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An integer linear programming model to improve the dependency graph discovery step of heuristics miner methods

KNOWLEDGE AND INFORMATION SYSTEMS 2023年第5期65卷 2087-2121页

作者： Tavakoli-Zaniani, Maryam Gholamian, Mohammad Reza Golpayegani, S. Alireza Hashemi Ghazanfari, Mehdi Iran Univ Sci & Technol Sch Ind Engn 16844 Tehran Iran Amirkabir Univ Technol Comp Engn & IT Dept 15875 Tehran Iran

Heuristic mining techniques are among the most popular methods in the process discovery area. This category of methods is composed of two main steps: (1) discovering a dependency graph and (2) determining the split/join patterns of the dependency graph. The current dependency graph discovery techniques of heuristic-based methods select the initial set of graph arcs according to dependency measures and then modify the set regarding some criteria. This can lead to selecting the non-optimal set of arcs. Also, the modifications can result in modeling rare behaviors and, consequently, low precision and non-simple process models. The motivation of this paper is to improve the heuristic mining methods by addressing the mentioned issues. The contribution of this paper is to propose a new integer linear programming model that determines the optimal set of graph arcs regarding dependency measures. Simultaneously, the proposed method can eliminate some other issues that the existing methods cannot handle completely;i.e., even in the presence of loops, it guarantees that all tasks are on a path from the initial to the final tasks. This approach also allows utilizing domain knowledge by introducing appropriate constraints, which can be a practical advantage in real-world problems. To assess the results, we modified two existing methods of evaluating process models to make them capable of measuring the quality of dependency graphs. According to assessments, the proposed method's outputs are superior to those of the most prominent dependency graph discovery methods in terms of fitness, precision, and especially simplicity.

关键词： Dependency graphs Heuristic-based process discovery integer linear programming Process mining

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integer linear programming Model for Profit Maximization using Branch and Bound Algorithm in Retail Companies: Case of a Peruvian Company

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Procedia Computer Science 2024年 238卷 1054-1061页

作者： John Diego Chancahuana Castillo Willy Noe Parisuaña Yucra Mario Ninaquispe Soto Sonia Castro Ynfantes Universidad Nacional Mayor de San Marcos Lima Perú Universidad Privada del Norte Lima Peru

This article presents an inventory management model for profit maximization in a Peruvian retail company (FIDEL) using linear programming techniques and the Branch and Bound algorithm. To introduce this paper we refute, through a review of previous studies in the same field, the use of this approach for its effectiveness in business decision-making. Gathering data on costs, demand and the available capital for the company’s different product lines was done through the use of interviews. The proposed model aims to maximize revenue based on the quantities of goods purchased, while considering minimum demand and capital constraints. Validation was performed with Lingo software to confirm the consistency and feasibility of the model. The resulting values revealed a significant increase in projected profits compared to actual data.

关键词： integer linear programming Simplex method Branch bound algorithm Operational optimization

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Solving the constrained Single-Row Facility Layout Problem with integer linear programming

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2023年第6期61卷 1882-1897页

作者： Maier, Kerstin Taferner, Veronika Alpen Adria Univ Klagenfurt Dept Math A-9020 Klagenfurt Austria

The Single-Row Facility Layout Problem (SRFLP) is one of the most studied facility layout problems in the literature. It asks for an optimal arrangement of departments with given lengths on a row such that the weighted sum of all centre-to-centre distances between department pairs is minimised. Real-world facility layouts may require taking different restrictions on the placement of departments into account, such as arrangement on a fixed position, pairwise placement, or precedence considerations. Therefore, we consider the constrained Single-Row Facility Layout Problem (cSRFLP) that additionally considers positioning, ordering, and relation constraints on single-row facility layouts. In this work, we suggest a new integer linear programming (ILP) formulation for the cSRFLP, which outperforms the best available exact approach in literature. In an extensive computational study, we apply our ILP approach as well as an LP-based cutting plane algorithm on SRFLP and cSRFLP instances from the literature. We provide optimal cSRFLP layouts as well as strong lower bounds for instances with up to 42 departments. Further, we present new results for SRFLP instances from the literature. Additionally, we demonstrate the individual impact of the constraint sets on the run times of cSRFLP instances to emphasise further research on this rarely studied practice-oriented Facility Layout Problem.

