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Benchmark of mixed-integer linear programming formulations for district heating network design

ENERGY 2024年 308卷

作者： Lambert, Jerry Ceruti, Amedeo Spliethoff, Hartmut Tech Univ Munich Chair Energy Syst TUM Sch Engn & Design Boltzmannstr 15 D-85747 Garching Germany

Optimal routing and investment decisions are key design criteria to reduce the high investment costs of district heating systems. However, these optimization problems have prohibitively high computational costs for large districts. Four different mixed-integer linear optimization frameworks are benchmarked in this study in order to compare their computational scaling. The frameworks exhibit significant differences in solving times for synthetic benchmarks and real-world urban districts of up to 9587 potential edges. The new open-source framework topotherm, developed for this work, exhibits the best computational performance when only one time step is optimized. The comparison between the models R & eacute;simont, DHmin, DHNx, and topotherm shows two main trends. First, fewer integer variables do not necessarily translate to lower solving times, and second, using redundant binary variables, which introduce symmetries into the constraints, leads to higher solving times. None of the considered optimization frameworks is able to solve the largest benchmark problems for five time steps within the allowed time limit and tolerance. These findings highlight the challenges of and pressing need to develop efficient models for simultaneous optimization of district heating network topology, pipe sizing, and operation.

关键词： Energy system optimization District heating mixed integer linear programming Benchmark Computational scaling

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STL and wSTL control synthesis: A disjunction-centric mixed-integer linear programming approach

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NONlinear ANALYSIS-HYBRID SYSTEMS 2025年 56卷

作者： Cardona, Gustavo A. Kamale, Disha Vasile, Cristian-Ioan Lehigh Univ Dept Mech Engn & Mech Bethlehem PA 18015 USA

This paper introduces an efficient optimization-based control synthesis methodology tailored for Signal Temporal Logic (STL) and its extension, weighted Signal Temporal Logic (wSTL). While STL captures Boolean and temporal operators, wSTL further allows users to express preferences and priorities over concurrent and sequential tasks denoted by weights over logical and temporal operators along with satisfaction times. The proposed approach utilizes mixed integer linear programming (MILP) for synthesis with both STL and wSTL formulae. We introduce efficient disjunction-centric encodings for STL and wSTL that capture both qualitative and quantitative semantics. This encoding minimizes the number of variables and constraints necessary to represent STL and wSTL formulae by efficiently handling conjunction operations (e.g., conjunction, always operators) and only introducing variables when disjunction operations are used (e.g., disjunction, eventually). Multiple case studies are conducted to demonstrate the proposed methodology's operation and computational efficiency for the control synthesis with STL and wSTL specifications. While non-linear dynamics and predicates can be considered using piecewise linear functions, this work focuses on linear predicates and dynamics. We show how cost functions involving potentially conflicting objectives expressed in terms of states, controls, and satisfaction robustness impact the solutions to the control synthesis problem for STL and wSTL. We conduct a sensitivity analysis of weights used in wSTL formulae, offering detailed insights into how these weights modulate solutions for given formulae. Finally, the time performance of the disjunction-centric encodings for both STL and wSTL is compared against state-of-the-art frameworks, comprehensively evaluating their efficiency and practical applicability.

关键词： Signal Temporal Logic Control synthesis mixed integer linear programming Disjunction-centric encoding

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Sustainable Coal Mining Optimization with mixed integer linear programming

Sustainable Coal Mining Optimization with Mixed Integer Line...

