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A Bi-criterion Steiner Traveling Salesperson Problem with Time Windows for Last-mile Electric Vehicle Logistics 最后一英里电动汽车物流的带时间窗的双准则Steiner旅行销售员问题
IF 4.3 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-10-04 DOI: 10.1016/j.cor.2025.107286
Prateek Agarwal , Debojjal Bagchi , Tarun Rambha , Venktesh Pandey
This paper addresses the problem of energy-efficient and safe routing of last-mile electric freight vehicles. With the rising environmental footprint of the transportation sector and the growing popularity of E-Commerce, freight companies are likely to benefit from optimal time window feasible tours that minimize energy usage while reducing traffic conflicts at intersections and thereby improving safety. We formulate this problem as a Bi-criterion Steiner Traveling Salesperson Problem with Time Windows (BSTSPTW) with energy consumed and the number of left turns at intersections as the two objectives while also considering regenerative braking capabilities. We first discuss an exact mixed-integer programming model with scalarization to enumerate points on the efficiency frontier for small instances. For larger networks, we develop an efficient local search-based heuristic, which uses several operators to intensify and diversify the search process. We demonstrate the utility of the proposed methods using benchmark data and real-world instances from Amazon delivery routes in Austin, US. Comparisons with state-of-the-art solvers show that our heuristics can generate near-optimal solutions within reasonable time budgets, effectively balancing energy efficiency and safety under practical delivery constraints.
本文研究了最后一英里电动货运车辆的节能与安全路线问题。随着运输部门对环境的影响不断增加和电子商务的日益普及,货运公司可能会从最佳时间窗口可行的旅行中受益,这种旅行可以最大限度地减少能源消耗,同时减少十字路口的交通冲突,从而提高安全性。我们将该问题表述为以能量消耗和交叉口左转弯数为目标,同时考虑再生制动能力的双准则Steiner带时间窗旅行销售员问题(BSTSPTW)。我们首先讨论了一个精确的混合整数规划模型,该模型具有标量化,可以枚举小实例的效率边界上的点。对于较大的网络,我们开发了一种高效的基于局部搜索的启发式算法,该算法使用多个算子来强化和多样化搜索过程。我们使用基准数据和来自美国奥斯汀的亚马逊送货路线的实际实例来演示所提出方法的实用性。与最先进的求解器的比较表明,我们的启发式算法可以在合理的时间预算内生成接近最优的解决方案,在实际交付约束下有效地平衡了能源效率和安全性。
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引用次数: 0
A multi-time-window multi-objective hybrid fleet home health care routing optimization problem considering caregiver utilization and compatibility 考虑护理人员利用率和兼容性的多时间窗口多目标混合车队家庭医疗护理路径优化问题
IF 4.3 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-10-04 DOI: 10.1016/j.cor.2025.107288
Wendi Li , Gang Du , Xiaohang Yue
Home healthcare plays a key role in the era of an aging population and limited healthcare resources in hospitals, and one of its important tasks is to develop optimal caregiver visit routines. In the context of sustainable development and dual carbon goals, home healthcare must also address carbon emissions during caregiver visits. One of the most effective initiatives is the use of electric vehicles to gradually replace fuel vehicles as an important means of transportation. Therefore, this paper investigates a multi-objective home healthcare path optimization problem based on a mixed fleet of vehicles. In this problem, the transportation of caregivers is either electric or fuel vehicles, and this paper considers the case of patients with different numbers of multiple time windows, defines compatibility, and optimizes five conflicting objectives under the constraints of time windows, doctor-patient skill matching, electric vehicle battery capacity, compatibility, and maximum working hours. To address this problem, we develop a mixed integer programming model to optimize five objectives: cost minimization, caregiver utilization maximization, workload deviation minimization, patient-caregiver compatibility maximization, and skill level deviation minimization. In addition, this paper proposes a hybrid algorithmic solution model with hybrid simulated annealing and a third-generation non-dominated sorting genetic algorithm and designs two neighborhood structures based on the problem characteristics as well as heuristics for charging station insertion. The results show that the improved hybrid algorithm solves the problem more comprehensively and effectively and can cover a wider solution space with good distribution and diversity.
