constraints. Based on the principle, the HUC model considering operation constraint priorities is proposed. When the initial model fails to obtain a feasible solution, low-priority soft constraints are destroyed automati-cally. Finally, the proposed model is linearized to a mixed-integer linear programming (MILP) model. The commercial solver Lingo is adopted to obtain a feasible solution. The modeling results of Guangzhao hydropower station reveal that: The proposed method can effectively solve the problem of no feasible solution due to con-flicting constraints in HUC. Comparing to the penalty function method, the proposed method has better convergence, and strictly reflects the priority of soft constraints.

关键词： Hydro unit commitment Constraint grading mixed -integer linear programming

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A unified framework for bivariate clustering and regression problems via mixed-integer linear programming

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DISCRETE APPLIED MATHEMATICS 2023年 336卷 15-36页

作者： Warwicker, John Alasdair Rebennack, Steffen Karlsruhe Inst Technol KIT Inst Operat Res IOR D-76185 Karlsruhe Baden Wurttembe Germany

Clustering and regression are two of the most important problems in data analysis and machine learning. Recently, mixed-integer linear programs (MILPs) have been presented in the literature to solve these problems. By modelling the problems as MILPs, they are able to be solved very quickly by commercial solvers. In particular, MILPs for bivariate clusterwise linear regression (CLR) and (continuous) piecewise linear regression (PWLR) have recently appeared. These MILP models make use of binary variables and logical implications modelled through big -M constraints. In this paper, we present these models in the context of a unifying MILP framework for bivariate clustering and regression problems. We then present two new formulations within this framework, the first for ordered CLR, and the second for clusterwise piecewise linear regression (CPWLR). The CPWLR problem concerns simultaneously clustering discrete data, while modelling each cluster with a continuous PWL function. Extending upon the framework, we discuss how outlier detection can be implemented within the models, and how specific decomposition methods can be used to find speedups in the runtime. Experimental results show when each model is the most effective.& COPY;2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).

关键词： Clustering Regression mixed -integer linear programming Outlier detection Decomposition Function fitting

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Decentralised multi-grid coupling for energy supply of a hybrid bus depot using mixed-integer linear programming

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SMART ENERGY 2022年 8卷

作者： Roth, Maximilian Franke, Georg Rinderknecht, Stephan Tech Univ Darmstadt Inst Mechatron Syst Mech Engn Otto Berndt Str 2 D-64287 Darmstadt Germany

The present work refers to two current problems in the context of achieving Greenhouse gas (GHG) neutrality: first the curtailment of renewable, volatile power generation units and secondly the high share of the mobility domain in total GHG-emissions. Both problems can be countered by a decentralised, smart energy system that supplies electricity, gas and heat to a hybrid public transport bus fleet and is simultaneously coupled to the public gas grid, public electricity grid and the district heating grid (Multi-Grid-Coupling). The enabling energy conversion unit is a reversible solid oxide cell (rSOC), which is operated in combined heat and power (CHP) mode or in power-to-gas (P2G) mode. P2G is primarily a solution approach for the first-mentioned problem and can thus successively lead to the replacement of fossil energy sources. Furthermore, by integrating industrial waste gases - as a necessary CO2 source for the P2G process - an additional benefit is gained from the CO2 that is emitted anyhow. The hybrid bus fleet constitutes an ecological alternative concept in public transport and therefore addresses the second-mentioned problem. The system, developed under the current state of the art technologies and the current ecological and economic conditions for Europe and Germany, can be operated profitably from the perspective of the system operator. This applies to the economically and ecologically optimised operating schedule of the controllable system elements such as the electrical, thermal and compressed gas storages, rSOC, compressor and the energy exchange with the public grids. To derive the optimal operating schedule of the crosssectoral system, a mixed-integer linear programming (MILP) model is implemented and simulated under the current legal situation.

