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A mixed-integer linear programming Model for Simultaneous Optimal Reconfiguration and Optimal Placement of Capacitor Banks in Distribution Networks

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IEEE ACCESS 2022年 10卷 52655-52673页

作者： Gallego, Luis A. Lopez-Lezama, Jesus M. Carmona, Oscar Gomez Londrina State Univ UEL Dept Elect Engn BR-86057970 Londrina Parana Brazil Univ Antioquia UdeA Fac Ingn Dept Ingn Elect Grp Invest GIMEL Medellin 050010 Colombia Univ Tecnolog Pereira UTP Grp Invest LIDER Programa Tecnologia Elect Pereira 660003 Colombia

Optimal capacitor placement and network reconfiguration are well-known methods to minimize losses, enhance reliability, and improve the voltage profile of electric distribution networks (EDNs). Distribution network reconfiguration (DNR) consists of altering the system topology by changing the states of ties and sectionalizing switches, while the optimal placement of capacitors (OPCAs) involves sizing and finding the optimal location of capacitor banks within the distribution network for reactive power control. DNR and OPCAs are challenging optimization problems involving both integer and continuous decision variables. Due to the nature of these problems (combinatorial optimization problems), most approaches that deal with DNR and OPCAs resort to metaheuristic techniques, and they are limited to applications in small-size distribution networks. Although these techniques have proven to be effective when dealing with non-convex optimization problems, their main drawbacks lie in the fact that they require the fine-tuning of several parameters and do not guarantee the finding of a globally optimal solution. This paper presents a mixed-integer linear programming (MILP) model to solve simultaneous DNR and OPCAs in radial distribution networks. The proposed model can be solved by commercially available software;it guarantees to obtain globally optimal solutions and requires low computational effort when compared with metaheuristic techniques employed for the same purpose. Several tests were carried out on seven benchmark EDNs ranging from 33 to 417 buses. In all cases, the proposed methodology was able to replicate the results reported in the specialized literature. Regarding the DNR alone, a novel solution was found for the 119-bus test system which is 1.86 % better than that previously reported in the specialized literature. Furthermore, new solutions are reported for the simultaneous optimal DNR and OPCAs for medium and large-size EDNs. The power loss reduction in the te

关键词： Capacitors Metaheuristics Distribution networks Voltage Search problems Genetic algorithms Particle swarm optimization Capacitor placement distribution systems mixed-integer linear programming network reconfiguration

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Optimal scheduling algorithm in point merge system including holding pattern based on mixed-integer linear programming

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART G-JOURNAL OF AEROSPACE ENGINEERING 2020年第10期234卷 1638-1647页

作者： Lee, Somang Hong, Youkyung Kim, Youdan Seoul Natl Univ Dept Aerosp Engn Seoul 08826 South Korea Seoul Natl Univ Inst Adv Aerosp Technol Seoul 08826 South Korea

An optimal scheduling algorithm of the point merge system that considers a holding pattern is presented based on mixed-integer linear programming. The route structure of the point merge system is constructed by adopting virtual fixes, and appropriate constraints are included to integrate a holding pattern into the formulation of point merge system. The performance of the proposed point merge system holding algorithm is demonstrated by comparing with the point merge system and first-come first-served algorithms via Monte Carlo simulation. Simulation reveals that the point merge system holding algorithm shows the best performance in terms of delay reduction and intervention rate by air traffic controllers. The proposed point merge system holding algorithm is expected to assist human air traffic controllers as a decision support tool.

