Computers & Operations Research最新文献_第7页

Seru order acceptance and scheduling in the distributed production network considering preventive maintenance 考虑预防性维护的分布式生产网络中批量订单的接收与调度

IF 4.3 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Operations Research

Pub Date : 2025-11-19 DOI: 10.1016/j.cor.2025.107329

P. Hajipour, J. Behnamian

In today’s globalized manufacturing environment, producers encounter unprecedented challenges stemming from intense competition, volatile customer demands, and the imperative to deliver high-quality, customized products. Collaborative production within multi-factory networks has emerged as a vital strategy for optimizing workflows and increasing flexibility. Complementing this approach, seru systems—which segment production lines into smaller, autonomous units—enhance responsiveness to fluctuating demand patterns. However, coordinating and scheduling operations across such networks introduces significant complexity, posing a substantial challenge for production-optimization research. Moreover, preventive maintenance is essential for sustaining system productivity by minimizing unplanned downtime and extending equipment lifespan. This study examines scheduling and order acceptance in a distributed production network that integrates seru systems, requiring customer orders to be allocated among factories—some of which operate under seru configurations. A mixed‑integer nonlinear programming (MINLP) model is proposed and implemented in GAMS. For larger-scale instances, the study introduces two memetic algorithms, each integrating a distinct local-search strategy: one utilizing simulated annealing and the other applying hill-climbing. Comparative analysis against a genetic algorithm demonstrates the superior efficiency of both memetic approaches in solving complex instances. The findings offer significant practical implications, such as reduced operational costs, increased production flexibility, and accelerated order fulfillment. Results further demonstrate that integrating seru systems with preventive maintenance strategies in multi-factory networks enhances system stability and efficiency, supports customized manufacturing, and mitigates downtime.

在当今全球化的制造环境中，生产商面临着前所未有的挑战，这些挑战来自激烈的竞争、多变的客户需求以及提供高质量、定制化产品的必要性。多工厂网络中的协同生产已经成为优化工作流程和提高灵活性的重要策略。作为这种方法的补充，seru系统——将生产线分割成更小的、自主的单元——提高了对波动需求模式的响应能力。然而，在这样的网络中协调和调度作业带来了极大的复杂性，给生产优化研究带来了巨大的挑战。此外，预防性维护对于通过减少计划外停机时间和延长设备寿命来维持系统生产力至关重要。本研究考察了集成seru系统的分布式生产网络中的调度和订单接受情况，要求客户订单在工厂之间分配，其中一些工厂在seru配置下运行。提出了一种混合整数非线性规划（MINLP）模型并在GAMS中实现。对于更大规模的实例，该研究引入了两种模因算法，每种算法都集成了不同的局部搜索策略：一种利用模拟退火，另一种应用爬坡。与遗传算法的比较分析表明，这两种模因方法在求解复杂实例时都具有优越的效率。研究结果提供了重要的实际意义，如降低运营成本，提高生产灵活性，加快订单履行。结果进一步表明，在多工厂网络中，将seru系统与预防性维护策略集成可以提高系统的稳定性和效率，支持定制制造，并减少停机时间。

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引用次数: 0

A novel learning model with dynamic heterogeneous graph network for uncertain multimode resource-constrained project scheduling problem 不确定多模式资源约束项目调度问题的动态异构图网络学习模型

IF 4.3 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Operations Research

Pub Date : 2025-11-10 DOI: 10.1016/j.cor.2025.107319

Zheng Wang , Huiran Liu , Xiaojun Fan

This paper addresses a multi-scenario multi-mode resource-constrained project scheduling problem with the goal of minimizing both the makespan and cost of the project. In order to visualize the changing process of modes and priority relationships in a project, a dynamic activity-mode network graph is introduced. Based on this network, a deep reinforcement learning model based on dynamic heterogeneous graph neural network is designed, and 12 solving models are obtained by training this model using the proximal policy optimization algorithm. The convergence of the model was verified using benchmark instances from the Project Scheduling Problem Library. Meanwhile, based on the characteristics of the solved problem, 360 instances are generated by reproducing the algorithm for generating benchmark instances. The problems are addressed using these 12 solution models and 9 additional comparison algorithms. Furthermore, a sensitivity analysis is conducted regarding the configuration parameters of the problem. The results validate the optimal effectiveness, stability, and generalization ability of the proposed learning model. It also demonstrates that this model can be a robustly better solving model and scheduling scheme according to actual demands.

