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Link Restriction: Methods of Testing and Avoiding Braess Paradox in Networks Considering Traffic Demands

JOURNAL OF TRANSPORTATION ENGINEERING PART A-SYSTEMS 2018年第2期144卷

作者： Ma, Jie Li, Dawei Cheng, Lin Lou, Xiaoming Sun, Chao Tang, Wenyun Southeast Univ Sch Transportat 2 Si Pai Lou Rd Nanjing 210096 Jiangsu Peoples R China

Braess paradox is a well-known paradox in transportation researches. In urban cities, there are many different kinds of complex road networks. Unavoidably, some of them fall into the Braess paradox and it is hardly realized. In this paper, two proposed approaches are applied to find and avoid the Braess paradox in urban road networks. With the first approach, the links that cause the Braess paradox in the urban road networks with the current origination-destination (OD) matrix can be tested. The other approach is to calculate the range of the OD flows that makes these links fall into the Braess paradox. Unlike other approaches proposed in literature, this proposed approach can figure out the range of traffic demands in the networks with multiple OD pairs. Moreover, by applying these two approaches, the authors design a traffic management called link restriction which can easily figure out which link should be closed down temporarily and when to resume operation to reduce the total travel times of networks with flexible managements. (C) 2017 American Society of Civil Engineers.

关键词： Bilevel mixed-integer programming Nonlinear programming User equilibrium Bureau of Public Road (BPR) function Path flows Link flows Multiple origination-destination (OD) pairs

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An efficient Ant Colony algorithm based on wake-vortex modeling method for aircraft scheduling problem

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2017年 317卷 157-170页

作者： Xu, Bo Univ Shanghai Sci & Technol Sch Business Shanghai 200093 Peoples R China

The aircraft scheduling problem (ASP) is a salient problem in airport runway scheduling system. This paper originally proposes an Ant Colony (AC) algorithm based on the wake vortex modeling (WVM) method for ASP. Numerical results validate that this new method has better performance than CPLEX, general AC algorithm, and approximation algorithm in Ma et al. (2014). It is a promising method to improve the efficiency of the aircraft scheduling system from a theoretical standpoint. (c) 2016 Elsevier B.V. All rights reserved.

关键词： Aircraft scheduling problem WVM Rank 2 matrix approximation mixed-integer programming

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A New General-Purpose Algorithm for mixed-integer Bilevel Linear Programs

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OPERATIONS RESEARCH 2017年第6期65卷 1615-1637页

作者： Fischetti, Matteo Ljubic, Ivana Monaci, Michele Sinnl, Markus Univ Padua Dept Informat Engn I-35131 Padua Italy ESSEC Business Sch Paris F-95021 Cergy Pontoise France Univ Bologna DEI Guglielmo Marconi I-40136 Bologna Italy Univ Vienna Dept Stat & Operat Res A-1090 Vienna Austria

Bilevel optimization problems are very challenging optimization models arising in many important practical contexts, including pricing mechanisms in the energy sector, airline and telecommunication industry, transportation networks, critical infrastructure defense, and machine learning. In this paper, we consider bilevel programs with continuous and discrete variables at both levels, with linear objectives and constraints (continuous upper level variables, if any, must not appear in the lower level problem). We propose a general-purpose branch-and-cut exact solution method based on several new classes of valid inequalities, which also exploits a very effective bilevel-specific preprocessing procedure. An extensive computational study is presented to evaluate the performance of various solution methods on a common testbed of more than 800 instances from the literature and 60 randomly generated instances. Our new algorithm consistently outperforms (often by a large margin) alternative state-of-the-art methods from the literature, including methods exploiting problem-specific information for special instance classes. In particular, it solves to optimality more than 300 previously unsolved instances from the literature. To foster research on this challenging topic, our solver is made publicly available online.

关键词： bilevel optimization mixed-integer programming cutting planes intersection cuts branch and cut computational analysis

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Lagrangian Heuristics for Large-Scale Dynamic Facility Location with Generalized Modular Capacities

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INFORMS JOURNAL ON COMPUTING 2017年第3期29卷 388-404页

作者： Jena, Sanjay Dominik Cordeau, Jean-Francois Gendron, Bernard Univ Montreal CIRRELT Montreal PQ H3C 3J7 Canada Univ Montreal Dept Informat & Rech Operat Montreal PQ H3C 3J7 Canada HEC Montreal CIRRELT Montreal PQ H3T 2A7 Canada HEC Montreal Canada Res Chair Logist & Transportat Montreal PQ H3T 2A7 Canada

