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Optimization models and algorithms for the hyperplane clustering problem

4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH 2010年第2期8卷 213-216页

作者： Dhyani, Kanika Politecn Milan I-20133 Milan Italy

This is a summary of the author's PhD thesis supervised by Edoardo Amaldi and defended on 3 April 2009 at the Politecnico di Milano. The thesis is written in English and is available from the author upon request. In this work, we extensively study two challenging variants of the general problem of clustering a given set of data points with respect to hyperplanes so as to extract collinearity between them. After pointing out the similarities and differences with previous work on related problems, we propose mathematical programming formulations for our problem variants. Since these problems are difficult to handle due to the nonlinear nonconvexity that arises because of the a"" (2)-norm in the distance function and a large number of binary assignment variables, we develop column generation algorithms and heuristics to tackle them. The efficiency of the methods developed is demonstrated on realistic randomly generated instances along with applications in piecewise linear model fitting and line segment detection in digital images.

关键词： Column generation Hyperplane clustering mixed integer nonlinear programming

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Decision-making model for risk management of cascade hydropower stations

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Journal of Southeast University(English Edition) 2008年第S1期24卷 22-26页

作者： Pan, Bangchuan Chi, Hong Xu, Jianguo Qi, Mingliang Institute of Policy and Management Chinese Academy of Sciences Beijing 100190 China Graduate University Chinese Academy of Sciences Beijing 100049 China

In a medium-term electricity market,in order to reduce the risks of price and inflow uncertainties, the cascade hydropower stations may use the options contract with electricity supply companies. A profit-based model for risk management of cascade hydropower stations in the medium-term electricity market is presented. The objective function is profit maximization of cascade hydropower stations. In order to avoid the risks of price and inflow uncertainties, two different risk-aversion constraints: a minimum profit constraint and a minimum conditional value-at-risk, are introduced in the model. In addition, the model takes into account technology constraints of the generating units, which includes reservoir flow balance, reservoir capacity limits, water discharge constraints, etc. The model is formulated as a mixed integer nonlinear programming problem. Because the search space of the solution is very large, a genetic algorithm is used to deal with the problem.

关键词： cascade hydropower station mixed integer nonlinear programming risk management medium-term electricity market

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An assembly-type supply chain system controlled by kanbans under a just-in-time delivery policy

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2005年第1期162卷 153-172页

作者： Wang, SJ Sarker, BR Louisiana State Univ Dept Ind & Mfg Syst Engn Baton Rouge LA 70803 USA SE Missouri State Univ Dept Ind & Engn Technol Cape Girardeau MO 63701 USA

This research studies the assembly-type supply chain system controlled by kanban mechanism. First, a supply chain system is modeled as a mixed-integer nonlinear programming (MINLP) problem. A composite formulation of the assembly-type supply chain system is developed by appropriately aggregating the individual branch models as a whole system. The batch size, the number of batches, and the total quantity over one period in the mainline and each branch line are determined. The small size MINLP problems are solved optimally by a branch-and-bound method. For the large size MINLP problems, a heuristic is developed which divides the ATSCS into several small size problems, and then conquers them individually. Next, the kanban operation between two adjacent plants is developed to schedule the loading and unloading, and transportation. Coupled with plant-wide efforts for cost control and management commitment, a logistics system is built for controlling the production as well as the supply chain system, which results in minimizing the total cost of the supply chain system. Numerical examples are presented to illustrate the two heuristic procedures and a better solution is obtained for the ATSCS problem. (C) 2003 Elsevier B. V. All rights reserved.

关键词： kanban supply chain inventory control mixed integer nonlinear programming

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Joint optimization of electric bus charging and energy storage system scheduling

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Frontiers of Engineering Management 2024年第4期11卷 676-696页

作者： Lingshu ZHONG Ziling ZENG Zikang HUANG Xiaowei SHI Yiming BIE School of Systems Science and Engineering Sun Yat-Sen UniversityGuangzhou 510399China Department of Architecture and Civil Engineering Chalmers University of TechnologyGothenburg SE-41296Sweden School of Civil Engineering and Transportation South China University of TechnologyGuangzhou 510641China Department of Civil and Environmental Engineering University of Wisconsin-MilwaukeeMilwaukeeWI 53211United States School of Transportation Jilin UniversityChangchun 130012China

The widespread use of energy storage systems in electric bus transit centers presents new opportunities and challenges for bus charging and transit center energy management.A unified optimization model is proposed to jointly optimize the bus charging plan and energy storage system power *** model optimizes overall costs by considering battery aging,time-of-use tariffs,and capacity service *** model is linearized by a series of relaxations of the nonlinear *** means that we can obtain the exact solution of the model quickly with a commercial solver that is fully adapted to the time scale of day-ahead *** numerical simulations demonstrate that the proposed method can optimize the bus charging time,charging power,and power profile of energy storage systems in *** Carlo simulations reveal that the proposed method significantly reduces the cost and has sufficient robustness to uncertain fluctuations in photovoltaics and office loads.