本文研究了一个多场景、多模式、资源约束的项目调度问题，其目标是最小化项目的完工时间和成本。为了可视化项目中模式和优先级关系的变化过程，引入了动态活动模式网络图。在此基础上，设计了基于动态异构图神经网络的深度强化学习模型，并利用近端策略优化算法对该模型进行训练，得到了12个求解模型。利用项目调度问题库中的基准实例验证了模型的收敛性。同时，根据所解决问题的特点，通过再现生成基准实例的算法，生成360个实例。使用这12个解决方案模型和9个额外的比较算法来解决这些问题。此外，对问题的构型参数进行了敏感性分析。结果验证了该学习模型的最佳有效性、稳定性和泛化能力。结果表明，该模型是一种鲁棒性较好的求解模型和调度方案。

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引用次数: 0

International travel time prediction for China–Europe Express trains via interpretable deep learning models 基于可解释深度学习模型的中欧班列国际旅行时间预测

IF 4.3 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Operations Research

Pub Date : 2025-11-10 DOI: 10.1016/j.cor.2025.107330

Jingwei Guo , Xiang Guo , Zhen-Song Chen , Witold Pedrycz

Accurate travel time forecasting for China–Europe Express (CRE) trains in the international section has become a significant challenge for railway practitioners and academics, with even mainstream deep forest (DF) models and variants encountering unresolved technical issues. This paper introduces a novel dual mechanism DF regression model (DMDFR) that enhances both the predictive performance and interpretability of the DF model to predict travel times of CRE trains in the international section. The proposed DMDFR model incorporates a dual mechanism consisting of an internal and an external mechanism. The internal mechanism addresses the problem of uneven dataset partitioning by adjusting the importance of each sub-forest during cross-validation. Meanwhile, a more interpretable and transparent external mechanism is embedded within the DF framework to tackle technical issues related to error transfer. In addition, the information transfer process utilizes an incremental information transfer approach to minimize the loss of internally represented information and improve the interpretability of the model. The DMDFR model deconstructs the DF gray-box arithmetic principle and develops model arithmetic algorithms using a straightforward, explanatory computational process. Through example analysis, we demonstrate the superiority of the DMDFR model across various statistical metrics. Given the rapid advancement of deep learning, the significant improvements achieved by the DMDFR underscore the importance of researching interpretable deep learning algorithms.

对中欧班列（CRE）国际段的准确旅行时间预测已经成为铁路从业者和学者面临的重大挑战，即使是主流的深森林（DF）模型和变体也遇到了尚未解决的技术问题。本文提出了一种新的双机制DF回归模型（DMDFR），提高了DF模型对国铁国际段列车运行时间预测的预测性能和可解释性。提出的DMDFR模型采用了由内部机制和外部机制组成的双重机制。内部机制通过在交叉验证过程中调整每个子森林的重要性来解决数据集划分不均匀的问题。同时，在DF框架内嵌入了一个更可解释和透明的外部机制，以解决与错误传递相关的技术问题。此外，信息传递过程采用增量信息传递方法，最大限度地减少内部表示信息的丢失，提高模型的可解释性。DMDFR模型解构了DF灰盒算法原理，并使用直接的、解释性的计算过程开发了模型算法。通过实例分析，我们证明了DMDFR模型在各种统计指标上的优越性。鉴于深度学习的快速发展，DMDFR所取得的重大进步强调了研究可解释深度学习算法的重要性。

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引用次数: 0

Dual-driven path elimination for vehicle routing with idle times and arrival-time consistency 具有空闲时间和到达时间一致性的车辆路径的双驱动路径消除

