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16th International Conference on Scalable Uncertainty Management, SUM 2024

作者： Baioletti, Marco Capotorti, Andrea Petturiti, Davide Vantaggi, Barbara University of Perugia Perugia Italy Sapienza University of Rome Rome Italy

ISBN: (纸本)9783031762345

We propose a mixed integer programming (MIP) procedure to find an outer belief approximation of a lower conditional joint cumulative distribution function (lower conditional joint CDF) obtained by the statistical matching of several sources of information, given a common variable. We assume that the variables have finite supports and we provide a procedure based on the MIP technique that produces a sparse solution with at most a given finite number of focal elements, permitting to obtain an outer approximation with a conditional belief function. In turn, the family of sparse solutions given the common variable, allows us to efficiently perform coherent inferences on new items, relying on the generalized Bayesian conditioning rule. We finally show the effectiveness of the proposed approach in the domain of company fraud detection. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： mixed-integer linear programming

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Strategic evacuation planning with pedestrian guidance and bus routing: a mixed integer programming model and heuristic solution

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JOURNAL OF ADVANCED TRANSPORTATION 2016年第7期50卷 1314-1335页

作者： Heydar, Mojtaba Yu, Jie Liu, Yue Petering, Matthew E. H. Univ Newcastle Callaghan NSW Australia Univ Wisconsin Dept Civil & Environm Engn Milwaukee WI 53211 USA Univ Wisconsin Dept Ind & Mfg Engn Milwaukee WI 53201 USA

This paper presents a mathematical model to plan emergencies in a densely populated urban zone where a certain numbers of pedestrians depend on transit for evacuation. The proposed model features an integrated operational framework, which simultaneously guides evacuees through urban streets and crosswalks (referred to as the pedestrian network) to designated pickup points (e.g., bus stops), and routes a fleet of buses at different depots to those pick-up points and transports evacuees to their destinations or safe places. In this level, the buses are routed through the so-called vehicular network. An integrated mixed integer linear program that can effectively take into account the interactions between the aforementioned two networks is formulated to find the maximal evacuation efficiency in two networks. Because the large instances of the proposed model are mathematically difficult to solve to optimality, a two-stage heuristic is developed to solve larger instances of the model. Results from hundreds of numerical examples analysis indicate that proposed heuristic works well in providing (near) optimal or feasibly good solutions for medium-scale to large-scale instances that may arise in real transit-based evacuation situations in a much shorter amount of computational time compared with cplex (can find optimal/feasible solutions for only five instances within 3hours of running). Copyright (c) 2016 John Wiley & Sons, Ltd.

关键词： evacuation mixed-integer linear programming vehicle routing public transit system transportation

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Two new mixed-integer programming models for the integrated train formation and shipment path optimization problem

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NETWORKS 2023年第3期81卷 359-377页

作者： Arsalani, Pouria Reisi-Nafchi, Mohammad Dardashti, Vahid Moslehi, Ghasem Isfahan Univ Technol Dept Ind & Syst Engn Esfahan Iran CIRRELT Montreal PQ Canada Isfahan Univ Technol Dept Ind & Syst Engn Esfahan *** Iran

Railcars are known as the heart of the freight rail transportation industry. Hence, any improvements in their operations can lead to sharp reductions in various operating costs. One of the most critical operations on railcars is blocking and routing their transportation. Railway companies face continuous challenged about what blocks should be formed to carry shipments across different origin-destination pairs (O-D pairs) and reclassify them in intermediate yards to minimize transportation reclassification costs. In addition, it is necessary to determine train service between O-D pairs and the number of trains. Along with the shipment routing plans, this problem is called train formation and shipment path optimization (TFSP). In TFSP, some substructure and rail network operational constraints should be considered, including link capacity, classification capacity, the number of sorting tracks, and path length. This paper presents two arc-based mixed-integer linear programming (MILP) models to formulate the TFSP problem. To the best of the authors' knowledge, no MILP arc-based model has been published for the problem that does not need any preprocess before solving. Computational results of solving models on the datasets showed that the first model could obtain a feasible solution with a maximum 0.05% gap up to 48 yards instance. The second model also could find a solution with a small gap compared to the optimal solution in a reasonable time for instances up to 128 yards. Also, the proposed models were compared to the best methods in the literature, and their superiority was shown.

关键词： mixed-integer linear programming railcar blocking railway transportation shipment path routing single-block train train formation

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Stronger mixed-integer programming-formulations for order- and rack-sequencing in robotic mobile fulfillment systems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第3期305卷 1063-1078页

作者： Justkowiak, Jan-Erik Pesch, Erwin Univ Siegen Management Informat Sci Kohlbettstr 15 D-57072 Siegen Germany HHL Leipzig Ctr Adv Studies Management Jahnallee 59 D-04109 Leipzig Germany

This paper addresses the order-and rack-sequencing problem at a single picking station in the context of robotic mobile fulfillment systems, a warehouse technology typically applied in large distribution centers. Following the parts-to-picker concept, items are stored on movable racks that are lifted and transported by automated guided vehicles from the storage area to picking stations for order-processing. The order-picking process involves two linked decisions: How to sequence the processing of orders and how to se-quence the rack visits to supply the picking station with the requested items. We present a novel mixed-integer linear programming formulation achieving stronger linear programming bounds than a previous formulation. Including preprocessing techniques it quickly solves instances of medium-size to proven op-timality for the first time in literature. For large real-world instances, we provide a three-stage heuristic solution procedure suitable in a dynamic environment, while providing competitive solutions within a short run time. Computational experiments on a broad set of benchmark instances and a comparative study with approaches from literature verify our results.(c) 2022 Elsevier B.V. All rights reserved.