在人口老龄化和医院医疗资源有限的时代,家庭医疗保健发挥着关键作用,其重要任务之一是制定最佳的护理人员就诊程序。在可持续发展和双碳目标的背景下,家庭保健还必须解决护理人员就诊期间的碳排放问题。其中最有效的举措之一是使用电动汽车逐步取代燃油汽车作为重要的交通工具。因此,本文研究了一个基于混合车队的多目标家庭医疗路径优化问题。在该问题中,护理人员的交通工具为电动汽车或燃油汽车,本文考虑患者具有不同数量的多个时间窗口的情况,定义兼容性,并在时间窗口、医患技能匹配、电动汽车电池容量、兼容性和最大工作时间的约束下,对5个冲突目标进行优化。为了解决这个问题,我们开发了一个混合整数规划模型来优化五个目标:成本最小化、护理人员利用率最大化、工作量偏差最小化、患者-护理人员兼容性最大化和技能水平偏差最小化。此外,本文提出了混合模拟退火和第三代非支配排序遗传算法的混合算法求解模型,并根据问题特点和启发式设计了充电站插入的两种邻域结构。结果表明,改进后的混合算法能更全面有效地解决问题,覆盖更广的解空间,具有良好的分布和多样性。
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引用次数: 0
Optimizing production–transportation–delivery in global supply chain with demand ambiguity by branch-and-cut algorithm 基于分支切断算法的需求模糊全球供应链生产-运输-交付优化
IF 4.3 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-10-03 DOI: 10.1016/j.cor.2025.107293
Zheng Wang , Pingyuan Dong , Ying Liu
The complexity incorporated in global supply chain (GSC) means the production, transportation, and delivery are totally operating and completing in the dynamic business environment with unforeseen events. At present, there are two key challenges in the transnational supply chain network: addressing the demand ambiguity and enhancing cooperation among supply chain entities. To optimize the production–transportation–delivery decision in GSC, a novel globalized distributionally robust GSC (GDR-GSC) model with horizontal cooperation is proposed, in which the ambiguity of demand distribution is characterized by inner and outer ambiguity sets. Subsequently, the proposed model is transformed into mixed integer nonlinear programming (MINLP) model by duality theory. It is commonly difficult to solve in high-dimensional case. Therefore, a customized Branch-and-Cut (B&C) algorithm tailored for the GDR-GSC model is designed to handle complex MINLP problems, and improves computational efficiency and solution quality. The case study based on Apple’s sales operations in China and Malaysia demonstrates the effectiveness and superiority of the B&C algorithm in solving the GDR-GSC model. Numerical experiments show that the customized B&C algorithm can improve the average solving time by 18% while maintaining the same solution quality. Based on realistic cases, we know that horizontal cooperation can increase profits by at least 6.25%.