关键词： electric vehicle energy storage mixed integer nonlinear programming Monte Carlo simulations public transit

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A n - D ant colony optimization with fuzzy logic for air traffic flow management

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OPERATIONAL RESEARCH 2022年第5期22卷 5035-5053页

作者： Ntakolia, Charis Lyridis, Dimitrios, V Hellen Air Force Acad Dekelia Air Base Dept Aeronaut Studies Sect Mat Engn Machining Technol & Prod Management 1919 Acharnes Athens Greece Natl Tech Univ Athens Lab Maritime Transport Athens 15772 Greece

Recent studies show that the number of flights is expected to be increased significantly by 2030, leading to air traffic capacity and congestion issues in the air sectors. This challenging management of the anticipated volume of flights has emerged new derivatives and procedures from the European Union and EUROCONTROL. Aligned with the new vision of future Air Traffic Flow Management (ATFM), such as Trajectory Based Operations, this study proposes a mixed integer nonlinear formulation of ATFM based on 4D trajectories and free flight aspects. The model targets to minimize the total costs derived from airborne and ground holding delays, speed deviations, route alterations and cancellation policies. To solve the proposed nonlinear formulation, a novel n - D ant colony optimization algorithm integrated with fuzzy logic (n - DACOF) is presented. Each flight level is represented as graph and the n - D stands for the n number of permitted flight levels. n - DACOF can solve the ATFM problem by constructing a route moving among n graphs. Due to the multi-objective formulation, fuzzy logic permits the qualitative evaluation of the generated routes by the algorithm. The results showed that n - DACOF outperformed the baseline algorithm ACO, as well as, the CPLEX solver within computing time limits.

关键词： mixed integer nonlinear programming 4D trajectories Air traffic flow management Ant colony optimization Fuzzy logic Metaheuristic algorithm

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The unit commitment model with concave emissions costs: a hybrid Benders' Decomposition with nonconvex master problems

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ANNALS OF OPERATIONS RESEARCH 2013年第1期210卷 361-386页

作者： Van Dinter, Jennifer Rebennack, Steffen Kallrath, Josef Denholm, Paul Newman, Alexandra Colorado Sch Mines Div Econ & Business Golden CO 80401 USA Univ Florida Dept Astron Gainesville FL 32611 USA NREL Energy Forecasting & Modeling Grp Golden CO 80401 USA

We present a unit commitment model which determines generator schedules, associated production and storage quantities, and spinning reserve requirements. Our model minimizes fixed costs, fuel costs, shortage costs, and emissions costs. A constraint set balances the load, imposes requirements on the way in which generators and storage devices operate, and tracks reserve requirements. We capture cost functions with piecewise-linear and (concave) nonlinear constructs. We strengthen the formulation via cut addition. We then describe an underestimation approach to obtain an initial feasible solution to our model. Finally, we constitute a Benders' master problem from the scheduling variables and a subset of those variables associated with the nonlinear constructs;the subproblem contains the storage and reserve requirement quantities, and power from generators with convex (linear) emissions curves. We demonstrate that our strengthening techniques and Benders' Decomposition approach solve our mixed integer, nonlinear version of the unit commitment model more quickly than standard global optimization algorithms. We present numerical results based on a subset of the Colorado power system that provide insights regarding storage, renewable generators, and emissions.

关键词： integer programming applications Unit commitment model Power systems Benders' Decomposition Spinning reserves mixed integer nonlinear programming Storage Renewables Convex underestimators

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A Timetable Optimization Model for Passenger and Freight Transport on Airport Rail Line 23

A Timetable Optimization Model for Passenger and Freight Tra...