IF 4.3 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Operations Research

Pub Date : 2025-11-10 DOI: 10.1016/j.cor.2025.107326

Jorge Riera-Ledesma , Inmaculada Rodríguez-Martín , Hipólito Hernández–Pérez

We present a simple dual-driven methodology for generating infeasible path elimination constraints within branch-and-cut algorithms for vehicle routing problems that incorporate idle times and arrival-time consistency requirements. By leveraging dual information from a feasibility-checking subproblem, the approach systematically identifies the combinatorial sources of infeasibility and uses them to generate and strengthen valid inequalities. We apply the method to the Consistent Traveling Salesperson Problem with idling, which enforces temporal consistency across multiple service days while allowing idle time between tasks. This problem, defined by basic routing and synchronization constraints, serves as an ideal case study to demonstrate the method’s effectiveness. Computational experiments on a benchmark set of 756 instances, based on multi-period extensions of classical TSPLIB datasets, show that the approach solves 536 instances to proven optimality, including cases with up to 100 customers and a five-day planning horizon, all within a two-hour time limit.

我们提出了一种简单的双驱动方法，用于在包含空闲时间和到达时间一致性要求的车辆路线问题的分支切断算法中生成不可行的路径消除约束。通过利用来自可行性检查子问题的对偶信息，该方法系统地识别不可行性的组合来源，并使用它们来生成和加强有效不等式。我们将该方法应用于具有空转的一致旅行销售人员问题，该问题在多个服务日之间强制执行时间一致性，同时允许任务之间有空闲时间。这个问题由基本的路由和同步约束定义，作为一个理想的案例研究来演示该方法的有效性。基于经典TSPLIB数据集的多周期扩展，在756个实例的基准集上进行的计算实验表明，该方法解决了536个实例，证明了最优性，包括多达100个客户和5天规划范围的案例，所有这些都在两个小时的时间限制内。

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引用次数: 0

Benders decomposition for stochastic facility location and production planning 弯管机分解用于随机设备定位和生产计划

IF 4.3 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Operations Research

Pub Date : 2025-11-10 DOI: 10.1016/j.cor.2025.107316

Tao Wu , Jingwen Zhang , Canrong Zhang , Zhe Liang , Xiaoning Zhang

This study is motivated by industrial applications on manufacturing companies facing complex production planning problems encompassing location, production mix, and lot sizing decisions against uncertain demand. Historically, manufacturing companies often relied on deterministic optimization models to optimize these decisions by addressing uncertain demand using average values derived from forecasting techniques. Our investigation reveals that the deterministic model effectively handles stochastic demand with normal distribution patterns. However, we observe that deterministic models encounter challenges when dealing with sustained demand shifts—instances triggered by factors like mergers, acquisitions, or unforeseen events such as the global pandemic. Hence, it becomes imperative for manufacturing companies to adopt stochastic models for effective decision-making. While these models provide invaluable insights, their complexity presents hurdles for traditional methods such as branch-and-cut. In response, our study introduces a machine learning (ML)-empowered Benders decomposition method—augmented with novel inequalities and ML-empowered Benders reformulation. Our computational experiments demonstrate the significant cost savings attainable through our proposed methodology.

本研究的动机是工业应用制造公司面临复杂的生产计划问题，包括位置，生产组合，以及针对不确定需求的批量决策。从历史上看，制造公司经常依靠确定性优化模型来优化这些决策，通过使用来自预测技术的平均值来解决不确定的需求。我们的研究表明，确定性模型有效地处理了正态分布的随机需求。然而，我们观察到，确定性模型在处理持续的需求变化时遇到了挑战，这些变化是由合并、收购或全球大流行等不可预见事件等因素引发的。因此，制造企业采用随机模型进行有效决策势在必行。虽然这些模型提供了宝贵的见解，但它们的复杂性给传统方法（如分支-切割）带来了障碍。作为回应，我们的研究引入了一种机器学习(ML)-授权的Benders分解方法-增强了新的不等式和ML-授权的Benders重构。我们的计算实验表明，通过我们提出的方法可以显著节省成本。

