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integer linear programming formulations for the maximum flow blocker problem

European Journal of Operational Research 2025年第3期324卷 742-758页

作者： Bentoumi, Isma Furini, Fabio Mahjoub, A. Ridha Martin, Sébastien Department of Statistics and Operations Research College of Science Kuwait University Kuwait LAMSADE UMR CNRS 7243 University Paris-Dauphine PSL Place du Marechal de Lattre de Tassigny Paris75016 France Department of Computer Control and Management Engineering "Antonio Ruberti" Sapienza University of Rome Via Ariosto 25 Roma00185 Italy Huawei Technologies France 19 Quai du Point du Jour Boulogne-Billancourt92100 France

Given a network with capacities and blocker costs associated with its arcs, we study the maximum flow blocker problem (FB). This problem seeks to identify a minimum-cost subset of arcs to be removed from the network, ensuring that the maximum flow value from the source to the destination in the remaining network does not exceed a specified threshold. The FB finds applications in telecommunication networks and monitoring of civil infrastructures, among other domains. We undertake a comprehensive study of several new integer linear programming (ILP) formulations designed for the FB. The first type of model, featuring an exponential number of constraints, is solved through tailored Branch-and-Cut algorithms. In contrast, the second type of ILP model, with a polynomial number of variables and constraints, is solved using a state-of-the-art ILP solver. The latter formulation establishes a structural connection between the FB and the maximum flow interdiction problem (FI), introducing a novel approach to obtaining solutions for each problem from the other. The ILP formulations proposed for solving the FB are evaluated thanks to a theoretical analysis assessing the strength of their LP relaxations. Additionally, the exact methods presented in this paper undergo a thorough comparison through an extensive computational campaign involving a set of real-world and synthetic instances. Our tests aim to evaluate the performance of the exact algorithms and identify the features of instances that can be solved with proven optimality. © 2025 Elsevier B.V.

关键词： integer linear programming

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Fault Diagnosis of Labeled Petri Nets Under Attacks Using integer linear programming

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2025年 22卷 11881-11893页

作者： Li, Tengbo Ren, Huorong Liu, Ruotian Pia Fanti, Maria Li, Zhiwu Xidian Univ Sch Mechanoelect Engn Xian 710071 Peoples R China Polytech Univ Bari Dept Elect & Informat Engn I-70125 Bari Italy Macau Univ Sci & Technol Inst Syst Engn Macau Peoples R China

This paper deals with the online fault diagnosis problem of discrete event systems under malicious external attacks. We consider a scenario where an attacker can intercept certain sensor measurements and alter them arbitrarily, potentially causing a diagnoser to malfunction. In the framework of labeled Petri nets, a novel integer linear programming problem is formulated by introducing binary variables to estimate the possible transition sequences of an observation that may have been tampered with by an attacker. The proposed approach makes two main contributions. The first one is that, by specifying two different objective functions to the integer linear programming problem, we can obtain the diagnosis results in the presence of attacks, which classic diagnosers may fail to achieve;the second is computational efficiency. In the absence of attacks, the proposed approach is experimentally verified to have lower computational overhead compared with the existing results that are based on integer linear programming and those using basis markings. Finally, the proposed approach is illustrated through a manufacturing system for assembling brake valves.

关键词： Fault diagnosis Petri nets integer linear programming Discrete-event systems State estimation Manufacturing systems linear programming Computational modeling Computational efficiency Communication channels Cyber attack discrete event system fault diagnosis integer linear programming labeled Petri net

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An integer linear programming model for the label printing problem

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2025年第1期32卷 270-288页

作者： Xu, Dehua Shen, Yuan Cao, Yu Xu, Limin Yang, Fengzhao Xie, Yunzhou Nanjing Univ Finance & Econ Sch Int Econ & Business Nanjing 210023 Peoples R China Nanjing Univ Finance & Econ Sch Appl Math Nanjing 210023 Peoples R China Imperial Coll London Fac Nat Sci London SW7 2AZ England

In a recent paper published in this journal, Alonso-Pecina et al. collect several sets of benchmark instances for the label printing problem from the literature and they also propose their own instances. Due to the intractability of the problem, no optimal solutions were declared for most of these instances. In this paper, we propose an integer linear programming model for the problem. We obtain optimal solutions or show that the solutions provided in the literature are already optimal for most of these instances based on the model. For some of the rest instances, we provide better solutions compared to the previous best solutions in the literature.