We consider the dynamic facility location problem with generalized modular capacities, a multiperiod facility location problem in which the costs for capacity changes may differ for all pairs of capacity levels. The problem embeds a complex cost structure and generalizes several existing facility location problems, such as those that allow temporary facility closing or capacity expansion and reduction. As the model may become very large, general-purpose mixed-integer programming (MIP) solvers are limited to solving instances of small to medium size. In this paper, we extend the generalized model to the case of multiple commodities. We propose Lagrangian heuristics, based on subgradient and bundle methods, to find good quality solutions for large-scale instances with up to 250 facility locations and 1,000 customers. To improve the final solution quality, a restricted MIP model is solved based on the information collected through the solution of the Lagrangian dual. Computational results show that the Lagrangian-based heuristics provide highly reliable results for all problem variants considered. They produce good quality solutions in short computing times even for instances where state-of-the-art MIP solvers do not find feasible solutions. The strength of the formulation also allows the method to provide tight bounds on the optimal value.

关键词： dynamic facility location modular capacities Lagrangian heuristics mixed-integer programming

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MILP models for the selection of a small set of well-distributed points

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OPERATIONS RESEARCH LETTERS 2017年第1期45卷 46-52页

作者： D'Ambrosio, Claudia Nannicini, Giacomo Sartor, Giorgio Ecole Polytech CNRS LIX UMR7161 Palaiseau France IBM TJ Watson Yorktown Hts NY USA Singapore Univ Technol & Design ESD Singapore Singapore

Motivated by the problem of fitting a surrogate model to a set of feasible points in the context of constrained derivative-free optimization, we consider the problem of selecting a small set of points with good space-filling and orthogonality properties from a larger set of feasible points. We propose four mixed-integer linear programming models for this task and we show that the corresponding optimization problems are NP-hard. Numerical experiments show that our models consistently yield well-distributed points that, on average, help reducing the variance of model fitting errors. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Model fitting mixed-integer programming Derivative-free optimization Experimental design

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A mixed-integer optimization approach for homogeneous magnet design

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TECHNOLOGY 2018年第2期6卷 49-58页

作者： Dayarian, Iman Chan, Timothy C. Y. Jaffray, David Stanescu, Teo Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA Univ Toronto Dept Mech & Ind Engn Toronto ON M5S 3G8 Canada Techna Inst 124-100 Coll St Toronto ON M5G 1L5 Canada Univ Hlth Network Princess Margaret Canc Ctr Toronto ON M5G 2M9 Canada Univ Toronto Dept Radiat Oncol Toronto ON M5S 3E2 Canada

Magnetic resonance imaging (MRI) is a powerful diagnostic tool that has become the imaging modality of choice for soft-tissue visualization in radiation therapy. Emerging technologies aim to integrate MRI with a medical linear accelerator to form novel cancer therapy systems (MR-linac), but the design of these systems to date relies on heuristic procedures. This paper develops an exact, optimization-based approach for magnet design that 1) incorporates the most accurate physics calculations to date, 2) determines precisely the relative spatial location, size, and current magnitude of the magnetic coils, 3) guarantees field homogeneity inside the imaging volume, 4) produces configurations that satisfy, for the first time, small-footprint feasibility constraints required for MR-linacs. Our approach leverages modern mixed-integer programming (MIP), enabling significant flexibility in magnet design generation, e.g., controlling the number of coils and enforcing symmetry between magnet poles. Our numerical results demonstrate the superiority of our method versus current mainstream methods.

关键词： Magnetic Resonance Imaging MRI Magnet Design Optimization Method mixed-integer programming Linear programming MR-Guided Radiation Therapy

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Optimizing global thermal coal shipments

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2017年 72卷 118-127页

作者： Arigoni, Ashley Newman, Alexandra Turner, Cameron Kaptur, Casey Colorado Sch Mines Dept Mech Engn 1500 Illinois St Golden CO 80401 USA Clemson Univ Dept Mech Engn 206 Fluor Daniel EIB Clemson SC USA RungePincockMinarco 500 S Union Blvd Lakewood CO USA

