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Machine learning augmented branch and bound for mixed integer linear programming

MATHEMATICAL programming 2024年 1-44页

作者： Scavuzzo, Lara Aardal, Karen Lodi, Andrea Yorke-Smith, Neil Delft Univ Technol Delft Netherlands Cornell Tech Jacobs Technion Cornell Inst New York NY USA Technion IIT New York NY USA

mixed integer linear programming (MILP) is a pillar of mathematical optimization that offers a powerful modeling language for a wide range of applications. The main engine for solving MILPs is the branch-and-bound algorithm. Adding to the enormous algorithmic progress in MILP solving of the past decades, in more recent years there has been an explosive development in the use of machine learning for enhancing all main tasks involved in the branch-and-bound algorithm. These include primal heuristics, branching, cutting planes, node selection and solver configuration decisions. This article presents a survey of such approaches, addressing the vision of integration of machine learning and mathematical optimization as complementary technologies, and how this integration can benefit MILP solving. In particular, we give detailed attention to machine learning algorithms that automatically optimize some metric of branch-and-bound efficiency. We also address appropriate MILP representations, benchmarks and software tools used in the context of applying learning algorithms.

关键词： mixed integer linear programming Branch and bound Machine learning Metrics Benchmarks

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Hybrid simulated annealing and mixed integer linear programming algorithm for optimal planning of radial distribution networks with distributed generation

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ELECTRIC POWER SYSTEMS RESEARCH 2014年 108卷 211-222页

作者： Popovic, Z. N. Kerleta, V. Dj. Popovic, D. S. Univ Novi Sad Fac Tech Sci Novi Sad 21000 Serbia Univ Novi Sad Tech Fac Mihailo Pupin Zrenjanin 23000 Serbia

This paper presents a hybrid simulated annealing (SA) and mixed integer linear programming (MILP) approach for static expansion planning of radial distribution networks with distributed generators (DGs). The expansion planning problem is first modeled as MILP optimization problem with the goal of minimizing the investment cost, cost of losses, cost of customer interruptions due to failures at the branches and at DGs and the cost of lost DG production due to failures at branches. In order to reduce the complexity of planning problems the decomposition of the original problem is proposed into a number of sequences of sub-problems (local networks) that are solved using the MILP model. The decomposition and solution process is iteratively guided and controlled by the proposed SA algorithm that employs the proper intensification and diversification mechanism to obtain the minimum total cost solution. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Distribution network planning Distributed generators Decomposition approach mixed integer linear programming Simulated annealing

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An MILP (mixed integer linear programming) model for optimal design of district-scale distributed energy resource systems

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ENERGY 2015年第Part2期90卷 1901-1915页

作者： Yang, Yun Zhang, Shijie Xiao, Yunhan Chinese Acad Sci Inst Engn Thermophys Key Lab Adv Energy & Power Beijing 100190 Peoples R China Chinese Acad Sci Res Ctr Clean Energy & Power Lianyungang 222069 Jiangsu Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China

This study focuses on the optimal design of district-scale DER (distributed energy resource) systems in which energy is produced outside energy-consuming buildings and sent to the buildings through the energy distribution networks. A MILP (mixed integer linear programming) model is constructed. The model can achieve simultaneous optimization of locations (i.e., site for energy generation), synthesis (i.e., type, capacity, and number of equipment as well as structure of the energy distribution networks), and operation strategies of the entire system. The model is built in consideration of discreteness of equipment capacities, equipment partial load operation and output bounds as well as the influence of ambient temperature on gas turbine performance. The objective function is the total annual cost for investing, maintaining, and operating the system. The model is applied to an urban area in Guangzhou (China), and its validity and effectiveness is verified. Results show that the adoption of the proposed DER system provides significant economic benefits in respect to the conventional energy system. (C) 2015 Published by Elsevier Ltd.

关键词： Distributed energy resource Optimal design Synthesis and operation strategies Energy distribution networks mixed integer linear programming

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Multi-parametric mixed integer linear programming under global uncertainty

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COMPUTERS & CHEMICAL ENGINEERING 2018年 116卷 279-295页

作者： Charitopoulos, Vassilis M. Papageorgiou, Lazaros G. Dua, Vivek UCL Ctr Proc Syst Engn Dept Chem Engn Torrington Pl London WC1E 7JE England

Major application areas of the process systems engineering, such as hybrid control, scheduling and synthesis can be formulated as mixed integer linear programming (MILP) problems and are naturally susceptible to uncertainty. Multi-parametric programming theory forms an active field of research and has proven to provide invaluable tools for decision making under uncertainty. While uncertainty in the righthand side (RHS) and in the objective function's coefficients (OFC) have been thoroughly studied in the literature, the case of left-hand side (LHS) uncertainty has attracted significantly less attention mainly because of the computational implications that arise in such a problem. In the present work, we propose a novel algorithm for the analytical solution of multi-parametric MILP (mp-MILP) problems under global uncertainty, i.e. RHS, OFC and LHS. The exact explicit solutions and the corresponding regions of the parametric space are computed while a number of case studies illustrates the merits of the proposed algorithm. (C) 2018 The Authors. Published by Elsevier Ltd.