关键词： label printing benchmark instances optimal solutions integer linear programming

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Designing unit Ising models for logic gate simulation through integer linear programming

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INTERNATIONAL JOURNAL OF PARALLEL EMERGENT AND DISTRIBUTED SYSTEMS 2025年第2期40卷 116-136页

作者： Tsukiyama, Shunsuke Nakano, Koji Parque, Victor Ito, Yasuaki Kato, Takumi Kawamata, Yuya Ii, Kaiki Hiroshima Univ Grad Sch Adv Sci & Engn Kagamiyama 1-4-1 Higashihiroshima Hiroshima 7398527 Japan NTT DATA Grp Corp Res & Dev Headquarters Koto ku Tokyo Japan

Ising models minimizing a quadratic objective function with spin variables of either $ {-}1 $ -1 or $ +1 $ +1 are instrumental in tackling combinatorial optimization problems by programmable Quantum Annealers. This paper introduces unit Ising models, where non-zero coefficients are restricted to $ {-}1 $ -1 or $ +1 $ +1. Due to the limited resolution of quantum annealers, unit Ising models are more suitable for quantum annealers. A fixed unit Ising model for logic circuits could lead to Application-Specific Unit Quantum Annealers (ASUQAs) for inverse function computation, similar to ASICs. Our findings suggest a powerful new method for compromising the RSA cryptosystem by leveraging ASUQAs for factorization.

关键词： Quantum computing one-way function factorization application specific hardware integer linear programming

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Last fifty years of integer linear programming: A focus on recent practical advances

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European Journal of Operational Research 2025年第3期324卷 707-731页

作者： Clautiaux, François Ljubić, Ivana Université de Bordeaux Institut de Mathématiques de Bordeaux CNRS Inria France ESSEC Business School Cergy-Pontoise France

Mixed-integer linear programming (MILP) has become a cornerstone of operations research. This is driven by the enhanced efficiency of modern solvers, which can today find globally optimal solutions within seconds for problems that were out of reach a decade ago. The versatility of these solvers allowed successful applications in many areas, such as transportation, logistics, supply chain management, revenue management, finance, telecommunications, and manufacturing. Despite the impressive success already obtained, many challenges remain, and MILP is still a very active field. This article provides an overview of the most significant results achieved in advancing the MILP solution methods. Given the immense literature on this topic, we made deliberate choices to focus on computational aspects and recent practical performance improvements, emphasizing research that reports computational experiments. We organize our survey into three main parts, dedicated to branch-and-cut methods, Dantzig–Wolfe decomposition, and Benders decomposition. The paper concludes by highlighting ongoing challenges and future opportunities in MILP research. © 2024 The Authors

关键词： integer linear programming

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Schedule optimization and staff allocation for airport security checkpoints using guided simulated annealing and integer linear programming

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JOURNAL OF AIR TRANSPORT MANAGEMENT 2025年 124卷

作者： Brun, Alexis Feron, Eric Alam, Sameer Delahaye, Daniel Ecole Natl Aviat Civile ENAC 7 Ave Edouard Belin F-31400 Toulouse France King Abdullah Univ Sci & Technol KAUST Thuwal 23955 Saudi Arabia Nanyang Technol Univ NTU 50 Nanyang Ave Singapore 639798 Singapore

Security checkpoints are an important matter of concern for airport operators. When functioning effectively, they not only maintain the airport overall safety at a high level, but also provide passengers with a positive airport experience. The perceived quality of service at the airport greatly depends on the time spent by passengers at the security lines. To ensure optimal safety performance, screening lines have a limited capacity of passengers they can handle. Thus, to prevent extended waiting times for passengers, airports can only adjust the number of simultaneously open check lines. The airport operator must establish optimal schedules for opening security checkpoints and allocating necessary staff. Building upon a prior study focused on predicting the flow of passengers through the security checkpoints, this paper explores simulated annealing algorithm in conjunction with a queue simulator and an integer programming algorithm to establish the most effective opening schedule for security checkpoints based on the prediction given by this previous study. The presented approach also determines the best allocation for dedicated staff based on the forecasted passenger flow. This approach limits the number of open security lines and ensures awaiting time below the maximum limit of 45 min set by the airport. It also complies with the work regulations that security agents are subject to.

关键词： Airport security checkpoint Schedule optimization Simulated annealing integer linear programming Security screening lines Staff allocation

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Enhancing Course Planning with BERT-Infused GAT Embeddings and integer linear programming 15

Enhancing Course Planning with BERT-Infused GAT Embeddings a...

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15th IEEE Annual Computing and Communication Workshop and Conference, CCWC 2025

作者： Olmos, Luis Kaplan, Adam Jalalitabar, Maryam California State University Northridge Department of Computer Science Northridge United States

ISBN: (纸本)9798331507695

Integrating BERT-augmented Graph Neural Networks (GNNs) with integer linear programming (ILP) provides a novel framework for academic course recommendation and scheduling. Our approach enriches node representations with BERT embeddings to capture the semantic context of course descriptions. These representations are further refined using supervised contrastive loss within the GNN to enhance the understanding of course relationships and dependencies, leading to more accurate and context-aware recommendations. The framework incorporates an ILP scheduler that optimizes course sequences under academic constraints, including prerequisites, elective requirements, major-specific pathways, and semester unit limits. This method supports the creation of personalized multi-semester schedules tailored to students' academic goals, such as double majors or major-minor combinations. Evaluated on synthetic data, the approach demonstrates improved alignment with academic pathways, showcasing its potential to bridge the gap between semantic understanding and effective course planning. © 2025 IEEE.