关键词： Facility planning and design Facility Layout Problem single-row layout integer linear programming cutting planes

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integer linear programming Formulations for the RCPSP considering Multi-Skill, Multi-Mode, and Minimum and Maximum Time Lags

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IEEE LATIN AMERICA TRANSACTIONS 2021年第1期19卷 5-16页

作者： Melo, Luciana Vieira Queiroz, Thiago Alves Univ Fed Goias Reg Catalao Programa Posgrad Engn Prod BR-75708560 Catalao Goias Brazil

The project scheduling problem is essential both in the theoretical part, as in the field of operational research, and practice, with the project management in corporate environments. integer linear programming formulations indexed on time are studied for the Resource-Constrained Project Scheduling Problem (RCPSP). Moreover, the multi-skill, multiple modes, and time lag constraints are taken into consideration. The objective of the RCPSP is to minimize the makespan. The formulations are solved with the default branch-and-cut algorithm of the solver Gurobi Optimizer. The formulations and solver are analyzed concerning the runtime, the number of optimal solutions, and the gap on the resolution of more than 2000 instances. Results indicate the solver can have better performance when instances with up to 50 activities are solved. Then, to develop models to handle hard instances of this problem is a challenge. Moreover, it can bring significant advantages to the corporate environment, helping managers to make accurate decisions and reduce costs.

关键词： Computational modeling Scheduling Optimal scheduling integer linear programming Mathematical model IEEE transactions Software Mathematical model Optimal scheduling Optimization

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Single-Source-Single-Target Interleaved-Dyck Reachability via integer linear programming

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2023年第POPL期7卷 1003-1026页

作者： Li, Yuanbo Zhang, Qirun Reps, Thomas Georgia Inst Technol Atlanta GA 30332 USA Univ Wisconsin Madison Madison WI USA

An interleaved-Dyck (InterDyck) language consists of the interleaving of two or more Dyck languages, where each Dyck language represents a set of strings of balanced parentheses. InterDyck-reachability is a fundamental framework for program analyzers that simultaneously track multiple properly-matched pairs of actions such as call/return, lock/unlock, or write-data/read-data. Existing InterDyck-reachability algorithms are based on the well-known tabulation technique. This paper presents a new perspective on solving InterDyck-reachability. Our key observation is that for the single-source-single-target InterDyck-reachability variant, it is feasible to summarize all paths from the source node to the target node based on path expressions. Therefore, InterDyck-reachability becomes an InterDyck-path-recognition problem over path expressions. Instead of computing summary edges as in traditional tabulation algorithms, this new perspective enables us to express InterDyck-reachability as a parenthesis-counting problem, which can be naturally formulated via integer linear programming (ILP). We implemented our ILP-based algorithm and performed extensive evaluations based on two client analyses (a reachability analysis for concurrent programs and a taint analysis). In particular, we evaluated our algorithm against two types of algorithms: (1) the general all-pairs InterDyck-reachability algorithms based on linear conjunctive language (LCL) reachability and synchronized pushdown system (SPDS) reachability, and (2) two domain-specific algorithms for both client analyses. The experimental results are encouraging. Our algorithm achieves 1.42x, 28.24x, and 11.76x speedup for the concurrency-analysis benchmarks compared to all-pair LCL-reachability, SPDS-reachability, and domain-specific tools, respectively;1.2x, 69.9x, and 0.98x speedup for the taint-analysis benchmarks. Moreover, the algorithm also provides precision improvements, particularly for taint analysis, where it achieves

关键词： Interleaved-Dyck Reachability Path Expressions integer linear programming Single-Source-Single-Target Variant

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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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Storage location assignment of steel coils in a manufacturing company: an integer linear programming model and a greedy randomized adaptive search procedure

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TOP 2023年第1期31卷 67-109页

作者： Edis, Emrah B. Araz, Ozlem Uzun Eski, Ozgur Edis, Rahime Sancar Manisa Celal Bayar Univ Dept Ind Engn Sehit Prof Dr Ilhan Varank Kampusu TR-45140 Manisa Turkey

Warehouse operations have a significant role to survive in today's competitive world. Hence, companies introduce various solutions to improve efficiency of warehouses which is mainly affected by the performance of storage operations. This study deals with a real-life storage location and assignment problem encountered in a fastener company where several orders consisting steel coils are to be assigned into storage areas. Three individual objective functions;minimizing the number of lanes to be used, minimizing area usage, and maximizing volume utilization are considered. For the investigated problem, first, an integer linear programming (ILP) model is developed. Then, a greedy randomized adaptive search procedure (GRASP) which provides quick and efficient solutions is proposed. The proposed methods are applied to the real problem case and the results are compared with the current storage assignment. Moreover, through an extensive computational study, the performances of proposed methods are evaluated on a set of test problems with different range of characteristics. The computational results show that the ILP model proves optimality in most of the problem instances within reasonable computation times, while the GRASP gives quick solutions with small optimality gaps.

关键词： Storage location assignment problem Round item integer linear programming Greedy randomized adaptive search procedure

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CELL TRACKING BASED ON integer linear programming AND PROBABILITY SCORES 21

CELL TRACKING BASED ON INTEGER LINEAR PROGRAMMING AND PROBAB...