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23rd COTA International Conference of Transportation Professionals (CICTP) - Innovation-Empowered Technology for Sustainable, Intelligent, Decarbonized, and Connected Transportation

作者： Wang, Baifan Li, Wenquan Yu, Jingcai Deng, Anxin Southeast Univ Sch Transportat Nanjing Peoples R China Southeast Univ Jiangsu Prov Collaborat Innovat Ctr Modern Urban Nanjing Peoples R China

ISBN: (数字)9780784484869

ISBN: (纸本)9780784484869

The application of urban rail transit systems for fast, efficient, and environment-friendly freight transportation is a rising trend in some countries. This paper addresses an urban freight transportation strategy using surplus capacity resources of the airport rail line to solve the intercity freight transportation problem by inserting dedicated freight trains. First, we develop a hybrid nonlinear programming model to collaboratively optimize passenger and freight train timetables to maximize operating company profits. The model covers the relationship among the participants in the scheduling process, including delivery time, departure intervals, stopping schemes, and train capacity. Then, YALMIP and CPLEX are adopted to find a globally optimal solution after linearizing the model. Finally, the proposed method is demonstrated by the Capital Airport Line in Beijing, China. The results show that the proposed model can provide the potential for addressing various freight demands and increasing the operating company's profits.

关键词： Urban Freight Freight on Transit Airport Line mixed integer nonlinear programming

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Integrated optimisation of stope boundary and access layout for underground mining operations

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MINING TECHNOLOGY-TRANSACTIONS OF THE INSTITUTIONS OF MINING AND METALLURGY 2019年第4期128卷 193-205页

作者： Hou, Jie Xu, Chaoshui Dowd, Peter Alan Li, Guoqing Univ Sci & Technol Sch Civil & Resource Engn Beijing Peoples R China Univ Adelaide Sch Civil Environm & Min Engn Adelaide SA Australia Wuhan Univ Sci & Technol Sch Resource & Environm Engn Wuhan Hubei Peoples R China

For underground mines, two major designs that need to be optimised are the stope boundary and the access layout. The optimisation of these two components cannot be done independently as ore extracted from stopes is transported to the surface via the access network. Different stope locations result in different associated access development costs. This paper describes a proposed integrated optimisation model to optimise stope and access layouts simultaneously. The interactions and interdependency between stopes and access are ensured by a dynamic access development cost analysis based on recursive computations. mixed integer non-linear programming is used to maximise the overall economic value subject to the constraints of generating optimal stopes and access layout, which is solved by a Genetic Algorithm modified for computational efficiency. A stratiform gold deposit is used as a case study to demonstrate that the new approach can provide a more profitable solution compared with traditional approaches.

关键词： Underground mine optimisation optimal stope layout and access development mixed integer nonlinear programming dynamic access development cost model

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Comparisons of solving a chromatographic separation problem using MINLP methods

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COMPUTERS & CHEMICAL ENGINEERING 2004年第5期28卷 673-682页

作者： Emet, S Westerlund, T Abo Akad Univ Proc Design Lab FIN-20500 Turku Finland Abo Akad Univ Dept Math FIN-20500 Turku Finland

In the present paper, comparisons of solving a cyclic chromatographic separation problem using mixed integer nonlinear programming (MINLP) methods are presented. The dynamics of the chromatographic separation process is modeled as a boundary value problem that is solved, repeatedly within the optimization, using a relatively fast and numerically robust finite difference method. The MINLP methods considered are the Extended Cutting Plane (ECP), the Branch and Bound (BB), and the Outer Approximation (OA) methods. The comparisons indicate the advantages of the ECP method that needs relatively few function evaluations. The results also show that the total efficiency of traditional OA and BB methods, that solves a sequence of nonlinear programming (NLP) subproblems, is substantially degradated in these kinds of optimization problems involving both a combinatorial task and time-consuming numerical evaluations. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： mixed integer nonlinear programming chromatographic separation extended cutting plane outer approximation branch and bound

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Solving Large MINLPs on Computational Grids

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OPTIMIZATION AND ENGINEERING 2002年第3期3卷 327-346页

作者： Goux, J. -P. Leyffer, S. Artelys F-92136 Issy Les Moulineaux France Argonne Natl Lab MCS Div Argonne IL 60439 USA

We consider the solution of mixed integer nonlinear programming (MINLP) problems by a parallel implementation of nonlinear branch-and-bound on a computational grid or meta-computer. Computational experience on a set o... 详细信息

关键词： mixed integer nonlinear programming parallel branch-and-bound computational grid metacomputing

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