全球供应链(GSC)的复杂性意味着生产、运输和交付都是在动态的商业环境中进行的,并在不可预见的事件中完成。目前,跨国供应链网络面临着两个关键挑战:解决需求歧义和加强供应链实体之间的合作。为了优化GSC中的生产-运输-交付决策,提出了一种具有横向合作的全球化分布鲁棒GDR-GSC模型,该模型将需求分布的模糊性划分为内部和外部模糊集。然后,利用对偶理论将该模型转化为混合整数非线性规划模型。在高维情况下,通常难以求解。因此,针对GDR-GSC模型,设计了一种定制化的Branch-and-Cut (B&;C)算法来处理复杂的MINLP问题,提高了计算效率和解的质量。以苹果公司在中国和马来西亚的销售业务为例,证明了B&;C算法在求解GDR-GSC模型中的有效性和优越性。数值实验表明,定制的B&;C算法在保持相同解质量的情况下,平均求解时间提高了18%。基于现实案例,我们知道横向合作至少可以增加6.25%的利润。
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引用次数: 0
Towards an unsupervised learning scheme for efficiently solving parameterized mixed-integer programs 一种有效求解参数化混合整数规划的无监督学习方案
IF 4.3 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-09-30 DOI: 10.1016/j.cor.2025.107290
Shiyuan Qu , Fenglian Dong , Zhiwei Wei , Chao Shang
Mixed integer programming (MIP) has been widely utilized to tackle a broad range of real-world decision-making problems, while its solution efficiency remains a key challenge. In this paper, we describe a novel unsupervised learning scheme for accelerating the solution of a family of MIP problems. Distinct substantially from existing learning-to-optimize methods, our proposal seeks to train an autoencoder (AE) for binary variables in an unsupervised learning fashion, using data of optimal solutions to historical instances for a parametric family of MIPs. By a deliberate design of AE architecture and exploitation of its statistical implication, we present a simple and straightforward strategy to construct a class of cutting plane constraints from the decoder parameters of an offline-trained AE. These constraints reliably enclose the optimal binary solutions of new problem instances thanks to the representation strength of AE. More importantly, their integration into the primal MIP problem of an unseen instance leads to a tightened MIP, which can be resolved at decision time using off-the-shelf solvers with much higher efficiency. Our method is applied to two benchmark problems: the batch process scheduling problem, formulated as a mixed-integer linear programming (MILP) problem, and the cart–pole system control problem, formulated as a mixed-integer quadratic programming (MIQP) problem. Comprehensive results demonstrate that our approach significantly reduces the computational cost of off-the-shelf MILP solvers while retaining a high solution quality. The codes of this work are open-sourced at https://github.com/qushiyuan/AE4BV.
混合整数规划(MIP)已被广泛应用于解决现实世界中的各种决策问题,但其求解效率仍然是一个关键挑战。在本文中,我们描述了一种新的无监督学习方案来加速求解一类MIP问题。与现有的学习优化方法有很大不同,我们的建议旨在以无监督学习的方式训练二进制变量的自编码器(AE),使用参数mip族历史实例的最优解数据。通过精心设计声发射体系结构并利用其统计含义,我们提出了一种简单直接的策略,从离线训练声发射的解码器参数构造一类切割平面约束。由于AE的表示强度,这些约束可靠地包含了新问题实例的最优二值解。更重要的是,将它们集成到未见实例的原始MIP问题中,可以得到更严格的MIP,从而可以在决策时使用现成的求解器以更高的效率进行求解。我们的方法应用于两个基准问题:批处理调度问题(表述为混合整数线性规划(MILP)问题)和车杆系统控制问题(表述为混合整数二次规划(MIQP)问题)。综合结果表明,我们的方法显着降低了现成的MILP求解器的计算成本,同时保持了高解决方案的质量。这项工作的代码是在https://github.com/qushiyuan/AE4BV上开源的。
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引用次数: 0
Dynamic crowdsourcing problem in urban–rural distribution using the learning-based approach 基于学习的城乡布局动态众包问题研究
IF 4.3 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-09-28 DOI: 10.1016/j.cor.2025.107292
Zongcheng Zhang , Maoliang Ran , Yanru Chen , M.I.M. Wahab , Mujin Gao , Yangsheng Jiang
Inspired by real-world urban and rural distribution logistics scenarios, this study explores the dynamic crowdsourcing multi-depot pickup and delivery problem (DCMDPDP) through an online platform (OCP), where requests and crowdsourced vehicles arrive dynamically. Vehicles either collect from multiple depots for deliveries or pick up from customers to depots. To maximize the OCP’s daily total gain, the net value of completed task revenue minus vehicle compensation costs, we integrate anticipated future gains into each decision-making process and formulate the DCMDPDP as a Markov decision process. A learning-based hybrid heuristic algorithm is proposed for the DCMDPDP. Specifically, we develop an enhanced adaptive large neighborhood search algorithm leveraging the heat map to batch orders into multiple groups and assign them to depots, where the heat map is learned offline using a graph convolutional residual network with an attention mechanism model. A value learning-based algorithm is also developed to obtain optimal matches between order batches and vehicles, and near-optimal travel routes. Experimental results demonstrate that the proposed algorithm improves the OCP total gain by 46.09%, 57.13%, 0.49%, 2.45%, 1.08%, and 2.77% over six benchmarks. Furthermore, the proposed algorithm reduces unserved customers to 7.83 on average, outperforming six benchmarks by 2.19–167.52 fewer cases. Moreover, extensive experiments validate that the proposed algorithm is strongly generalizable in handling instances with varying customer sizes and different temporal, spatial, and demand distributions.