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引用次数: 0

Time-dependent Windy Rural Postman Problem: Mathematical formulation and adaptive metaheuristic 时变多风乡村邮差问题：数学公式与自适应元启发式

IF 4.3 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Operations Research

Pub Date : 2025-11-10 DOI: 10.1016/j.cor.2025.107327

Franklin A. Krukoski , Arinei C.L. Silva , Carise E. Schmidt

In this paper, we extend the classical Windy Rural Postman Problem on undirected graphs by incorporating time-dependent traffic conditions and direction-sensitive traversal costs to reflect realistic scenarios. We present a mixed-integer programming formulation that models the problem with discretized travel-time intervals and prohibits vehicle stops during the tour. We develop two variants of an adaptive meta-heuristic, each enhanced with specialized local-search operators, and embed a time-dependent shortest-path algorithm to handle time discretization. To generate high-quality initial solutions, we adopt a constructive heuristic and use it as a warm start for both the mathematical formulation and the adaptive meta-heuristic. We evaluate the proposed approaches on instances generated from real traffic data. Our computational results show that the mathematical formulation, when solved by a commercial solver, can prove optimality for small instances, while both meta-heuristic variants consistently produce high-quality solutions to this challenging problem. Our findings also reveal that assuming constant travel times systematically underestimates routing costs and produces suboptimal tour plans under realistic congestion patterns.

本文将经典的Windy乡村邮差问题扩展到无向图上，引入时变交通条件和方向敏感穿越成本来反映现实场景。我们提出了一个混合整数规划公式，用离散的旅行时间间隔对问题建模，并禁止车辆在旅行期间停车。我们开发了自适应元启发式的两个变体，每个变体都增强了专门的局部搜索算子，并嵌入了一个时间相关的最短路径算法来处理时间离散化。为了生成高质量的初始解，我们采用建设性启发式，并将其作为数学公式和自适应元启发式的热启动。我们在真实交通数据生成的实例上对所提出的方法进行了评估。我们的计算结果表明，当由商业求解器求解时，数学公式可以证明小实例的最优性，而两种元启发式变体一致地为这个具有挑战性的问题产生高质量的解决方案。我们的研究结果还表明，假设旅行时间不变会系统性地低估路线成本，并在现实拥堵模式下产生次优旅行计划。

{"title":"Time-dependent Windy Rural Postman Problem: Mathematical formulation and adaptive metaheuristic","authors":"Franklin A. Krukoski , Arinei C.L. Silva , Carise E. Schmidt","doi":"10.1016/j.cor.2025.107327","DOIUrl":"10.1016/j.cor.2025.107327","url":null,"abstract":"<div><div>In this paper, we extend the classical Windy Rural Postman Problem on undirected graphs by incorporating time-dependent traffic conditions and direction-sensitive traversal costs to reflect realistic scenarios. We present a mixed-integer programming formulation that models the problem with discretized travel-time intervals and prohibits vehicle stops during the tour. We develop two variants of an adaptive meta-heuristic, each enhanced with specialized local-search operators, and embed a time-dependent shortest-path algorithm to handle time discretization. To generate high-quality initial solutions, we adopt a constructive heuristic and use it as a warm start for both the mathematical formulation and the adaptive meta-heuristic. We evaluate the proposed approaches on instances generated from real traffic data. Our computational results show that the mathematical formulation, when solved by a commercial solver, can prove optimality for small instances, while both meta-heuristic variants consistently produce high-quality solutions to this challenging problem. Our findings also reveal that assuming constant travel times systematically underestimates routing costs and produces suboptimal tour plans under realistic congestion patterns.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"186 ","pages":"Article 107327"},"PeriodicalIF":4.3,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145526224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Investments under strategic competition and uncertainty: A literature review on real option games 战略竞争与不确定性下的投资：实物期权博弈的文献综述