关键词： Scheduling Robotic mobile fulfillment systems mixed-integer linear programming Warehouse logistics Order-sequencing

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Learning to Cut via Hierarchical Sequence/Set Model for Efficient mixed-integer programming

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2024年第12期46卷 9697-9713页

作者： Wang, Jie Wang, Zhihai Li, Xijun Kuang, Yufei Shi, Zhihao Zhu, Fangzhou Yuan, Mingxuan Zeng, Jia Zhang, Yongdong Wu, Feng Univ Sci & Technol China MoE Key Lab Brain Inspired Intelligent Percept & Hefei 230027 Peoples R China Huawei Noahs Ark Lab Shenzhen 518129 Peoples R China

Cutting planes (cuts) play an important role in solving mixed-integer linear programs (MILPs), which formulate many important real-world applications. Cut selection heavily depends on (P1) which cuts to prefer and (P2) how many cuts to select. Although modern MILP solvers tackle (P1)-(P2) by human-designed heuristics, machine learning carries the potential to learn more effective heuristics. However, many existing learning-based methods learn which cuts to prefer, neglecting the importance of learning how many cuts to select. Moreover, we observe that (P3) what order of selected cuts to prefer significantly impacts the efficiency of MILP solvers as well. To address these challenges, we propose a novel hierarchical sequence/set model (HEM) to learn cut selection policies. Specifically, HEM is a bi-level model: (1) a higher-level module that learns how many cuts to select, (2) and a lower-level module-that formulates the cut selection as a sequence/set to sequence learning problem-to learn policies selecting an ordered subset with the cardinality determined by the higher-level module. To the best of our knowledge, HEM is the first data-driven methodology that well tackles (P1)-(P3) simultaneously. Experiments demonstrate that HEM significantly improves the efficiency of solving MILPs on eleven challenging MILP benchmarks, including two Huawei's real problems.

关键词： mixed-integer linear programming cut selection deep reinforcement learning sequence/set to sequence learning

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Modelling overflow using mixed integer programming in short-term hydropower scheduling

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ENERGY SYSTEMS-OPTIMIZATION MODELING SIMULATION AND ECONOMIC ASPECTS 2023年 1-13页

作者： Litlabo, Tormod Aaslid, Per Riise, Tarjei Lid Haugland, Dag Sweco Norge AS Fantoftvegen 14P N-5072 Bergen Norway SINTEF Energy Res Dept Energy Syst Sem Saelands Vei 11 N-7034 Trondheim Norway Eviny Fornybar AS Solheimsgaten 5 N-5058 Bergen Norway Univ Bergen Dept Informat Thormohlensgate 55 N-5008 Bergen Norway

Short-term hydropower scheduling seeks to find a production schedule that maximizes profit, but must also consider the hydrological balance and risk of overflow. Overflow is by nature a non-linear and non-convex phenomenon. Common approximations and relaxations may cause non-physical results such as overflow from reservoirs that are not full. This paper presents a mixed-integer linear programming formulation that can be used to prevent non-physical overflow behaviour, but that comes at a cost of significant higher solving time. To achieve an acceptable solving time, we propose a heuristic to provide tight upper bounds on the overflow variables in each time step. When applied on the model of the Fossdal watercourse in Norway, the proposed method reduces the solving time with more than 90% compared to using a conservative fixed coefficient for all time steps.

关键词： Short-term hydropower scheduling Overflow mixed-integer linear programming Successive linear programming

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A sequential mixed-integer programming method for concurrent optimization of core topology and face sheet thickness of a sandwich beam

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JOURNAL OF SANDWICH STRUCTURES & MATERIALS 2023年第6期25卷 666-686页

作者： Larsson, Johan Goeransson, Peter Wennhage, Per KTH Royal Inst Technol Stockholm Sweden Ctr ECO2 Vehicle Design Stockholm Sweden KTH Royal Inst Technol Dept Engn Mech Teknikringen 8 S-11428 Stockholm Sweden

A method is proposed that allows for the concurrent optimization of core topology and face sheet thickness of a sandwich beam under compliance constraints. The problem is solved using a novel mixed-linear extension of the Topology Optimization of Binary Structure (TOBS) topology optimization method aiming to minimize the total mass of the beam. The method has been demonstrated on a clamped beam example and the results have been compared to results from topology optimization of the core with a range of a priori fixed face sheet thicknesses. It is shown that the new method, starting from a fully populated core, finds a minimum mass that is lower than but in the neighbourhood of the best results from the topology optimization with fixed face sheet thicknesses. By varying the compliance constraint it is shown that the core topology approaches an ideal corrugated geometry as the compliance constraint is relaxed. The trends observed in the results are compared to analytical models for an idealized core.