关键词： Microgrid scheduling mixed -integer linear programming Reversible solid oxide cell Power -to -Gas Combined heat and power Optimisation Operation strategy Clean vehicles directive Renewable energy directive II Sector -coupling Smart energy system Multi -grid -coupling

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A compact time horizon compression method for planning community integrated energy systems with long-term energy storage

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APPLIED ENERGY 2024年 361卷

作者： Lei, Zijian Yu, Hao Li, Peng Ji, Haoran Yan, Jinyue Song, Guanyu Wang, Chengshan Tianjin Univ Key Lab Smart Grid Minist Educ Tianjin 300072 Peoples R China Hong Kong Polytech Univ Dept Bldg Environm & Energy Engn Hong Kong Peoples R China

Long-term energy storage (LTES), such as hydrogen storage, has attracted significant attention due to its outstanding performance in storing energy over extended durations and seasonal balancing of power generation and consumption. However, planning for LTES usually necessitates the comprehensive coverage of its whole operation cycle, spanning from days to months, making the issue complex and intractable. To simplify the planning of a community integrated energy system (CIES) with LTES, this study proposes a time horizon compression (THC) method and formulates a concise long-term planning model for CIES with compressed time horizons. Then, robust optimization method with a budget uncertainty set is employed to develop a robust THC model, aimed at addressing data uncertainties in CIES planning. The proposed robust THC model is implemented in the planning of a CIES with high penetration of renewable energy sources, with the objective of minimizing the total annual cost. The results demonstrate that the proposed model can efficiently solve the complex CIES planning problem, resulting in a 42.77% acceleration in optimization speed. Additionally, the diversity and differentiation in THC configurations is investigated to enhance the implementation of THC in long-term CIES planning. The effectiveness of solution robustness and the significant effects of LTES on CIES are analyzed and validated in the case study.

关键词： Community integrated energy system Hydrogen storage Long-term energy storage mixed -integer linear programming Time horizon compression Robust optimization

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Life cycle techno-economic-environmental optimization for capacity design and operation strategy of grid-connected building distributed multi-energy system

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RENEWABLE ENERGY 2024年 230卷

作者： Han, Huizhen Ge, Yongkai Wang, Qingrui Yang, Qing Xing, Lu Ba, Shusong Chen, Guoqian Tian, Tian Chen, Xi Jian, Peiru Huazhong Univ Sci & Technol Sch Energy & Power Engn Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol State Key Lab Coal Combust Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol China EU Inst Clean & Renewable Energy Wuhan 430074 Peoples R China Harvard Univ John A Paulson Sch Engn & Appl Sci Cambridge MA 02138 USA Northumbria Univ Mech & Construct Engn Newcastle Upon Tyne NE1 8ST England Peking Univ HSBC Business Sch Shenzhen 518055 Peoples R China Peking Univ Coll Engn Beijing 100871 Peoples R China MIT Sch Engn 77 Massachusetts Ave Cambridge MA 02138 USA Huazhong Univ Sci & Technol Sch Architecture & Urban Planning Wuhan 430074 Peoples R China Wuhan Opt Valley Environm Protect Technol Co Ltd Wuhan 430205 Peoples R China

Distributed multi-energy systems (DMS) have received increasing attention. Many studies have optimized the capacity and operation strategies of DMS based on multiple objectives, but these studies must discuss the weights of different objectives and have not considered the internal coupling between different objectives. Besides, existing studies have not considered the changes in the actual value of environmental impacts. To address these shortcomings, this paper constructs a technology-economic-environmental optimization model by mixed-integer linear programming. Based on life-cycle assessment, the model quantifies the value of system life-cycle environmental impacts by introducing carbon price. The case results show that the proposed optimization model can reduce the total cost by 28.83 % and the life cycle environmental cost by 3.39 % compared to the traditional model. To reduce the strain on the grid, a new operation pattern (The grid provides fixed electricity to the system throughout the year.) is proposed. The electricity interaction of the system with the grid under the new operation pattern is more than 70 % lower than the system without electricity purchased quantity constraint. Sensitivity analysis shows the total system cost is more sensitive to natural gas and electricity price than carbon price. But carbon price volatility helps reduce system carbon emissions.

关键词： Building distributed multi -energy system Techno-economic-environmental optimization Life cycle assessment mixed -integer linear programming Operation pattern

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A mathematical model for the integrated problem of production network design and inventory positioning

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COMPUTERS & INDUSTRIAL ENGINEERING 2024年 191卷

作者： Duc, Nguyen Trong Tri Buddhakulsomsiri, Jirachai Tai, Pham Duc Can Tho Univ Coll Engn Technol Dept Ind Management Can Tho Vietnam Thammasat Univ Sirindhorn Int Inst Technol Sch Mfg Syst & Mech Engn Pathum Thani Thailand 99 Moo 18 Km 41 Paholyothin Highway Khlong Luang Pathum Thani 12120 Thailand

