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A HYBRID column generation algorithm BASED ON METAHEURISTIC OPTIMIZATION

TRANSPORT 2016年第4期31卷 389-407页

作者： Hu, Wenbin Du, Bo Wu, Ye Liang, Huangle Peng, Chao Hu, Qi Wuhan Univ Sch Comp Wuhan Hubei Province Peoples R China

The exact solution and heuristic solution have their own strengths and weaknesses on solving the Vehicle Routing Problems with Time Windows (VRPTW). This paper proposes a hybrid column generation algorithm with Metaheuristic Optimization (CGAMO) to overcome their weaknesses. Firstly, a Modified Labelling algorithm (MLA) in the sub-problem of path searching is analysed. And a search strategy in CGAMO based on the demand of sub-problem is proposed to improve the searching efficiency. While putting the paths found in the sub-problem into the main problems of CGAMO, the iterations may fall into endless loops. To avoid this problem and keep the main problems in a reasonable size, two conditions on saving the old paths in the main problem are used. These conditions enlarge the number of constraints considered in the iterations to strengthen the limits of dual variables. Through analysing the sub-problem, we can find many useless paths that have no effect on the objective function. Secondly, in order to reduce the number of useless paths and improve the efficiency, this paper proposes a heuristic optimization strategy of CGAMO for dual variables. It is supposed to accelerate the solving speed from the view of on the dual problem. Finally, extensive experiments show that CGAMO achieves a better performance than other state-of-the-art methods on solving VRPTW. The comparative experiments also present the parameters sensitivity analysis, including the different effects of MLA in the different path selection strategies, the characteristics and the applicable scopes of the two path-keeping conditions in the main problem.

关键词： vehicle routing problems with time windows column generation algorithm labelling algorithm sub-problem simplex method dual problem

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Real-time customized bus routes design with optimal passenger and vehicle matching based on column generation algorithm

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2021年 571卷 125836-125836页

作者： Shen, Chan Sun, Yao Bai, Zijian Cui, Hongjun Hebei Univ Technol Sch Civil Engn & Transportat Tianjin 300401 Peoples R China Tianjin Municipal Engn Design & Res Inst Tianjin Peoples R China

With the popularity and development of mobile Internet, new transportation network services such as customized buses are expected to become a new way of popular transportation in crowded metropolises. In this paper, we propose a real-time customized bus routes design model. We divide the proposed model into two-stage problem to solve. The first stage problem is the vehicle route problem with time window (VRPTW), and the second stage problem is bilateral matching problem. For the first stage, the column generation algorithm is used to solve the problem. For the second stage, we solve it by the improved H-R bilateral matching algorithm. Finally, data on customized bus in Tianjin city of China are used to verify the accuracy of the real-time customized bus routes design model. The optimized results show that the average attendance rate has reached 70.8%, and the service rate of passenger has reached 88.5%. The results have proved that the real-time customized bus routes design model has a practical applicability in operation. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Customized bus Real-time Two-stage column generation algorithm H-R bilateral matching algorithm

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Preemptive scheduling with changeovers: Using column generation technique and genetic algorithm

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COMPUTERS & INDUSTRIAL ENGINEERING 1999年第1-2期37卷 81-84页

作者： Figielska, E Warsaw Univ Technol Inst Control & Computat Engn PL-00665 Warsaw Poland

This paper considers the problem of the scheduling of preemptive jobs on unrelated parallel machines, which differs from those discussed in the literature in that it includes changeovers of machines as well as temporary constraints of resources. This problem is complicated to such an extent that even its mathematical formulation seems impossible. Its solution calls therefore for the introduction of some heuristics. The paper presents a two-stage heuristic integrating the column generation technique with a genetic algorithm for the purpose of minimizing the makespan and the total cost of changeovers. The quality of this heuristic is evaluated by comparing the solutions to a lower bound on the objective function optimal value. An integer-linear programming procedure determining the lower bound is proposed. Extensive experimental study shows that the two-stage heuristic presented is effective for medium-size problems with strong temporary resource constraints in the case of the total cast of changeovers being not in excess of 10% of the makespan cost. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： preemptive scheduling parallel machines resource constraints changeover costs column generation algorithm genetic algorithm

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Urban rail-bus-walk network service integration towards accessibility and heat exposure consideration: Models and column generation solution approaches

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2024年 165卷

作者： Huang, Xianting Wei, He Zhang, Xiaodong Tong, Lu (Carol) Carnegie Mellon Univ Pittsburgh PA 15213 USA Beijing Municipal Inst City Planning & Design Beijing 100045 Peoples R China Beihang Univ Sch Elect Informat Engn Beijing 100191 Peoples R China State Key Lab CNS ATM Beijing 100191 Peoples R China