关键词： Air traffic management point merge system holding pattern mixed-integer linear programming sequencing and scheduling

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Alternative mixed integer linear programming Optimization for Joint Job Scheduling and Data Allocation in Grid Computing

arXiv

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arXiv 2025年

作者： Feng, Shengyu Kim, Jaehyung Yang, Yiming Boudreau, Joseph Chowdhury, Tasnuva Hoisie, Adolfy Khan, Raees Kilic, Ozgur O. Klasky, Scott Korchuganova, Tatiana Nilsson, Paul Outschoorn, Verena Ingrid Martinez Park, David K. Podhorszki, Norbert Ren, Yihui Suter, Frederic Vatsavai, Sairam Sri Yang, Wei Yoo, Shinjae Maeno, Tadashi Klimentov, Alexei Carnegie Mellon University PittsburghPA United States Yonsei University Seoul Korea Republic of University of Pittsburgh PittsburghPA United States Brookhaven National Laboratory UptonNY United States Oak Ridge National Laboratory Oak RidgeTN United States University of Massachusetts Amherst AmherstMA United States SLAC National Accelerator Laboratory Menlo ParkCA United States

This paper presents a novel approach to the joint optimization of job scheduling and data allocation in grid computing environments. We formulate this joint optimization problem as a mixed integer quadratically constrained program. To tackle the nonlinearity in the constraint, we alternatively fix a subset of decision variables and optimize the remaining ones via mixed integer linear programming (MILP). We solve the MILP problem at each iteration via an off-the-shelf MILP solver. Our experimental results show that our method significantly outperforms existing heuristic methods, employing either independent optimization or joint optimization strategies. We have also verified the generalization ability of our method over grid environments with various sizes and its high robustness to the algorithm hyper-parameters. Copyright © 2025, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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An inexact CVaR two-stage mixed-integer linear programming approach for agricultural water management under uncertainty considering ecological water requirement

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ECOLOGICAL INDICATORS 2018年 92卷 342-353页

作者： Zhang, Chenglong Guo, Ping China Agr Univ Ctr Agr Water Res China Tsinghuadong St 17 Beijing 100083 Peoples R China

In this study, an inexact CVaR (conditional value-at-risk) two-stage mixed-integer linear programming (ICTMLP) approach is developed for agricultural water management under uncertainty considering ecological water requirement. Techniques of interval parameter programming (IPP), two-stage stochastic programming (TSP), CVaR and integer programming (IP) are jointly incorporated into the general optimization framework. The developed model can deal with uncertainties presented as discrete intervals and probability distributions. It has advantages in: (1) considering economic benefits and risk in the objective function simultaneously, (2) reflecting the tradeoffs between conflicting economic benefits and penalties due to violated policies, (3) facilitating dynamic analysis of decision making and (4) generating more flexible solutions under different risk-aversion levels. The model is applied to a realistic case study of agricultural water resources allocation in the middle reaches of Heihe River Basin, northwest China, where three scenarios with different types of ecological water requirements are taken into account. Therefore, optimal water allocation solutions from the ICTMLP model can support in-depth analysis of interactions among economic benefits, violated policies and risk-aversion levels. Moreover, these results are useful for helping decision makers find better decision alternatives to support regional ecological protection and agricultural production. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Agricultural water allocation Two-stage stochastic programming Conditional value-at-risk mixed-integer linear programming Uncertainty Ecological water requirement

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A mixed-integer linear programming formulation for the modular layout of three-dimensional connected systems

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MATHEMATICS AND COMPUTERS IN SIMULATION 2022年 201卷 739-754页

作者： O'Neill, Sam Wrigley, Paul Bagdasar, Ovidiu Univ Derby Dept Elect Comp & Math Kedleston Rd Derby DE22 1GB England

Given the considerable complexity of process plants, there has been a great deal of research focused on aiding the design of plant layout through mathematical optimisation, i.e. optimising the positioning of the equipment in the plant for space and cost efficiency. Recently, the use of modular approaches within the construction industry, whereby work is performed off-site before being assembled on-site, has become a popular and powerful way of reducing build schedules and costs. Modular approaches have many other real applications where items must be packed to minimise the connections between them (e.g. piping, wiring, modular office and factory layouts) and consider the modular layout of the system. In this paper, we provide a formulation of the problem that, in addition to the standard layout problem, considers a modular block layout to allow modular construction and transportation of the plant. The problem is represented as a directed network, with the aim to pack the items into predefined containers and minimise the rectilinear distance between the connected items. We propose mixed-integer linear programming (MILP) models for the 2-dimensional and 3-dimensional problems and solve them using the state-of-the-art mathematical programming solver, Gurobi. Because of the combinatorial nature of the problem, solutions involving a large number of items may not converge and a suboptimal solution must be considered. However, our results suggest that even in the case of optimising a large number of items, the suboptimal solutions found after a reasonable number of iterations where deemed, by a domain expert, to be a good enough starting point to continue the design process, especially in the early concept phase. (c) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： Floor packing Bin packing Facility layout mixed-integer linear programming MILP Process plant design