IF 4.3 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Operations Research

Pub Date : 2025-11-05 DOI: 10.1016/j.cor.2025.107328

Bruno Mombello , Fernando Olsina , Rolando Pringles

Market dynamics are shaped by uncertainty and competitive rivalry. In such environments, firms commit capital-intensive, irreversible investments, while preserving flexibility in terms of timing, scale and sequencing. The interaction of these factors makes investment decision-making exceedingly complex. The Real Option Games (ROG) framework addresses this complexity by combining real options analysis with game theory, offering a robust, structured approach for evaluating strategic investment decisions under oligopolistic competition. This study provides a comprehensive and systematic review of ROG literature, with a focus on non-cooperative preemption and war-of-attrition models. The review classifies the most recurrent modeling approaches, solution methods, and thematic emphases, and identifies theoretical and practical gaps that constrain further development, highlighting areas requiring deeper exploration. A comprehensive citation and critical content analysis was conducted on more than 230 scholarly works published between 1991 and 2025. Each work was classified according to its game and temporal structure, agent symmetry, strategic options, and informational setting. A detailed taxonomy is proposed to organize ROG models and address the lack of methodological classification in existing literature. The dominant modeling frameworks and topics are thoroughly mapped alongside the underexplored areas. The synthesis of methodological advances and persistent theoretical challenges suggests the agenda for future research. This review serves as a consolidated reference for researchers and practitioners, as ROG insights improve strategic capital budgeting decisions in capital-intensive sectors with investment irreversibility and strategic rivalry, such as energy, infrastructure, and high-tech industries. These insights refine investment timing triggers, optimal scaling decisions, and competitive response strategies.

市场动态受不确定性和竞争性竞争的影响。在这样的环境下，企业进行资本密集型、不可逆转的投资，同时在时间、规模和顺序方面保持灵活性。这些因素的相互作用使得投资决策极其复杂。实物期权博弈（Real Option Games， ROG）框架通过将实物期权分析与博弈论相结合，解决了这种复杂性，为评估寡头垄断竞争下的战略投资决策提供了一种强大的、结构化的方法。本研究对ROG文献进行了全面和系统的回顾，重点关注非合作抢占和消耗战模型。该综述对最常见的建模方法、解决方法和专题重点进行了分类，并确定了限制进一步发展的理论和实践差距，突出了需要深入探索的领域。对1991年至2025年间出版的230多部学术著作进行了全面的引文和批评内容分析。每项工作都根据其游戏和时间结构、代理对称、战略选择和信息设置进行分类。提出了一个详细的分类法来组织ROG模型，并解决现有文献中缺乏方法分类的问题。主要的建模框架和主题与未开发的领域一起被彻底地映射出来。方法上的进步和持续的理论挑战的综合表明了未来研究的议程。本综述为研究人员和从业人员提供了综合参考，因为ROG的见解可以改善具有投资不可逆性和战略竞争的资本密集型行业（如能源、基础设施和高科技行业）的战略资本预算决策。这些见解细化了投资时机触发、最佳规模决策和竞争响应策略。

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引用次数: 0

An enhanced dual-population NSGA-II for solving multi-objective emergency supplies dispatch problem based on truck-drone-dispatch vehicle collaboration 基于卡车-无人机-调度车辆协同的增强型双种群NSGA-II应急物资多目标调度问题

IF 4.3 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Operations Research

Pub Date : 2025-11-01 DOI: 10.1016/j.cor.2025.107324

Qin Guo , Ya Qiu , Yong Shi , Qiaoxian Zheng , Haixiang Guo

Emergency supplies dispatch is a key component of emergency management. Most existing studies related to emergency supplies dispatch focused on the trucks transportation. Inspired by the successful application of drones in military operations and commercial logistics, this study proposes an emergency supplies dispatch model based on truck-drone-dispatch vehicle collaborative delivery, which is a further extension of the vehicle routing problem with drones (VRPD). Compared to the classical VRPD, the model in this paper incorporates dispatch vehicles to transport drones, making it more suitable for disaster scenarios. To solve the proposed model, an enhanced dual-population non-dominated sorting genetic algorithm-II is developed based on the traditional non-dominated sorting genetic algorithm-II. This algorithm incorporates a series of local search operators tailored to the model’s characteristics to enhance its local search capability. Additionally, the selection operator is improved to increase population diversity. Finally, the elite population is generated according to the Pareto front of the original population, so that the elite population searches in the vicinity of the Pareto front of the original population to improve the convergence accuracy of the algorithm. To verify the proposed model and algorithm, we randomly generate a set of instances. In small-size instances, we employed the