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Technology & Engineering Management Conference - Asia Pacific (TEMSCON-ASPAC), IEEE

作者： Alloysius Vendhi Prasmoro Nurhadi Siswanto Budi Santosa Farhan Triofani Department of Industrial and Systems Engineering Institut Teknologi Sepuluh Nopember Surabaya Indonesia Department of Industrial Engineering Universitas Bhayangkara Jakarta Raya Jakarta Indonesia

ISBN: (数字)9798331515881

ISBN: (纸本)9798331515898

Mining businesses in Indonesia, especially in the coal sector, experience several obstacles related to fluctuations in the Reference Coal Price (HBA) due to government regulations with production and export restrictions. These conditions affect the sustainability of coal mining business actors. Efficiency and optimization of the mining process needs to be implemented so that losses can be anticipated with efficient coal production costs and effective operations. This research aims to optimize production scheduling at one of the coal minings so that production is optimal and production costs can be reduced to obtain better profits. This research accommodates several important parameters for the mining process that can influence sustainable operations. Coal mining production scheduling uses mixed integer linear programming (MILP) with a mathematical model that is adjusted to existing variables and parameters to maximise profits. The results of the research show that there are four variations of the model profits according to the implementation period which produce different profits with the highest profit at 55.38% and the lowest profit at 37.78%. From these results, production scheduling can be a guide for companies in their operational activities.

关键词： Schedules Costs Production Companies Coal Mathematical models Coal mining mixed integer linear programming Optimization Business

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Efficient mixed integer linear programming Approaches to Dynamic Path Restoration

Efficient Mixed Integer Linear Programming Approaches to Dyn...

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International Black Sea Conference on Communications and Networking (BlackSeaCom)

作者： Alexander Rubtsov Bruno Bauwens Dmitri Shmelkin Elizaveta Rudenko Alexey Lavrov Faculty of computer science HSE University Moscow Russia Independent University of Moscow Moscow Russia Faculty of mathematics HSE University Moscow Russia

ISBN: (数字)9798350351859

ISBN: (纸本)9798350351866

We consider the problem of single link failure in an elastic optical network, (also known as flex-grid WDM network). The task is to reroute optical connections that go through the broken link using free capacity of other links of the network. Nowadays, dynamic restoration gains popularity, in which the possiblity of rerouting is only inspected after a link failure is detected. Since the problem of recovery is NP-hard, heuristic algorithms are used to either find such routes, or suggest that the routes do not exist. In order to understand the quality of these heuristics, often mixed integer linear programming is used to obtain exact positive and negative answers. We present a detailed such model that checks whether restoration is possible without the use of additional regenerators. This means, that the new light paths need to satisfy a length constraint. As preprossing we apply a trimming procedure that takes advantage of this length constraint, and significantly speeds up the evaluation of these models. Our model is more general, and besides solving the problem of link restoration, also solves the full problem of wavelength and spectrum assignment.

关键词： Adaptation models Heuristic algorithms Optical fiber networks WDM networks Repeaters mixed integer linear programming Dynamic programming

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A mixed integer linear programming-based Distributed Energy Management for Three-phase Unbalanced Active Distribution Network

A Mixed Integer Linear Programming-based Distributed Energy ...

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IEEE Kansas Power and Energy Conference

作者： Guodong Liu Maximiliano Ferrari Yang Chen Electrical Systems Integration Section Oak Ridge National Laboratory Dept. of Industrial and Systems Engineering North Carolina Agricultural and Technical State University

ISBN: (数字)9798350372403

ISBN: (纸本)9798350372410

A mixed integer linear programming (MILP)–based distributed optimization of three-phase unbalanced active distribution network is proposed. Modern distribution networks have becoming more and more active with increasing deployment of microgrids, distributed energy resources (DERs) and flexible loads. Considering various ownership and control models of microgrids, DERs and loads, a distributed optimization was formulated and solved using the alternating direction method of multipliers (ADMM) algorithm. By ADMM, the distribution management system (DMS) and these active components are coordinated through price signals, which are adjusted from the nodal power unbalance per node per phase. To enable resolution of the ADMM-based distributed optimization using MILP solver, various linearization methods were proposed to linearize the augmented Lagrangian and other nonlinear terms. Results of case studies using a three-phase active distribution system with three microgrids and several DERs and flexible loads validated the effectiveness of proposed MILP-based distributed optimization. In addition, the capability of proposed method in mitigating phase power unbalance has been demonstrated.