受现实城市和农村配送物流场景的启发,本研究通过在线平台(OCP)探索动态众包多仓库取货和交付问题(DCMDPDP),其中请求和众包车辆动态到达。车辆要么从多个仓库收集货物,要么从客户那里取货到仓库。为了最大化OCP的每日总收益,即已完成任务收益的净值减去车辆补偿成本,我们将预期未来收益整合到每个决策过程中,并将DCMDPDP制定为马尔可夫决策过程。提出了一种基于学习的混合启发式算法。具体来说,我们开发了一种增强的自适应大邻域搜索算法,利用热图将订单批处理成多个组并将它们分配到仓库,其中热图是使用带有注意机制模型的图卷积残差网络离线学习的。提出了一种基于价值学习的算法,以获得订单批次与车辆之间的最优匹配,以及接近最优的出行路线。实验结果表明,该算法在6个基准测试中分别提高了46.09%、57.13%、0.49%、2.45%、1.08%和2.77%的OCP总增益。此外,该算法将未服务的客户平均减少到7.83个,比六个基准减少2.19-167.52个案例。此外,大量的实验验证了所提出的算法在处理不同客户规模和不同时间、空间和需求分布的实例时具有很强的泛化性。
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引用次数: 0
Solving the strip packing problem with a decomposition framework and a generic solver: Implementation, tuning, and reinforcement-learning-based hybridization 用分解框架和通用求解器解决条形包装问题:实现、调整和基于强化学习的杂交
IF 4.3 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-09-27 DOI: 10.1016/j.cor.2025.107276
Fatih Burak Akçay, Maxence Delorme
In the strip packing problem, the objective is to pack a set of two-dimensional items into a strip of fixed width such that the total height of the packing is minimized. The current state-of-the-art exact approach for the problem uses a decomposition framework in which the main problem (MP) fixes the item abscissas and the strip height, whereas the subproblem (SP) determines whether a set of item ordinates resulting in a feasible packing exists. Even though this decomposition framework has already been used several times in the literature, implementation details were often obfuscated, limiting the outreach of the approach. We address this issue by thoroughly describing and testing various builds for this framework, investigating important features such as the way to forbid an infeasible solution in the MP (e.g., by rejecting them or through a no-good cut) and the techniques used to solve the MP and the SP. One of our findings is that a minor implementation tweak such as changing the random seed between two MP iterations can bring the same level of improvement as a more involved feature such as strengthening the no-good cuts. From our extensive experiments, we identify two versions of the framework that produce complementary results: one where the main problem is solved with integer linear programming and the other where it is solved with constraint programming. We then train a reinforcement learning agent to find the best hybridization of these two algorithms and show that the resulting approach obtains state-of-the-art results on benchmark instances.