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A Unifying Complexity-Certification Framework for Branch-and-Bound Algorithms for mixed-integer linear and Quadratic programming

arXiv

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arXiv 2025年

作者： Shoja, Shamisa Arnström, Daniel Axehill, Daniel Division of Automatic Control Department of Electrical Engineering Linköping University Sweden Division of Systems and Control Department of Information Technology Uppsala University Sweden

In model predictive control (MPC) for hybrid systems, solving optimization problems efficiently and with guarantees on worst-case computational complexity is critical, particularly in real-time applications. These optimization problems often take the form of mixed-integer linear programs (MILPs) or mixed-integer quadratic programs (MIQPs) that depend on system parameters. A common approach for solving such problems is the branch-and-bound (B&B) method. This paper extends existing complexity certification methods by presenting a unified complexity-certification framework for B&B-based MILP and MIQP solvers, specifically for the family of multi-parametric MILP and MIQP problems that arise in, e.g., hybrid MPC applications. The framework provides guarantees on worst-case computational metrics, including the maximum number of iterations or relaxations B&B algorithms require to reach optimality. It systematically accounts for different branching and node selection strategies, as well as heuristics integrated into B&B, ensuring a comprehensive certification framework. By offering theoretical guarantees and practical insights for solver customization, the proposed framework enhances the reliability of B&B for real-time application. The usefulness of the proposed framework is demonstrated through numerical experiments on both random MILPs and MIQPs, as well as on MIQPs arising from a hybrid MPC problem. © 2025, CC BY.

关键词： mixed-integer linear programming

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A new cross decomposition method for stochastic mixed-integer linear programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第2期256卷 487-499页

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

Two-stage stochastic mixed-integer linear programming (MILP) problems can arise naturally from a variety of process design and operation problems. These problems, with a scenario based formulation, lead to large-scale MILPs that are well structured. When first-stage variables are mixed-integer and second-stage variables are continuous, these MILPs can be solved efficiently by classical decomposition methods, such as Dantzig/Wolfe decomposition (DWD), Lagrangian decomposition, and Benders decomposition (BD), or a cross decomposition strategy that combines some of the classical decomposition methods. This paper proposes a new cross decomposition method, where BD and DWD are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. The method terminates finitely to an optimal solution or an indication of the infeasibility of the original problem. Case study of two different supply chain systems, a bioproduct supply chain and an industrial chemical supply chain, show that the proposed cross decomposition method has significant computational advantage over BD and the monolith approach, when the number of scenarios is large. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Stochastic programming mixed-integer linear programming Cross decomposition Benders decomposition Dantzig-Wolfe decomposition

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Dragline operation modelling and task assignment based on mixed-integer linear programming

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OPTIMIZATION AND ENGINEERING 2018年第4期19卷 1005-1036页

作者： Liu, Haoquan Kearney, Michael P. Austin, Kevin J. Univ Queensland Sch Mech & Min Engn Mansergh Shaw Bldg Brisbane Qld 4072 Australia

Draglines are among the largest earthmoving machines in surface mining, where they are used to remove the waste material (overburden) sitting above a target mineral or coal deposit. The effectiveness of their operation is highly dependent on decisions made by their operators, including the sequence of positions at which they operate and the bulk material movement (what to dig and where to dump) during excavation at each position. In this paper, we formulate a mixed-integer linear program that captures the operational constraints imposed in dragline excavation to determine the optimal material movement for a prescribed sequence of dragline positions. Through a simulation study, we show that the dragline productivity can be improved by more effective assignment of material movement tasks to individual dragline positions. We find that the improvement made compared to using a greedy'digging and dumping strategy depends on the dragline positioning sequence and the terrain profile in the specific environment. The solutions in terms of what to dig and where to dump provide insights into the optimal digging and dumping patterns for different types of dragline positioning sequences, and contribute towards solving the overall dragline operation planning problem that includes the planning of the dragline positioning sequence.