ϵ

-constraint method to validate the proposed model’s effectiveness and to demonstrate its advantages over the standard VRPD in emergency logistics scenarios. In medium- and large-size instances, we analyze the effects of three key enhancement strategies on the algorithm’s performance. Finally, the proposed model and algorithm are applied to a real-world case of the Wenchuan earthquake, showcasing their practicality and applicability.

应急物资调度是应急管理的重要组成部分。现有的应急物资调度研究大多集中在卡车运输上。受无人机在军事行动和商业物流中的成功应用启发，本研究提出了一种基于卡车-无人机-调度车辆协同配送的应急物资调度模型，该模型是无人机车辆路径问题（VRPD）的进一步扩展。与传统的VRPD模型相比，本文模型引入了调度车辆来运输无人机，使其更适合灾害场景。为了求解该模型，在传统非优势排序遗传算法的基础上，提出了一种改进的双种群非优势排序遗传算法。该算法结合了一系列针对模型特点的局部搜索算子，增强了模型的局部搜索能力。此外，改进了选择算子，增加了种群多样性。最后，根据原种群的帕累托前沿生成精英种群，使精英种群在原种群的帕累托前沿附近搜索，提高算法的收敛精度。为了验证所提出的模型和算法，我们随机生成一组实例。在小型实例中，我们采用ϵ-constraint方法验证了所提出模型的有效性，并展示了其在应急物流场景中优于标准VRPD的优势。在大中型实例中，我们分析了三种关键增强策略对算法性能的影响。最后，以汶川地震为例，验证了模型和算法的实用性和适用性。

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引用次数: 0

Workload balancing for flight dispatchers 航班调度员的工作负载平衡

IF 4.3 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Operations Research

Pub Date : 2025-10-31 DOI: 10.1016/j.cor.2025.107303

Serkan Turhan, Fatma Gzara, Samir Elhedhli

Flight dispatchers are responsible for flight planning prior to departure and flight monitoring while en-route. Their work involves multi-tasking and their workload is dynamic. We study such a problem under two nonlinear workload balancing measures: minimum peak workload and minimum absolute deviation. In order to solve practical instances efficiently, we use decomposition through Lagrangian relaxation to reduce the problem into easier-to-solve subproblems and prove that the Lagrangian lower bound has a closed-form expression for the peak workload objective. To find feasible solutions, we develop a Focus-Search-and-Improve heuristic with a genetic algorithm core where parts of the feasible solution set are explored and searched by a genetic algorithm, and solutions are further fine-tuned by an improvement heuristic. To test the efficiency of the proposed approach, we generated 231 instances based on 2019 U.S. Bureau of Transportation flight data that involve 17 different carriers and up to 3968 flights per instance. Numerical testing demonstrates the efficiency of the proposed approach in that the Lagrangian lower bound is very tight, and the heuristic finds optimal solutions in 33.4% of the instances and are on average 3.5% away from the Lagrangian lower bound. It also reveals that the difficulty of the problem increases for smaller workstation-to-flight ratios, and that the peak workload objective achieves the goal of balancing the workload at times where peaks occur but does not necessarily balance the workload throughout the workday. On the other hand, the absolute deviation objective achieves better balance between workstations at the expense of a slight increase in peak workload.