In this paper, an integrated approach is addressed to tackle the production network design and inventory positioning problem in a single -sourcing, multi -product, and multi -period context. The objective of our model is to simultaneously determine the optimal network structure, safety stock amounts, and their respective locations, considering normal demand conditions. The main goal is to minimize the overall production network cost. The proposed model merges the traditional network design formulation with that for inventory positioning using the concept of guaranteed service. The developed model is implemented and tested on a case study of office furniture manufacturing, where the bill of materials is considered. The effectiveness of the proposed model is demonstrated by comparing it to a sequential approach where the network structure and safety stock decisions are made sequentially. The results reveal that the integrated approach surpasses the sequential approach, with cost savings ranging from 1.7% to 3.7%. In addition, a higher optimal cycle service level is obtained by the integrated approach compared to that of the sequential approach. To further evaluate the model ' s performance, a sensitivity analysis is conducted to examine the influence of the model ' s parameters, i.e., committed service time and coefficient of variation of demand, on its solutions. The analysis shows that when the coefficient of the demand variation remains unchanged, longer committed service times lead to lower safety stock costs and higher optimal service levels. Moreover, it is observed that more safety stocks of components are kept in the upstream layer of the network than those of finished goods.

关键词： Network design Inventory positioning Integrated approach Guaranteed -service approach mixed -integer linear programming

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Peak shaving potential and its economic feasibility analysis of V2B mode

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JOURNAL OF BUILDING ENGINEERING 2024年 90卷

作者： Liu, Qingrong Li, Yunqi Xu, Tingting Qian, Fanyue Meng, Hua Yao, Yuting Ruan, Yingjun Shanghai Univ Elect Power Coll Energy & Mech Engn Shanghai 201306 Peoples R China Tongji Univ Coll Mech & Energy Engn Shanghai 200092 Peoples R China

Electric vehicles (EVs) as mobile energy-storage devices improve the grid's ability to absorb renewable energy while reducing peak-to-valley load differences. With a focus on smoothing the load curve, this study investigates the peak shaving potential and its economic feasibility analysis of V2B mode. First, based on the virtual microgrid system established in this paper, a Monte Carlo method was used to simulate the driving, charging, and discharging processes of EVs. Second, the effects of the number of charging stations, battery capacity of EVs, and photovoltaic (PV) penetration rate on the peak shaving results were evaluated separately by using the standard deviation of daily loads. Third, the V2B peak shaving strategy and cost composition were explored considering the battery aging costs. Moreover, the economic feasibility and factors influencing the proposed strategy were analyzed. The results indicate that 1) V2B effectively transfers peak power loads between 08:00 h And 20:00 h To low-demand periods at night;2) as the deployment ratio of charging station increases, the level of load fluctuation decreases significantly. When EV battery capacity is at or above 60 kW h, charging station deployment ratios of 0.43, 0.42, and 0.47 are required for saturated load smoothing in winter, transition period, and summer, respectively;3) the PV penetration rate for maximizing the collaborative peak shaving capability of V2B and PV power is 30%-40 % and 4) reducing battery costs or extending battery life has the most significant effect on V2B power costs, followed by charging station costs. This study provides a theoretical basis for determining the economic feasibility of charging station planning and provides technical guidance for the rational scheduling of EVs and their friendly interaction with the power grid.

关键词： V2B Distributed energy resources Monte Carlo Virtual microgrid mixed -integer linear programming

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Drone routing problem with swarm synchronization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第2期314卷 477-495页

作者： Li, Hongqi Wang, Feilong Zhan, Zhuopeng Beihang Univ Sch Transportat Sci & Engn 37 Xueyuan Rd Beijing 100191 Peoples R China

The advantages of rotary-wing drone (RWD) delivery modes have already been delineated. However, single-unit RWDs do not completely solve real problems in last-mile parcel deliveries because of limited payload capacity and flight endurance. Currently, drone swarm technology is being rapidly developed. An RWD swarm can deliver heavy or multiple packages to customers;therefore, the RWD swarm strategy can address the payload capacity limitation of RWDs. Herein, an RWD delivery mode that involves dynamic swarms of RWDs in addition to singleunit RWDs is explored. The "dynamic" characteristic permits the RWD members in swarms to vary by coupling/ decoupling operations at nodes. From the routing plan perspective, using RWD swarms for last-mile parcel deliveries is challenging;accordingly, we introduce a swarm synchronization mode that involves interactions among RWD routes. We formally define the drone routing problem with swarm synchronization (DRP-SS) and develop a mixed-integer linear programming model, which considers the decision on RWD swarms and multi trips. An adaptive large neighborhood search heuristic with specific operators is proposed. In the computational experiments, both small- and large-scale instances are used to validate the effectiveness of the mathematical formulation and the heuristic. Several managerial insights are obtained regarding the influence of detours, the utilization of RWD swarms, and the benefits of multi trips. The DRP-SS model and solution method can be used to estimate the performance of the selection of RWD swarms in practical situations.

