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

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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Mitigating unfairness in urban rail transit operation: A mixed-integer linear programming approach

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2021年 149卷 418-442页

作者： Wu, Yinghui Yang, Hai Zhao, Shuo Shang, Pan Jiangsu Univ Sci & Technol Sch Econ & Management Zhenjiang 212100 Jiangsu Peoples R China Hong Kong Univ Sci & Technol Dept Civil & Environm Engn Kowloon Clear Water Bay Hong Kong Peoples R China China Acad Railway Sci Corp Ltd Inst Comp Technol Beijing 100081 Peoples R China Beijing Jiaotong Univ Sch Traff & Transportat Beijing 10044 Peoples R China

In oversaturated urban rail transit systems, passengers departing from downstream stations often experience long waiting times due to unbalanced space-time demand and limited transit capacity. This is often prevalent during morning and evening peak periods in transit systems. This paper aims to mitigate the unfairness of waiting time among a time-varying number of passengers through train timetable's adjustment by optimizing the train skip-stopping pattern. We develop an approximate general model by clustering passengers into groups and introducing an aggregation granularity parameter. To characterize feasible passenger travel patterns, both rigid first-in-first-out rule and capacity constraints are incorporated in the proposed model. Preprocessing is proposed to reduce the space of solutions. Some small-scale case studies show that the proposed method outperforms the original timetable and the preprocessing is effective to reduce computation time. Case studies based on the Batong line of Beijing rail transit network are conducted, in which a variable neighborhood search algorithm is applied to obtain high-quality solutions in short computing times. The results show that the proposed approach not only mitigates the unfairness of waiting time among passengers but also improves other efficiency evaluation indexes, including the average waiting time and the maximum number of missed trains. We also investigate the impact of the aggregation granularity parameter on the computational effort and solution accuracy. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Unfairness Skip-stopping pattern Urban rail transit mixed-integer linear programming Variable neighborhood search

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mixed-time mixed-integer linear programming for optimal detailed scheduling of a crude oil port depot

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CHEMICAL ENGINEERING RESEARCH & DESIGN 2018年 137卷 434-451页

作者： Zhang, Haoran Liang, Yongtu Liao, Qi Gao, Jie Yan, Xiaohan Zhang, Wan China Univ Petr Beijing Key Lab Urban Oil & Gas Distribut Technol Fuxue Rd 18 Beijing 102249 Peoples R China Univ Tokyo Ctr Spatial Informat Sci 5-1-5 Kashiwanoha Kashiwa Chiba 2778568 Japan

Crude oil port depots are key hubs in oil trade and thus play a vital role in the crude oil supply chain. Based on the characteristics of the scheduling system in an oil port depot, the development of a precise schedule is essential for handling asynchronous upstream supply and downstream market demand, thereby reducing operation cost as well as the impact of market fluctuations. Most previous studies focused only on the depot system, and few have taken the export transport scheduling into consideration. In this study, the diversity of crude oil storage modes, complexity of operations, and variety of transportation modes are considered. To minimize the total operation cost, a mixed-time representation based on a mixed-integer linear programming model is established. Finally, three real cases in a crude oil port depot in China are studied, and the monthly schedules of the depot are developed. Compared with previous algorithms, this method yields more accurate results in a considerably shorter time with improved computational stability. (C) 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

关键词： Detailed scheduling Crude oil port depot mixed-integer linear programming mixed-time representation

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More mixed-integer linear programming models for solving three-stage remanufacturing system scheduling problem

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COMPUTERS & INDUSTRIAL ENGINEERING 2024年 194卷

作者： Wang, Wenjie Tian, Guangdong Luo, Mengqi Zhang, Honghao Yuan, Gang Niu, Kejia Zhengzhou Univ Sch Mech & Power Engn Zhengzhou 450001 Peoples R China Beijing Univ Civil Engn & Architecture Sch Machinery & Vehicles Beijing 100044 Peoples R China Shandong Univ Sch Mech Engn Jinan 250061 Peoples R China Southeast Univ Sch Mech Engn Nanjing 212000 Peoples R China Henan Univ Sci & Technol Sch Appl Engn Sanmenxia 472199 Peoples R China

This paper aims to deal with the three-stage remanufacturing system scheduling problem (3T-RSSP) that minimizes the maximum completion time i.e., makespan. To this end, inspired by distinct modeling ideas, four mixedinteger linear programming (MILP) models are formulated. The modeling ideas used in this paper are sequencebased idea, position-based idea, time-based idea, and adjacent sequence-based idea. Numerical experiments are executed on a set of small-scaled, medium-scaled and large-scaled instances to test the performance of these formulated MILP models in terms of size complexity and computation complexity. Experimental results demonstrate that the sequence-based MILP model (Model 1) is the most efficient one while the time-based MILP model (Model 3) is worst one. The Wilcoxon signed-rank test is also conducted to evaluate the four models. Model 1 is further compared with different optimization solvers, heuristic and some state-of-art heuristics. Comparison results verify the effectiveness and good portability of the MILP model. Moreover, some key parameters contained in 3T-RSSP including end-of-life (EOL) products count, reprocessing lines count, disassembly workstations/reassembly workstations count are also evaluated. Notably, it is concluded that the increase of disassembly workstations/reassembly workstations count can improve the three-stage remanufacturing system's flexibility and contribute to the enhancement of production efficiency.