飞行调度员负责起飞前的飞行计划和途中的飞行监控。他们的工作涉及多任务处理，他们的工作量是动态的。研究了两种非线性工作负载平衡措施：最小峰值工作负载和最小绝对偏差。为了有效地求解实际实例，我们利用拉格朗日松弛分解将问题分解为更容易求解的子问题，并证明了拉格朗日下界对于峰值负荷目标具有封闭形式的表达式。为了找到可行的解决方案，我们开发了一个具有遗传算法核心的焦点搜索和改进启发式算法，其中通过遗传算法探索和搜索部分可行解决方案，并通过改进启发式算法进一步微调解决方案。为了测试所提议方法的效率，我们基于2019年美国运输局的航班数据生成了231个实例，这些数据涉及17家不同的航空公司，每个实例最多有3968个航班。数值测试证明了该方法的有效性，因为拉格朗日下界非常紧，启发式方法在33.4%的实例中找到最优解，平均距离拉格朗日下界3.5%。它还表明，对于较小的工作站与飞行的比率，问题的难度会增加，并且高峰工作负载目标实现了在高峰发生时平衡工作负载的目标，但不一定在整个工作日平衡工作负载。另一方面，绝对偏差目标在工作站之间实现了更好的平衡，代价是略微增加峰值工作负载。

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引用次数: 0

Discovering heuristics with Large Language Models (LLMs) for mixed-integer programs: Single-machine scheduling 用大语言模型（llm）发现混合整数程序的启发式算法：单机调度

IF 4.3 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Operations Research

Pub Date : 2025-10-31 DOI: 10.1016/j.cor.2025.107325

İbrahim Oğuz Çetinkaya , İ. Esra Büyüktahtakın , Parshin Shojaee , Chandan K. Reddy

Our study contributes to the scheduling and combinatorial optimization literature with new heuristics discovered by leveraging the power of Large Language Models (LLMs). We focus on the single-machine total tardiness (SMTT) problem, which aims to minimize total tardiness by sequencing

n

jobs on a single processor without preemption, given processing times and due dates. We develop and benchmark two novel LLM-discovered heuristics, the EDD Challenger (EDDC) and MDD Challenger (MDDC), inspired by the well-known Earliest Due Date (EDD) and Modified Due Date (MDD) rules. In contrast to prior studies that employed simpler rule-based heuristics, we evaluate our LLM-discovered algorithms using rigorous criteria, including optimality gaps and solution time derived from a mixed-integer programming (MIP) formulation of SMTT. We compare their performance against state-of-the-art heuristics and exact methods across various job sizes (20, 100, 200, and 500 jobs). For instances with more than 100 jobs, exact methods such as MIP and dynamic programming become computationally intractable. Up to 500 jobs, EDDC improves upon the classic EDD rule and another widely used algorithm in the literature. MDDC consistently outperforms traditional heuristics and remains competitive with exact approaches, particularly on larger and more complex instances. This study shows that human-LLM collaboration can produce scalable, high-performing heuristics for NP-hard constrained combinatorial optimization, even under limited resources when effectively configured.

我们的研究通过利用大型语言模型（LLMs）的力量发现了新的启发式方法，为调度和组合优化文献做出了贡献。我们关注单机总延迟（SMTT）问题，该问题旨在通过在给定的处理时间和截止日期下，在没有抢占的情况下对单个处理器上的n个作业进行排序来最小化总延迟。受最早到期日期（EDD）和修改到期日期（MDD）规则的启发，我们开发了两个新的法学硕士发现的启发式算法，EDD挑战者（EDDC）和MDD挑战者（MDDC），并对其进行了基准测试。与之前使用更简单的基于规则的启发式方法的研究相比，我们使用严格的标准来评估llm发现的算法，包括SMTT的混合整数规划（MIP）公式的最优性差距和解决时间。我们将它们的性能与各种作业规模（20、100、200和500个作业）的最先进的启发式和精确方法进行比较。对于超过100个作业的实例，精确的方法，如MIP和动态规划，在计算上变得难以处理。EDDC在经典EDD规则和另一种在文献中广泛使用的算法的基础上进行了改进，最多可达500个作业。MDDC始终优于传统的启发式方法，并与精确方法保持竞争，特别是在更大更复杂的实例上。这项研究表明，即使在资源有限的情况下，人类与llm的合作也可以为NP-hard约束组合优化产生可扩展的高性能启发式算法。

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引用次数: 0