The evolution of urban transportation systems is increasingly driven by the integration of rail, bus, and walking pathways, forming a cohesive service network. This urban rail-bus-walk service network integration is pivotal in addressing urban challenges and ensuring seamless mobility. Nevertheless, the effectiveness of such integrated systems depends on their accessibility and the willingness of individuals to take them as their primary transportation mode. In the context of climate change, extreme heat events pose an increasing threat to passenger comfort and health, which in turn, affects individuals' decisions to use public transit. Additionally, walking to transit stops or waiting for transportation becomes more challenging during such extreme heat conditions. This paper tackles the challenge of comprehensively addressing the evolving issues related to public transit accessibility in response to rising temperatures, an area of research that has received limited attention until now. This paper introduced an approach aimed at optimizing the urban rail-bus-walk service network with a focus on both accessibility and heat exposure considerations. By calculating the transportation accessibility level under varying temperature conditions and identifying its vulnerability to high temperatures, this paper presents a methodology to enhance the transit service. Such improvement involves not only adjustments to the integration network but also considering of cooling facilities, such as shaded routes and shelters. column generation is applied to solve this problem and the optimization result demonstrates improvement of accessibility under the extreme heat condition.

关键词： Multi -modal transportation system Accessibility Heat exposure column generation algorithm

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AN APPLICATION OF AIRLINE CREW SCHEDULING BY USING A column generation APPROACH

JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GA...

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JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GAZI UNIVERSITY 2009年第1期24卷 43-50页

作者： Cankaya, Goezde Arikan, Murat Turkiye Vakiflar Bankasi Ankara Turkey Gazi Univ Endustri Muhendisligi Bolumu Muhendislik Mimarlik Fak TR-06570 Ankara Turkey

Crew scheduling problem is one of the hardest and most comprehensive problems encountered in airline planning. In crew scheduling problem, it is aimed to find the minimum costly set of pairings in that each flight leg is covered at least by one crew pairing. In this study, a column generation approach that is commonly used in crew scheduling literature in which variables are dynamically generated, is used to solve the problem. The master problem is formulated as a set covering problem while the subproblem is formulated as a shortest path problem. Initial pairings which are sufficient to obtain a feasible solution, are produced using a linear programming model. The master problem, sub-problem and the model used to generate initial pairings are encoded by GAMS optimization program in an integrated manner and this integrated model is solved iteratively. The algorithm is applied to a private airline company's crew scheduling problem using real data and optimal crew schedules are obtained.

关键词： Airline crew scheduling crew pairing problem set covering problem column generation algorithm

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Hierarchical two-stage robust optimisation dispatch based on co-evolutionary theory for multiple CCHP microgrids

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IET RENEWABLE POWER generation 2020年第19期14卷 4121-4131页

作者： Tan, Bifei Chen, Haoyong Zheng, Xiaodong South China Univ Technol Sch Elect Power Engn Guangzhou 510641 Guangdong Peoples R China

Combined cooling, heating, and power (CCHP) microgrids are a special form of a microgrid that is attracting increasing attention. This study contributes to the goal of minimising the operation cost of CCHP microgrids by proposing a hierarchical two-stage robust optimisation dispatch model for multiple CCHP microgrid systems. The uncertainties associated with wind power output, electric power, heating, and cooling loads, and transmission line failures are considered in the proposed model. Moreover, the electricity purchasing and selling prices of each microgrid are independently determined. The proposed model applies the outputs of fuel cells, energy storage devices, and gas turbines, the distribution factor of waste heat, and the power transmission between the microgrids and an external grid as control variables. The optimised dispatch problem is solved using McCormick envelopes relaxation and a novel column and constraint generation algorithm that provides enhanced optimisation performance by implementing co-evolutionary theory. In this way, the microgrid system is divided into several sections, and each section is represented as an individual min-max-min problem. The rationality and validity of the proposed model and the superiority of the solution performance of the improved algorithm are verified through simulation case studies involving a system composed of four CCHP microgrids.

关键词： power generation economics gas turbines power generation control wind power plants cogeneration distributed power generation minimax techniques power generation dispatch fuel cells power transmission co-evolutionary theory two-stage robust optimisation dispatch model multiple CCHP microgrid systems wind power output electric power cooling loads transmission line failures waste heat power transmission optimised dispatch problem enhanced optimisation performance hierarchical robust optimisation dispatch combined cooling-heating-power microgrids electricity purchasing fuel cells energy storage devices gas turbines distribution factor McCormick envelopes relaxation column generation algorithm constraint generation algorithm min-max-min problem

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Adaptive uncertainty sets-based two-stage robust optimisation for economic dispatch of microgrid with demand response

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IET RENEWABLE POWER generation 2020年第18期14卷 3608-3615页

作者： Qiu, Yibin Li, Qi Huang, Lanjia Sun, Cai Wang, Tianhong Chen, Weirong Southwest Jiaotong Univ Sch Elect Engn Chengdu 611756 Peoples R China

It is an effective way to regard the electric vehicles as the demand response for reducing the negative impact of large-scale introduction on the power system. Aiming at the microgrid with demand response, the adaptive uncertainty sets-based two-stage robust optimisation method is established in this study. The coordination of micro-gas turbine, energy storage, and demand response etc. are considered in the economic dispatch model. To effectively consider the uncertain variable contained in the microgrid, the concept of adaptive uncertainty sets is proposed in this study. The uncertainty sets are achieved by the long short-term memory network and modified fuzzy information granulation. To handle the adaptive uncertainty sets-based robust optimisation model, the column and constraint generation algorithm and strong duality theory are introduced to decompose the model into a master problem and a subproblem with mixed-integer linear structure. To verify the performance of the proposed adaptive uncertainty sets-based two-stage robust optimisation method, measured data from a plateau city of China are introduced in the simulation test. The simulation results demonstrate the effectiveness of the model and solution strategy.