关键词： Routing Drone swarm synchronization Time window mixed -integer linear programming Adaptive large neighborhood search

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ReCovNet: Reinforcement learning with covering information for solving maximal coverage billboards location problem

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INTERNATIONAL JOURNAL OF APPLIED EARTH OBSERVATION AND GEOINFORMATION 2024年 128卷

作者： Zhong, Yang Wang, Shaohua Liang, Haojian Wang, Zhenbo Zhang, Xueyan Chen, Xi Su, Cheng Claremont Grad Univ Sch Informat Syst & Technol Claremont CA 91711 USA Chinese Acad Sci Aerosp Informat Res Inst Key Lab Remote Sensing & Digital Earth Beijing 100094 Peoples R China Int Res Ctr Big Data Sustainable Dev Goals Beijing 100094 Peoples R China Jilin Univ Sch Artificial Intelligence Changchun 130012 Peoples R China Chinese Acad Sci Inst Geog Sci & Nat Resources Res Beijing Peoples R China Univ Southern Calif Viterbi Sch Engn Los Angeles CA 90089 USA UCL Dept Stat Sci London WC1E 6BT England

Maximizing billboard coverage with limited resources and different objective goals plays a vital role in social activities. The Maximal Coverage Billboard Location Problem (MCBLP) is complex, especially for multi -objective functions. A multi -objective spatial optimization model was developed using mixed -integer linear programming based on MCBLP to formulate the spatial optimization problem of determining billboard locations. Combining the distinctive features of location problems, we have developed a new approach called ReCovNet that utilizes Deep Reinforcement Learning (DRL) to solve the MCBLP. We applied the ReCovNet to address a real -world billboard location problem in New York City. To assess its performance, we implemented various algorithms such as Gurobi solver, Genetic Algorithm (GA) and a deep learning baseline called Attention Model (AM). The Gurobi reports the optimal solutions, while GA and AM serve as benchmark algorithms. Our proposed approach achieves a good balance between efficiency and accuracy and effectively solves MCBLP. The ReCovNet introduced in our study has potential to improve advertising effectiveness, and our proposed approach offers novel insights for addressing the MCBLP.

关键词： Maximal coverage billboards location problem (MCBLP) Attention model mixed -integer linear programming Deep reinforcement learning Spatial optimization

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Drone location and vehicle fleet planning with trucks and aerial drones

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第1期308卷 113-130页

作者： Rave, Alexander Fontaine, Pirmin Kuhn, Heinrich Catholic Univ Eichstatt Ingolstadt Ingolstadt Sch Management Dept Operat Schanz 49 D-85049 Ingolstadt Germany

In the context of parcel delivery, aerial drones have great potential that particularly applies in rural ar-eas. In these areas drones mostly operate faster than trucks. As drones are limited in their payload, a combination of trucks and drones can be beneficial in reducing last-mile delivery costs. There are two different delivery methods that combine truck and drone delivery: trucks and drones collaborating with each other with drones launched from trucks, and trucks and drones serving customers independently of each other with drones launched from microdepots or the central distribution *** develop a tactical planning model that decides on the cost-optimal vehicle fleet and the location of dedicated drone stations of a logistics service provider that minimizes total costs. The problem setting is modeled as a mixed-integer linear program that allows the assessment of benefits of different transport concepts as well as the impact of mixing different delivery modes. To solve larger instances we develop a specialized adaptive large neighborhood *** present a numerical study for parcel delivery in a rural area where customers live in scattered settlements, e.g., villages or hamlets. The case study shows that it is best to launch drones both from trucks and dedicated drone stations in 58% of all scenarios considered. This fleet mix leads to average cost savings of 33 . 3% compared to an only truck scenario and 14 . 1% if trucks and drones launched from trucks are considered for delivery. Moreover, we find 17 new best-known solutions for benchmark instances from the literature.(c) 2022 Elsevier B.V. All rights reserved.

关键词： Logistics Last -mile delivery Two -echelon location routing problem mixed -integer linear programming Adaptive large neighborhood search

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