关键词： Topology optimization sandwich structures mixed-integer linear programming concurrent optimization mass minimization

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Resilience-Oriented Train Rescheduling Optimization in Railway Networks: A mixed integer programming Approach

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2023年第5期24卷 4948-4961页

作者： Yin, Jiateng Ren, Xianliang Su, Shuai Yan, Fei Tao, Tang Beijing Jiaotong Univ State Key Lab Rail Traff Control & Safety Beijing Peoples R China CRSC Res & Design Inst Grp Co Ltd Beijing Peoples R China

Due to the inventible disruptions caused by e.g., flood, hurricane and blizzard, metro managers in recent years have gradually shifted their attention from prevention of disruptions to ability to withstand and quick recovery from these disruptions, hence the need for enhancing the resilience of an urban rail system. In this paper, we propose a resilience-oriented train rescheduling framework, which helps the rail transit system recover to the normal state as soon as possible in case of disruptions, with the help of pre-allocated rolling stocks at the depots, side tracks and timetable rescheduling of grains. Specifically, we first construct an event-activity network for an urban rail line with multiple depots and side tracks, in which the arrival and departure of trains are modeled as a set of events. Several groups of decision variables and linear constraints are denoted to model the rescheduling of trains. Considering the use of short-turning train rescheduling strategy and pre-allocated rolling stocks, we then formulate the problem into a mixed-integer linear programming (MILP) model, where the objective is to maximize the resilience of the urban rail line against disruptions. Through the analysis of model properties, we develop a branch-and-cut algorithm by deriving a series of linear inequalities, which we prove are valid inequalities, to strength the tightness of the MILP model. Finally, numerical experiments based on real-world data of Beijing metro are conducted to verify the effectiveness of our approach.

关键词： Rails Resilience Rail transportation Numerical models Computational modeling Optimization Real-time systems disruption management mixed-integer linear programming

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mixed-integer programming Model for Transmission Network Expansion Planning with Battery Energy Storage Systems (BESS)

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ENERGIES 2020年第17期13卷 4386页

作者： Andres Mora, Camilo Danilo Montoya, Oscar Rivas Trujillo, Edwin Univ Dist Francisco Jose de Caldas Fac Ingn Bogota 11021 DC Colombia Univ Tecnolog Bolivar Lab Inteligente Energia Cartagena 131001 Colombia

This article assesses the costs and benefits of incorporating battery energy storage systems (BESS) in transmission network expansion planning (TEP) over multiple time periods. We propose a mixed-integer programming model (MIP) for joint planning of the installation of battery energy storage systems (BESS) and construction of new transmission lines in multiple periods of time. The mathematical formulation of the presented model is based on the strategies of the agents of a transmission network to maximize their benefit, and on the operational restrictions of the power flows in transmission networks. This analysis is performed for the Garver 6 node test system takes into account the power losses in the lines and the restrictions for the energy stored in BESS. The power flows obtained with the MIP model are compared with AC power flows generated with specialized software for flows in power systems. This allows us to demonstrate the potential of models based on DC power flows to achieve approximate results applicable to the behavior and characteristics of real transmission networks. The results show that the BESS increase the net profit in the transmission networks and reduce their power losses.

关键词： mixed-integer linear programming transmission expansion planning battery energy storage systems

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On handling indicator constraints in mixed integer programming

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2016年第3期65卷 545-566页

作者： Belotti, Pietro Bonami, Pierre Fischetti, Matteo Lodi, Andrea Monaci, Michele Nogales-Gomez, Amaya Salvagnin, Domenico FICO Birmingham W Midlands England IBM Corp Madrid Spain Univ Padua Padua Italy Univ Bologna Bologna Italy Ecole Polytech Montreal Montreal PQ Canada Huawei France R&D Math & Algorithm Sci Lab Paris France IBM Corp Milan Italy

mixed integer programming (MIP) is commonly used to model indicator constraints, i.e., constraints that either hold or are relaxed depending on the value of a binary variable. Unfortunately, those models tend to lead to weak continuous relaxations and turn out to be unsolvable in practice;this is what happens, for e.g., in the case of Classification problems with Ramp Loss functions that represent an important application in this context. In this paper we show the computational evidence that a relevant class of these Classification instances can be solved far more efficiently if a nonlinear, nonconvex reformulation of the indicator constraints is used instead of the linear one. Inspired by this empirical and surprising observation, we show that aggressive bound tightening is the crucial ingredient for solving this class of instances, and we devise a pair of computationally effective algorithmic approaches that exploit it within MIP. One of these methods is currently part of the arsenal of IBM-Cplex since version 12.6.1. More generally, we argue that aggressive bound tightening is often overlooked in MIP, while it represents a significant building block for enhancing MIP technology when indicator constraints and disjunctive terms are present.

关键词： mixed-integer linear programming mixed-integer quadratic programming Indicator constraints

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