关键词： linearization techniques Microgrids Transforms Convex functions mixed integer linear programming Active distribution networks Energy management

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A New Planning Model for Optimal Feeder Routing of Radial Distribution System Using mixed integer linear programming Technique

A New Planning Model for Optimal Feeder Routing of Radial Di...

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International Middle-East Power System Conference, MEPCON

作者： Shazly Ahmed Shazly Hassan Mohamed Mahmoud Mohamed Shibl Albags Ahmed Elzawawy Department of Electrical Engineering Faculty of Engineering at Shoubra Benha University Benha Egypt Department of Electrical Engineering Faculty of Engineering Nahda University Beni Suef Egypt

ISBN: (数字)9798350379648

ISBN: (纸本)9798350379655

Several studies have been focused on developing the distribution system planning techniques, varying from classical to nontraditional soft computing techniques, to solve the distribution system planning problem. This paper presents a new planning model for accurate mathematical planning to get optimum feeder routing of radial distribution systems using a mixed integer linear programming (MILP) technique. The model treats the loads at different load buses as injected power. The model also considers the ohmic power loss of various branches as a variable for optimization. All cost items (capital cost, energy loss cost, cost of bays, and line interruption cost) are considered. Also, bus voltage and line capacity limits are considered in addition to the different line sizes. Model verification has been made using two test examples. Lingo software is used to verify the proposed planning model. The developed model can be extended to deal with the general distribution planning problem in which both feeding substations and feeders can be optimized. In addition, it is very important for getting the optimal feeder routing of the system.

关键词： Costs Substations Accuracy Computational modeling Routing Mathematical models Planning mixed integer linear programming Optimization Load modeling

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A multi-agent learning framework for mixed-integer linear programming

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INFOR 2024年第4期62卷 588-598页

作者： Jing, Yuchen Liang, Binyan Li, Siyuan Liu, Feifan Zhao, Wei Liu, Peng Harbin Inst Technol Fac Comp 92 West Dazhi St Harbin 150001 Peoples R China China Acad Launch Vehicle Technol Beijing Peoples R China

mixed integer linear programming (MILP) is an important problem in the combinatorial optimization domain, which has wide applications in practical optimization scenarios. Given that most MILP problems fall into the NP-hard category, which the traditional methods may fail to solve, recent research has tried to derive MILP solutions using machine learning techniques. The whole MILP-solving procedure involves lots of modules, such as pre-solving, cut selection, node section, etc., and these modules are closely related and influence each other. However, the previous machine learning-based approaches neglect the connections between these modules, and focus on single-module learning techniques. To address this, we propose an initial step towards a more comprehensive multi-agent learning framework that allows different modules to interact and collaborate. Specifically, our current implementation involves two key modules: HEM for cut selection applied at the root node and GCNN for variable selection. By employing HEM to influence the training of GCNN, these two agents thus work in unison. Through extensive experiments on four MILP datasets in diverse scenarios, we observe significant improvements in solving time and PD integral metrics compared with the state-of-the-art learning-based MILP solving methods. This work lays the groundwork for future development of a fully integrated multi-agent framework.

关键词： mixed integer linear programming multi-agent learning

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Research on the Optimization of Wind-Solar Energy Storage Systems in Park Microgrids Based on mixed integer linear programming and Monte Carlo Simulation

Research on the Optimization of Wind-Solar Energy Storage Sy...

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Sensors, Electronics and Computer Engineering (ICSECE), IEEE International Conference on

作者： Dongbin Wen Fan Zhang Chengyue Li Peizhi Sheng Huaneng Clean Energy Research Institute Beijing China School of Statistics and Information Shanghai University of International Business and Economics Shanghai China College of Mathematics and Computer Shantou University Shantou China School of Computer and Information Science School of Software Southwest University Chongqing China

ISBN: (数字)9798350373646

ISBN: (纸本)9798350373653

This paper delves into the optimization and economic benefits of wind-solar energy storage systems in park microgrids. By constructing and refining multiple mathematical models, the study provides scientific decision support for system configuration, aiming to meet the increasing demand for load and enhance overall economic benefits. Firstly, the paper proposes the Photovoltaic and Energy Storage Coordination Optimization Model (PCSO-Model), which combines mixed integer linear programming (MILP) with Monte Carlo simulation, effectively reducing the total supply cost of the park. Subsequently, considering the aging effect of energy storage systems, load forecasting errors at different time scales, and the impact of electricity price fluctuations on economic viability, the PCSO model is improved and solved using an improved genetic algorithm. Simulation and optimization results demonstrate that the introduction of energy storage systems reduces costs by approximately 10 % on average, decreases the curtailment of wind and solar power by about 15%, and increases the utilization rate of wind and solar power generation by 20%.