关键词： Optimisation under uncertainty Multi-parametric programming mixed integer linear programming Cylindrical algebraic decomposition Grobner bases Process scheduling

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An assembly timing planning method based on knowledge and mixed integer linear programming

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JOURNAL OF INTELLIGENT MANUFACTURING 2023年第2期34卷 429-453页

作者： Qian, Jiahui Zhang, Zhijing Shi, Lingling Song, Dan Beijing Inst Technol Sch Mech Engn 5 Zhongguancun South St Beijing 100081 Peoples R China

Assembly timing planning, which aims to solve the assembly action sequence and assembly part sequence with the shortest assembly time as the goal, is a necessary and critical step in intelligent assembly process planning. However, the current focus of assembly process planning is assembly sequence planning, whereas little research has been performed on assembly timing planning. A novel assembly timing planning method based on knowledge and mixed integer linear programming (MILP) is proposed in this paper. First, a knowledge base of the assembly process for timing planning is constructed using ontology. Then, based on the proposed strategy of dividing assembly timing planning into within-group planning and between-group planning, a MILP model of assembly timing planning for automatic assembly system is constructed. In addition, a software that realizes timing planning through human-machine collaboration is developed to verify and visualize the proposed timing planning method. The implementation is as follows: assembly action sentences are formed by searching the ontology keyword library, then timing knowledge for the action sequence and assembly sequence is established, and finally optimal assembly timing results are obtained after the calculation. Compared with the traditional serial assembly process, this method significantly reduces the assembly time, thereby improving the assembly efficiency, and the assembly schedule can be obtained automatically and quickly to guide the assembly process design.

关键词： Assembly timing planning Knowledge mixed integer linear programming Intelligent assembly

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A mixed integer linear programming Model for Resolution of the Antenna-Satellite Scheduling Problem

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2024年第1期60卷 463-473页

作者： Linares, Lorena Vazquez, Rafael Perea, Federico Galan-Vioque, Jorge Univ Seville Dept Aerosp Engn Fluids Mech ETSI Seville 41092 Spain Univ Seville Appl Math 2 EPS Seville 41004 Spain Univ Seville Appl Math II ETSI Seville 41092 Spain

This article deals with one of the types of "Satellite Range Scheduling" problems arising in Earth Observation Satellite operations, Antenna-Satellite Scheduling. Given a set of satellites, a set of available antennas and a time horizon, the problem consists of designing an operational plan that assigns satellites to antennas in an optimal fashion. Extending a previous integer linear programming (ILP) model (shortening model, with only integer variables), we propose a mixed ILP (MILP) (shaving model, which includes both continuous and integer variables), to more efficiently solve this problem. After computing the passes generated by the satellites' windows of visibility from the antennas, the optimal planner is able to cancel a pass, move it to another antenna, or shorten its duration, in order to avoid scheduling conflicts. In contrast to the shortening model, which used intersections between passes to determine the best schedule, the shortening operation is now referred to as shaving, since the shaving model can arbitrarily adjust the duration of a pass in a razor-like fashion, giving the model its name. Computational results obtained in tests over realistic scenarios prove that the shaving model outperforms the shortening model, producing fewer cancellations, smaller shaved times, and a fairer distribution of cancelled passes among satellites, with much shorter preprocessing times.