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21st IEEE International Symposium on Biomedical Imaging (ISBI)

作者： Lux, Filip Matula, Petr Masaryk Univ Fac Informat Bot 68a Brno 60200 Czech Republic

ISBN: (纸本)9798350313345;9798350313338

The cell tracking problem can be formulated as a global optimization problem based on integer linear (IL) programming. The obtained solution depends on the definition of the IL program and the chosen costs of the events considered in the problem formulation. In general, balancing meaningful costs across different events is difficult. To simplify this problem, we propose a cost assignment approach based on probability scores, allowing us to easily interpret the free parameters. The idea is presented based on the BF-C2DL-HSC dataset from the Cell Tracking Challenge. We show our method reaches state-of-the-art performance when evaluating both technical and biological tracking measures.

关键词： Cell Tracking Tracking-by-Assignment integer linear programming Cost Assignment

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New Support Size Bounds and Proximity Bounds for integer linear programming 49th

New Support Size Bounds and Proximity Bounds for Integer Lin...

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49th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM)

作者： Berndt, Sebastian Mnich, Matthias Stamm, Tobias Univ Lubeck Inst Theoret Comp Sci Lubeck Germany Hamburg Univ Technol Inst Algorithms & Complex Hamburg Germany

ISBN: (纸本)9783031521126;9783031521133

integer linear programming (ILP) is a fundamental research paradigm in algorithms. Many modern algorithms to solve structured ILPs efficiently follow one of two main approaches. The first one is to prove a small upper bound on the support size of the ILP, which is the number of variables taking non-zero values in an optimal solution, and then to only search for ILP solutions of small support. The second one is to apply an augmentation algorithm using Graver elements to an initial feasible solution obtained from a small proximity bound for the ILP, which is the distance between an optimal solution of the ILP and that of its LP relaxation. Our first contribution are new lower bounds for the support size of ILPs. Namely, we discover a connection between support sizes and an old number-theoretic conjecture by Erdos on subset-sum distinct sets. Further, we improve the previously best lower bounds on the support size of ILPs with m constraints and largest absolute value Delta of any coefficient in the constraint matrix from Omega(mlog(Delta)) to Omega(mlog(root m Delta)). This new lower bound asymptotically matches the best-known upper bounds. Our second contribution are new bounds on the size of Graver elements and on the proximity for ILPs. We first show nearly tight lower and upper bounds for g(1)(A), the largest 1-norm parallel to g parallel to(1) of any Graver basis element g of the constraint matrix A. Then we show that the proximity of any ILP in standard form with support size s is bounded by s center dot c(1)(A), where c(1)(A) is the largest 1-norm parallel to c parallel to(1) of any circuit c of A. This improves over the known proximity bound of n center dot g(1)(A), as s and c(1)(A) can be much smaller than n and g(1)(A), respectively.

关键词： integer linear programming proximity bounds Graver bases

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Hybrid Quantum-Classical Computing via Dantzig-Wolfe Decomposition for integer linear programming 33

Hybrid Quantum-Classical Computing via Dantzig-Wolfe Decompo...

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33rd IEEE International Conference on Computer Communications and Networks (ICCCN)

作者： Wei, Xinliang Liu, Jiyao Fan, Lei Guo, Yuanxiong Han, Zhu Wang, Yu Temple Univ Dept Comp & Informat Sci Philadelphia PA 19122 USA Univ Houston Dept Engn Technol Houston TX USA Univ Houston Dept Elect & Comp Engn Houston TX USA Univ Texas San Antonio Dept Informat Syst & Cyber Secur San Antonio TX USA

ISBN: (纸本)9798350348439;9798350384611

Numerous optimization scenarios such as industrial production planning, network communication routing, and logistic scheduling can be modeled as large-scale integer linear programming problems. However, due to the NP-Hardness of these problems, it is very challenging to optimally solve these problems in a short time on classical computers. Quantum computers have emerged as a new computing platform to provide new computing paradigms to tackle these problems. However, the scalability and efficiency of current quantum computers pose significant challenges in practical implementations of quantum optimization algorithms. In this paper, we propose a novel hybrid quantum-classical approach, termed Hybrid quantum-classical Dantzig-Wolfe Decomposition (HyDWD), aimed at solving these problems. In this framework, the subproblems can be solved in parallel on quantum computers. Our results demonstrate the benefits of integrating parallel quantum computing with the proposed hybrid quantum-classical framework via Dantzig-Wolfe decomposition, paving the way for advancements in optimization and decision-making processes.

关键词： Quantum computing Dantzig-Wolfe decomposition hybrid quantum-classical method integer linear programming quantum network

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