关键词： integer linear programming

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Fine-Grained Equivalence for Problems Related to integer linear programming 16

Fine-Grained Equivalence for Problems Related to Integer Lin...

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16th Innovations in Theoretical Computer Science Conference, ITCS 2025

作者： Rohwedder, Lars Węgrzycki, Karol Odense Denmark Saarland University Saarbrücken Germany Max Planck Institute for Informatics Saarbrücken Germany

ISBN: (纸本)9783959773614

integer linear programming with n binary variables and m many 0/1-constraints can be solved in time 2Õ(m2)poly(n) and it is open whether the dependence on m is optimal. Several seemingly unrelated problems, which include variants of Closest String, Discrepancy Minimization, Set Cover, and Set Packing, can be modelled as integer linear programming with 0/1 constraints to obtain algorithms with the same running time for a natural parameter m in each of the problems. Our main result establishes through fine-grained reductions that these problems are equivalent, meaning that a 2O(m2-Ε)poly(n) algorithm with Ε > 0 for one of them implies such an algorithm for all of them. In the setting above, one can alternatively obtain an nO(m) time algorithm for integer linear programming using a straightforward dynamic programming approach, which can be more efficient if n is relatively small (e.g., subexponential in m). We show that this can be improved to n′O(m) + O(nm), where n′ is the number of distinct (i.e., non-symmetric) variables. This dominates both of the aforementioned running times. © Lars Rohwedder and Karol Węgrzycki.

关键词： integer linear programming

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Top-k Rule List Learning via integer linear programming 21st

Top-k Rule List Learning via Integer Linear Programming

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21st Pacific Rim International Conference on Artificial Intelligence, PRICAI 2024

作者： Sasaki, Yoichi Okajima, Yuzuru NEC Corporation 1753 Shimonumabe Kanagawa Nakahara-ku Kawasaki Japan

ISBN: (纸本)9789819601271

Rule lists, one of the best-known rule-based models, have been intensively studied in recent years because its high interpretability is desirable for use in important decision-making tasks. Although rule lists often achieve relatively higher accuracy than other rule-based models such as decision trees, they still have considerably lower accuracy than complex, uninterpretable models such as deep neural networks or large tree ensembles. In this paper, in order to improve the accuracy of rule lists, we propose a new model called a top-k rule list. In contrast to the traditional rule list, which makes a prediction by using the first rule in the list whose conditions are satisfied by the input, the top-k rule list utilizes an ensemble of the first k rules instead of just the first one. The top-k rule list can be viewed as a generalization of the traditional rule list, which is a special case with k=1, and this generalization enables the user to obtain a preferable trade-off between accuracy and interpretability by selecting different values of k. Learning the traditional rule list is known as a computationally hard combinatorial optimization problem, and learning the top-k rule list can be even harder because multiple rules must be considered for each prediction. To enable efficient learning, we propose an integer linear programming formulation for learning the top-k rule list, and effectively reduce the number of variables and constraints by introducing an assumption that the rules are ordered by certainty score. The experimental results show that the top-k rule list learned with the ILP formulation for k>1 outperformed the traditional rule list in accuracy for most datasets. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： integer linear programming

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integer linear programming-based constructive heuristics for Space Division Multiplexing networks

Journal of Engineering Research (Kuwait)

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Journal of Engineering Research (Kuwait) 2025年

作者： Mrad, Mehdi Suryahatmaja, Umar S. Elsayed, Abdelrahman Ossama Gharbi, Anis Esmail, Maged Abdullah Department of Industrial Engineering College of Engineering King Saud University Riyadh Saudi Arabia Communications and Networks Engineering Department College of Engineering Prince Sultan University Riyadh Saudi Arabia

Industrial engineering plays a vital role in optimizing resource allocation and system performance, including the rapidly evolving domain of fiber optic network design. Integrating mesh topology with Space Division Multiplexing (SDM) presents a promising solution to increase fiber capacity. SDM exploits spatial dimensions to significantly expand system transmission capabilities, effectively overcoming the limitations of conventional optical networks. This paper proposes a constructive heuristic approach that solves a sequence of newly formulated integer linear programming (ILP) models to optimize SDM-based flexible optical networks. The experimental results demonstrate the efficiency of the proposed method in optimizing resource allocation by minimizing the maximum spectrum slices utilized across links and network cores. These findings highlight the potential of the approach to substantially improve network performance and scalability in response to increasing data demands. © 2025

关键词： Constructive heuristic Elastic optical networks integer linear programming Internet traffic routing Slice assignment Space Division Multiplexing

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