Thermal coal is used to produce energy;with changing emissions standards and advents in renewable technology, the thermal coal market has seen significant transformation over the past decade. We develop a mixed-integer optimization problem that seeks to minimize shipment costs while meeting demand for thermal coal, and which respects quality constraints, supply limits, and port capacity;we use this model to analyze the following scenarios: (i) a counterfactual setting in which we compare historical shipping patterns to model results using a 2012 base year;(ii) the explicit effect of Chinese mandates on coal shipments;(iii) the impact on our shipping patterns of reduced Chinese and Indian demand;(iv) the effects of the Baltic Dry Index and oil prices;and (v) a comparison of shipments prior and subsequent to Panama Canal expansion. Our work can be used to inform policy, study responses to variable price and demand scenarios, and provide insight to both coal producers and consumers about the international coal market. For example, removal of mandates set by the Chinese government to fill its own demand decreases coal flows from Northern to Southern China by 56%, which has a spill-over effect on European and American markets;and, expansion of the Panama Canal leads to only modest shipping increases through the canal (6.7%), with more coal originating from Colombia serving Asian demand. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Thermal coal Blending Commodity Shipping mixed-integer programming Underlying network structure

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A Decomposition Method for Multiperiod Railway Network Expansion-With a Case Study for Germany

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TRANSPORTATION SCIENCE 2017年第4期51卷 1102-1121页

作者： Baermann, Andreas Martin, Alexander Schuelldorf, Hanno Friedrich Alexander Univ Erlangen Nurnberg Dept Math D-91058 Erlangen Germany Deutsch Bahn AG DB Analyt D-60329 Frankfurt Germany

In this work, we report about the results of a joint research project between Friedrich-Alexander-Universitat Erlangen-Nurnberg and Deutsche Bahn AG on the optimal expansion of the German railway network until 2030. The need to increase the throughput of the network is given by company-internal demand forecasts that indicate an increase in rail freight traffic of about 50% over the next two decades. Our focus is to compute an optimal investment strategy into line capacities given an available annual budget, i.e., we are to choose the most profitable lines to upgrade with respect to the demand scenario under consideration and to provide a schedule according to which the chosen measures are implemented. This leads to a multiperiod network design problem- a class of problems that has received increasing interest over the past decade. We develop a mixed-integer programming formulation to model the situation and solve it via a novel decomposition approach that we call multiple-knapsack decomposition. The method can both be used as a quick heuristic and allows for the extension to an exact algorithm for the problem. We demonstrate its potential by solving a real-world problem instance provided by Deutsche Bahn AG and use the results as the basis for a broad case study for the expansion of the German railway network until 2030.

关键词： railway transport multiperiod network design decomposition infrastructure planning mixed-integer programming

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PATH COVER AND PATH PACK INEQUALITIES FOR THE CAPACITATED FIXED-CHARGE NETWORK FLOW PROBLEM

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SIAM JOURNAL ON OPTIMIZATION 2017年第3期27卷 1943-1976页

作者： Atamturk, Alper Kucukyavuz, Simge Tezel, Birce Univ Calif Berkeley Dept Ind Engn & Operat Res Berkeley CA 94720 USA Univ Washington Dept Ind & Syst Engn Seattle WA 98195 USA

Capacitated fixed-charge network flows are used to model a variety of problems in telecommunication, facility location, production planning, and supply chain management. In this paper, we investigate capacitated path substructures and derive strong and easy-to-compute path cover and path pack inequalities. These inequalities are based on an explicit characterization of the submodular inequalities through a fast computation of parametric minimum cuts on a path, and they generalize the well-known flow cover and flow pack inequalities for the single-node relaxations of fixed-charge flow models. We provide necessary and sufficient facet conditions. Computational results demonstrate the effectiveness of the inequalities when used as cuts in a branch-and-cut algorithm.

关键词： valid inequalities submodular functions covers and packs fixed-charge networks mixed-integer programming

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Supply chain design to guarantee quoted lead time and inventory replenishment: model and insights

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2017年第12期55卷 3431-3450页

作者： Hammami, Ramzi Frein, Yannick Bahli, Bouchaib ESC Rennes Sch Business Dept Supply Chain Management Rennes France CNRS UJF Grenoble INP Lab G SCOP Grenoble France

Do lead time constraints only lead to re-think and re-optimise the inventory positioning along the supply chain or can they impact on the design of the supply chain itself? To answer such a question, we integrate the lead time constraints in a multi-echelon supply chain design model and challenge the difficulty of combining in the same model the long-term decisions (facility location, supplier selection) with the midterm decisions (inventory placement and replenishment, delivery lead time). The model guarantees the respect of the quoted lead time associated with each customer order and the replenishment of the different stocks (raw materials, intermediate and final products) in the different stages of the supply chain between any pair of consecutive orders. We use the model to investigate the impact of the quoted lead time and customer's order frequency on supply chain design decisions and costs. Some of our results indicate that the lead time constraints can lead to bringing the sites of manufacturing and distribution close to the demand zone and to select local suppliers in spite of their higher cost.

关键词： supply chain design quoted lead time inventory placement mixed-integer programming

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