关键词： Satellites Satellite antennas Task analysis Computational modeling Genetic algorithms Optimal scheduling Antennas Antenna-satellite allocation deconfliction mixed integer linear programming optimal satellite scheduling satellite range scheduling

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Volt/var optimization of unbalanced distribution feeders via mixed integer linear programming

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2015年第Nov.期72卷 40-47页

作者： Borghetti, Alberto Napolitano, Fabio Nucci, Carlo Alberto Univ Bologna I-40126 Bologna Italy

The paper presents a mixed integer linear programming (MILP) model for the solution of the three-phase volt/var optimization (WO) of medium voltage unbalanced distribution feeders. The WO of a distribution feeder is aimed at calculating the most efficient operating conditions by means of the scheduling of transformers equipped with an on-load tap changer and distributed reactive power resources (such as embedded generators and switchable capacitors banks). The proposed model allows the representation of feeders composed by three-phase, two-phase, and single-phase lines, by transformers with different winding connections, by unbalanced wye- and delta-connected loads, by three-phase and single phase capacitor banks and embedded generators. The accuracy of the results is verified by using IEEE test feeders. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Power distribution feeders Unbalanced networks Volt/var optimization mixed integer linear programming

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Exact augmented Lagrangian duality for mixed integer linear programming

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MATHEMATICAL programming 2017年第1-2期161卷 365-387页

作者： Feizollahi, Mohammad Javad Ahmed, Shabbir Sun, Andy Georgia State Univ Robinson Coll Business Atlanta GA 30303 USA Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

We investigate the augmented Lagrangian dual (ALD) for mixed integer linear programming (MIP) problems. ALD modifies the classical Lagrangian dual by appending a nonlinear penalty function on the violation of the dualized constraints in order to reduce the duality gap. We first provide a primal characterization for ALD for MIPs and prove that ALD is able to asymptotically achieve zero duality gap when the weight on the penalty function is allowed to go to infinity. This provides an alternative characterization and proof of a recent result in Boland and Eberhard (Math Program 150(2):491-509, 2015, Proposition 3). We further show that, under some mild conditions, ALD using any norm as the augmenting function is able to close the duality gap of an MIP with a finite penalty coefficient. This generalizes the result in Boland and Eberhard (2015, Corollary 1) from pure integer programming problems with bounded feasible region to general MIPs. We also present an example where ALD with a quadratic augmenting function is not able to close the duality gap for any finite penalty coefficient.

关键词： mixed integer linear programming Lagrangian duality Penalty functions

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A multi-period multiple parts mixed integer linear programming model for AM adoption in the spare parts supply Chain

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INTERNATIONAL JOURNAL OF COMPUTER INTEGRATED MANUFACTURING 2024年第5期37卷 550-571页

作者： Mecheter, Asma Pokharel, Shaligram Tarlochan, Faris Tsumori, Fujio Qatar Univ Dept Mech & Ind Engn Doha Qatar Kyushu Univ Fac Engn Dept Aeronaut & Astronaut Fukuoka Japan Qatar Univ Dept Mech & Ind Engn POB 2713 Doha Qatar

This research proposes a multi-period multiple parts mixed-integer linear programming optimization model for the trade-off analysis of spare parts supply through computer numerical control (CNC) manufacturing and additive manufacturing (AM). The multiple spare parts have different characteristics such as volume, shape size, and geometry complexity. The model focuses on minimizing lead times and thus reducing downtime costs. Scenario analyses are developed for some parameters to assess the robustness of the model. The analysis shows that the mix between AM-based spare parts and CNC-based spare parts is sensitive to changes in demand. For the given data, the findings demonstrate that AM is cost-effective with spare parts having high geometry complexity while CNC-based manufacturing is economically feasible for spare parts with low geometry complexity and large sizes. The proposed model can support decision-makers in selecting the optimal manufacturing method for multiple spare parts having different characteristics and attributes. The paper concludes with limitations and future directions.

关键词： Additive manufacturing supply chain spare parts optimization mixed integer linear programming conventional manufacturing

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Compact mixed integer linear programming models to the minimum weighted tree reconstruction problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第1期256卷 242-251页

作者： Fortz, Bernard Oliveira, Olga Requejo, Cristina Univ Libre Bruxelles Dept Comp Sci B-1050 Brussels Belgium INRIA Lille Nord Europe Lille France Univ Aveiro Dept Math P-3810193 Aveiro Portugal

The Minimum Weighted Tree Reconstruction (MWTR) problem consists of finding a minimum length weighted tree connecting a set of terminal nodes in such a way that the length of the path between each pair of terminal nodes is greater than or equal to a given distance between the considered pair of terminal nodes. This problem has applications in several areas, namely, the inference of phylogenetic trees, the modeling of traffic networks and the analysis of internet infrastructures. In this paper, we investigate the MWTR problem and we present two compact mixed-integer linear programming models to solve the problem. Computational results using two different sets of instances, one from the phylogenetic area and another from the telecommunications area, show that the best of the two models is able to solve instances of the problem having up to 15 terminal nodes. (C) 2016 Elsevier B.V. All rights reserved.

关键词： mixed integer linear programming Tree realization Topology discovery Routing topology inference Minimum evolution problem

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