关键词： Wind energy generation Photovoltaic systems Costs Monte Carlo methods Optimization models Microgrids Wind power generation mixed integer linear programming Optimization Energy storage

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PAAMP: Polytopic Action-Set And Motion Planning for Long Horizon Dynamic Motion Planning via mixed integer linear programming

PAAMP: Polytopic Action-Set And Motion Planning for Long Hor...

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IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

作者： Akshay Jaitly Siavash Farzan Robotics Engineering Department Worcester Polytechnic Institute Worcester MA USA Electrical Engineering Department California Polytechnic State University San Luis Obispo CA USA

ISBN: (数字)9798350377705

ISBN: (纸本)9798350377712

Optimization methods for long-horizon, dynamically feasible motion planning in robotics tackle challenging nonconvex and discontinuous optimization problems. Traditional methods often falter due to the nonlinear characteristics of these problems. We introduce a technique that utilizes learned representations of the system, known as Polytopic Action Sets, to efficiently compute long-horizon trajectories. By employing a suitable sequence of Polytopic Action Sets, we transform the long-horizon dynamically feasible motion planning problem into a linear Program. This reformulation enables us to address motion planning as a mixed integer linear Program (MILP). We demonstrate the effectiveness of a Polytopic Action-Set and Motion Planning (PAAMP) approach by identifying swing-up motions for a torque-constrained pendulum as fast as 0.75 milliseconds. This approach is well-suited for solving complex motion planning and long-horizon Constraint Satisfaction Problems (CSPs) in dynamic and underactuated systems such as legged and aerial robots.

关键词： Dynamics Optimization methods Transforms Autonomous aerial vehicles Planning Trajectory mixed integer linear programming Dynamic programming Intelligent robots

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A mixed integer linear programming Model for the Distribution of Transport Tasks Among Heterogeneous Robots in a Factory

A Mixed Integer Linear Programming Model for the Distributio...

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IEEE International Conference on Industrial Technology (ICIT)

作者： Igor Pardal Latini Wilson Eduardo Barioni Marco Teixeira Flavio Neves-Jr Lucia Valeria Ramos de Arruda CPGEI-UTFPR Curitiba Parana Brazil Universidade Tecnologica Federal do Parana (UTFPR) Curitiba Parana Brazil Automation and Advanced Control System Laboratory (LASCA) Graduate Program in Electrical and Computer Engineering (CPGEI) Pontificia Universidade Catolica do Parana (PUCPR) Curitiba Parana Brazil PPGla-PUCPR Curitiba Parana Brazil

ISBN: (数字)9798350340266

ISBN: (纸本)9798350340273

The growing need for automation of factories and their processes determines a constant increase in the use of robots to carry out various tasks. Multiple robots can do different tasks simultaneously, speeding up processes. This practice raises the question of how many robots are needed to service the entire process, given all the limitations of the operation. One of these limitations is due to the navigation systems used by the several robots in the environment. Line-followers robots, for example, can only meet some tasks but are cheaper than free-movement ones. In this work, we develop an optimization model for task allocation among the available robots to minimize execution delays using mixed integer linear programming, considering their navigation systems. With the model, it is possible to obtain the best task allocation for each robot and the order to perform such tasks, thus avoiding delays as much as possible and getting zero delays for the presented case, that emulates the process of a vehicle assembler factory line.

关键词： Service robots Navigation Search problems Production facilities Delays mixed integer linear programming Batteries

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