关键词： mixed-integer linear programming Optimization Mining robotics Excavation planning

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Antenna tracking profile generation using mixed-integer linear programming

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ADVANCES IN SPACE RESEARCH 2023年第10期71卷 4104-4117页

作者： Hyun, Jeong Hoon Korea Aerosp Res Inst Daejeon South Korea 169 84 Gwahak Ro Daejeon 16984 South Korea

The increasing demand for the improved quantitative and qualitative performance of Earth observation images requires an increase in image data sizes and satellite agility, and that requires an increased effectiveness of antenna operations transmitting data to a ground station. Here, a mixed-integer linear programming (MILP)-based algorithm generating a tracking profile for an antenna subjected to operational constraints was utilized to maximize data transmission time. The constraints included angle and angular velocity limits. This algorithm considers a transition between two sets of angles for the elevation-over-azimuth mechanism to avoid rapid movement. Data transmission angle ranges are depicted as polygons representing the mission environment as mathematical equations in the MILP model. To reduce computation time, two assumptions were applied to simplify the algorithm, which extracts sampling points that can represent interior points. The proposed algorithm was verified by general imaging mission scenarios from a high-mobility satellite with special mis-sion scenarios (i.e., worst-case scenarios for antenna maneuvers). The results were then compared with the preliminary tracking profile from the ground station searching method, which is a heuristic method. The MILP-based algorithm created solutions where data could be transmitted for 97.87% of the entire contact duration;total maneuvers of azimuth and elevation angles averaged at below 45.49% and 60.88% than of those constantly directed at the ground station, respectively. Operational constraints were satisfied in all scenarios, con-firming that the algorithm is well suited to both general and worst-case scenario missions.(c) 2023 COSPAR. Published by Elsevier B.V. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).

关键词： Antenna tracking profile optimization mixed-integer linear programming Elevation-over-azimuth mechanism High-agility Earth observa-tion satellite

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Evaluating the effectiveness of mixed-integer linear programming for day-ahead hydro-thermal self-scheduling considering price uncertainty and forced outage rate

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ENERGY 2017年 122卷 182-193页

作者： Esmaeily, Ali Ahmadi, Abdollah Raeisi, Fatima Ahmadi, Mohammad Reza Nezhad, Ali Esmaeel Janghorbani, Mohammadreza Islamic Azad Univ Dept Elect Engn Karaj Branch Karaj Iran Islamic Azad Univ Dept Elect Engn Marvdasht Branch Marvdasht Iran Hormozgan Univ Dept Management Bandarabbas Iran Islamic Azad Univ Young Researchers & Elite Club Shiraz Branch Shiraz Iran Islamic Azad Univ Dept Elect Engn Cent Tehran Branch Tehran Iran

A new optimization framework based on MILP model is introduced in the paper for the problem of stochastic self-scheduling of hydrothermal units known as HISS Problem implemented in a joint energy and reserve electricity market with day-ahead mechanism. The proposed MILP framework includes some practical constraints such as the cost due to valve-loading effect, the limit due to DRR and also multi-POZs, which have been less investigated in electricity market models. For the sake of more accuracy, for hydro generating units' model, multi performance curves are also used. The problem proposed in this paper is formulated using a model on the basis of a stochastic optimization technique while the objective function is maximizing the expected profit utilizing MILP technique. The suggested stochastic self scheduling model employs the price forecast error in order to take into account the uncertainty due to price. Besides, LMCS is combined with roulette wheel mechanism so that the scenarios corresponding to the non-spinning reserve price and spinning reserve price as well as the energy price at each hour of the scheduling are generated. Finally, the IEEE 118-bus power system is used to indicate the performance and the efficiency of the suggested technique. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： mixed-integer linear programming Uncertainty Modeling Electricity market Self-scheduling

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