关键词： duality (mathematics) fuzzy set theory linear programming distributed power generation power generation dispatch gas turbines integer programming power generation economics demand side management recurrent neural nets power engineering computing electric vehicles energy storage demand response robust optimisation model adaptive uncertainty sets-based two-stage robust optimisation method electric vehicles economic dispatch model power system microgrid microgas turbine coordination energy storage long short-term memory network modified fuzzy information granulation constraint generation algorithm column generation algorithm strong duality theory mixed-integer linear structure simulation test

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Green scheduling model of shuttle tanker fleet considering carbon tax and variable speed factor

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JOURNAL OF CLEANER PRODUCTION 2019年 234卷 1134-1143页

作者： Xin, Xu Wang, Xiaoli Tian, Xuecheng Chen, Zigen Chen, Kang Tongji Univ Sch Econ & Management Shanghai 200092 Peoples R China Wuhan Univ Sch Econ & Management Wuhan 430072 Hubei Peoples R China Dalian Maritime Univ Transportat Engn Coll Dalian 116026 Liaoning Peoples R China Dalian Maritime Univ Sch Shipping Econ & Management Dalian 116026 Liaoning Peoples R China

Green scheduling is an important means to achieve sustainable industrial development and enhance the green efficiency of enterprises. Given the characteristics of a modern crude oil supply system, the shuttle tanker fleet green scheduling problem (FGSP) is discussed considering a carbon tax and variable tanker speed factor. To minimize the green operating cost (i.e., sum of general operating cost and carbon tax) of the tanker fleet, an integer programming model for shuttle tanker fleet green scheduling (FGSM) is established. The FGSM optimizes the number and sizes of tankers, the number and positions of floating production storage and offloading units (FPSO) at which to berth and the scheduling plan (i.e., berthing order and sailing speed) of each tanker in the fleet. Based on the column generation algorithm, a shuttle tanker fleet green scheduling algorithm is designed to solve the above model accurately. The experimental results show that considering the speed factor, the green operating cost of an example fleet decreases. For different carbon tax rates, speed optimization is an effective way to reduce the green operating cost of the fleet. The above results also show that the FGSM and algorithm can effectively solve the FGSP, improve the operation level and efficiency, and reduce the green operating cost of oil companies. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Shuttle tanker Ship scheduling Green scheduling Carbon tax Vessel speed column generation algorithm

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Integrated fleet assignment and aircraft routing based on delay propagation

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SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES 2016年第7期41卷 713-719页

作者： Liu, Wan-ming Zhu, Xing-hui Qi, Yan-long Nanjing Univ Aeronaut & Astronaut Coll Civil Aviat Nanjing 210016 Jiangsu Peoples R China

Airlines' expensive resources, especially aircraft, are to be optimally scheduled to cover flights of timetables. However, the irregular flight, due to bad weather, mechanical fault and so on, is inevitable. Moreover, flight delays become more severe with the rapid development of the air transport industry in China and have huge irregular flight cost. In order to alleviate flight delays impact on the flight plan, we present a double objective multi-commodity network flow model of flight delay propagation-based aircraft scheduling and minimize the total delay propagation and airline operation cost as the optimization objective. Branch-and-price solution and column generation algorithm are used to solve the problem. Computational results obtained by using data from a major domestic airline show that our approach can reduce delay propagation significantly, thus improving on-time performance and robustness of aircraft scheduling, and decreasing the total cost simultaneously.

关键词： Aircraft scheduling delay propagation column generation algorithm branch-and-price

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A bi-level programming for bus lane network design

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2015年第Jun.期55卷 310-327页

作者： Yu Bin Kong Lu Sun Yao Yao Baozhen Gao Ziyou Dalian Maritime Univ Transportat Management Coll Dalian 116026 Peoples R China Dalian Univ Technol Sch Automot Engn Dalian 116024 Peoples R China Beijing jiaotong Univ Sch Traff & Transportat Beijing 100044 Peoples R China

This paper proposes a bi-level programming model to solve the design problem for bus lane distribution in multi-modal transport networks. The upper level model aims at minimizing the average travel time of travelers, as well as minimizing the difference of passengers' comfort among all the bus lines by optimizing bus frequencies. The lower level model is a multi-modal transport network equilibrium model for the joint modal split/traffic assignment problem. The column generation algorithm, the branch-and-bound algorithm and the method of successive averages are comprehensively applied in this paper for the solution of the bi-level model. A simple numerical test and an empirical test based on Dalian economic zone are employed to validate the proposed model. The results show that the bi-level model performs well with regard to the objective of reducing travel time costs for all travelers and balancing transit service level among all bus lines. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Bus lane distribution Bi-level programming Benefit equilibrium column generation algorithm

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