关键词： Three-stage remanufacturing system scheduling Makespan mixed-integer linear programming Modeling and optimization

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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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Optimal scheduling of a renewable micro-grid in an isolated load area using mixed-integer linear programming

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RENEWABLE ENERGY 2010年第1期35卷 151-156页

作者： Morais, Hugo Kadar, Peter Faria, Pedro Vale, Zita A. Khodr, H. M. Polytech Inst Porto ISEP GECAD Knowledge Engn & Decis Support Res Ctr Elect Engn P-4200072 Oporto Portugal Budapest Univ Technol & Econ H-1111 Budapest Hungary

In the energy management of the isolated operation of small power system, the economic scheduling of the generation units is a crucial problem. Applying right timing can maximize the performance of the supply. The optimal operation of a wind turbine, a solar unit, a fuel cell and a storage battery is searched by a mixed-integer linear programming implemented in General Algebraic Modeling Systems (GAMS). A Virtual Power Producer (VPP) can optimal operate the generation units, assured the good functioning of equipment, including the maintenance, operation cost and the generation measurement and control. A central control at system allows a VPP to manage the optimal generation and their load control. The application of methodology to a real case study in Budapest Tech, demonstrates the effectiveness of this method to solve the optimal isolated dispatch of the DC micro-grid renewable energy park. The problem has been converged in 0.09 s and 30 iterations. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： mixed-integer linear programming Renewable energy park Scheduling Virtual power producer

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Reduction in the number of binary variables for inter-sample avoidance in trajectory optimizers using mixed-integer linear programming

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INTERNATIONAL JOURNAL OF ROBUST AND NONlinear CONTROL 2016年第16期26卷 3662-3669页

作者： Afonso, Rubens J. M. Galvao, Roberto K. H. Kienitz, Karl H. Inst Tecnol Aeronaut Dept Elect Engn Sao Paulo Brazil

This note proposes the use of a tuple encoding scheme to reduce the number of binary variables involved in trajectory optimization problems with inter-sample avoidance constraints. Copyright (c) 2016 John Wiley & ... 详细信息

关键词： inter-sample avoidance binary variables mixed-integer linear programming

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A mixed-integer linear programming Approach for Multi-Stage Security-Constrained Transmission Expansion Planning

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IEEE TRANSACTIONS ON POWER SYSTEMS 2012年第2期27卷 1125-1133页

作者： Zhang, Hui Vittal, Vijay Heydt, Gerald Thomas Quintero, Jaime Arizona State Univ Dept Elect Engn Tempe AZ 85287 USA

The transmission expansion planning (TEP) problem in modern power systems is a large-scale, mixed-integer, non-linear and non-convex problem. Although remarkable advances have been made in optimization techniques, finding an optimal solution to a problem of this nature can still be extremely challenging. Based on the linearized power flow model, this paper presents a mixed-integer linear programming (MILP) approach that considers losses, generator costs and the N - 1 security constraints for the multi-stage TEP problem. The losses and generator cost are modeled as piecewise linear functions of the line flows and the generator outputs, respectively. The IEEE 24-bus system is used to compare the lossy and the lossless model. The results show that the lossy model provides savings in total cost in the long run. The selection of the best number of piecewise linear sections L is also shown. Then a complete planning framework is presented and a multi-stage TEP is performed on the IEEE 118-bus test system. Simulation results show that the proposed approach is accurate and efficient, and has the potential to be applied to large-scale power system planning problems.

关键词： Generator cost modeling loss modeling mixed-integer linear programming N-1 contingency modeling piecewise linearization transmission engineering transmission expansion planning

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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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A mixed-integer linear programming approach for the T-row and the multi-bay facility layout problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第2期295卷 443-462页

作者： Dahlbeck, Mirko TU Dortmund Univ Fac Business & Econ Vogelpothsweg 87 D-44227 Dortmund Germany Georg August Univ Gottingen Inst Numer & Appl Math Lotzestr 16-18 D-37083 Gottingen Germany

We introduce a new facility layout problem, the so-called T-Row Facility Layout Problem (TRFLP). The TRFLP consists of a set of one-dimensional departments with pairwise transport weights between them and two orthogonal rows which form a T such that departments in different rows cannot overlap. The aim is to find a non-overlapping assignment of the departments to the rows such that the sum of the weighted center-to-center distances measured in rectilinear directions is minimized. The TRFLP is a generalization of the well-known Multi-Bay Facility Layout Problem with three rows (3-BFLP). Both problems, the TRFLP and the 3-BFLP, have wide applications, e.g., factory planning, semiconductor fabrication and arranging rooms in hospitals. In this work we present a mixed-integer linear programming approach for the TRFLP and the 3-BFLP based on an extension of the well-known betweenness variables which now can be equal to one if the corresponding departments lie in different rows. One advantage of our formulation is the calculation of inter-row distances without big-M-type constraints. We provide cutting planes exploiting the crossroad structure in the layout, and hence T-row (3-Bay) instances with up to 18 (17) departments are solved to optimality in less than 7 h. The best known approach for the 3-BFLP is clearly outperformed. Additionally, tight lower bounds for larger instances are calculated to evaluate our heuristically determined layouts. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Facilities planning and design mixed-integer linear programming Row layout problem

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