在条形包装问题中,目标是将一组二维物品包装成固定宽度的条形,使包装的总高度最小。目前最先进的精确方法是使用一个分解框架,其中主问题(MP)确定项目的横坐标和条形高度,而子问题(SP)确定是否存在一组导致可行包装的项目坐标。尽管这个分解框架已经在文献中被使用了几次,但是实现细节经常被混淆,限制了方法的扩展。为了解决这个问题,我们彻底地描述和测试了这个框架的各种构建,研究了一些重要的特性,比如如何在MP中禁止一个不可行的解决方案(例如:我们的发现之一是,一个小的执行调整(如改变两次MP迭代之间的随机种子)可以带来与更复杂的功能(如加强无益处切割)相同水平的改进。从我们广泛的实验中,我们确定了产生互补结果的框架的两个版本:其中一个主要问题是用整数线性规划解决的,另一个是用约束规划解决的。然后,我们训练一个强化学习代理来找到这两种算法的最佳杂交,并表明所得到的方法在基准实例上获得了最先进的结果。
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引用次数: 0
Minimizing the weighted number of tardy jobs: data-driven heuristic for single-machine scheduling 最小化延迟作业的加权数:单机调度的数据驱动启发式算法
IF 4.3 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-09-26 DOI: 10.1016/j.cor.2025.107281
Nikolai Antonov , Přemysl Šůcha , Mikoláš Janota , Jan Hůla
Existing research on single-machine scheduling is largely focused on exact algorithms, which perform well on typical instances but can significantly deteriorate on certain regions of the problem space. In contrast, data-driven approaches provide strong and scalable performance when tailored to the structure of specific datasets. Leveraging this idea, we focus on a single-machine scheduling problem where each job is defined by its weight, duration, due date, and deadline, aiming to minimize the total weight of tardy jobs. We introduce a novel data-driven scheduling heuristic that combines machine learning with problem-specific characteristics, ensuring feasible solutions, which is a common challenge for ML-based algorithms. Experimental results demonstrate that our approach significantly outperforms the state-of-the-art in terms of optimality gap, number of optimal solutions, and adaptability across varied data scenarios, highlighting its flexibility for practical applications. In addition, we conduct a systematic exploration of ML models, addressing a common gap in similar studies by offering a detailed model selection process and demonstrating why the chosen model is the best fit.
现有的单机调度研究主要集中在精确算法上,这些算法在典型情况下表现良好,但在问题空间的某些区域会严重恶化。相反,数据驱动的方法在针对特定数据集的结构进行定制时提供强大的可伸缩性能。利用这一思想,我们将重点放在单机调度问题上,其中每个作业由其权重、持续时间、到期日期和截止日期定义,旨在最小化延迟作业的总权重。我们引入了一种新颖的数据驱动调度启发式算法,将机器学习与问题特定特征相结合,确保可行的解决方案,这是基于ml的算法面临的共同挑战。实验结果表明,我们的方法在最优性差距、最优解的数量和不同数据场景的适应性方面明显优于最先进的方法,突出了其实际应用的灵活性。此外,我们对机器学习模型进行了系统的探索,通过提供详细的模型选择过程并演示为什么所选择的模型是最适合的,从而解决了类似研究中的常见差距。
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引用次数: 0
Optimal placement of electric vehicle slow-charging stations: A continuous facility location problem under uncertainty 电动汽车慢充电站优化布局:不确定条件下的连续设施选址问题
IF 4.3 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-09-26 DOI: 10.1016/j.cor.2025.107289
H.W. Ljósheim, S. Jenkins, K.D. Searle, J.K. Wolff
Electric vehicles (EVs) are becoming a key mechanism to reduce emissions in the transportation industry, and hence contribute to the green transition. In this paper, we present a mathematical programming model which determines the optimal placement of EV charging stations such that chargers are placed in the most cost-efficient way possible for all stakeholders, assuming additionally that EV charging demand is inherently stochastic in nature. The model is formulated as a two-stage, continuous location–allocation model in the form of a generalised Weber problem in two dimensions. However, this formulation is non-convex and notoriously difficult to solve. We therefore propose a suitable discretisation procedure to find high quality solutions in suitable time. The discretisation procedure shows strong performance across a variety of computational experiments using randomly generated scenarios, maintaining robustness in terms of the objective value and overall solution quality.
A part of this solution procedure was entered into the 15th AIMMS-MOPTA Optimisation Modelling Competition.
电动汽车(ev)正在成为交通运输行业减少排放的关键机制,从而有助于绿色转型。在本文中,我们提出了一个数学规划模型,该模型确定了电动汽车充电站的最佳布局,使充电器以最具成本效益的方式放置,并假设电动汽车充电需求本质上是随机的。该模型以二维广义韦伯问题的形式表述为一个两阶段、连续的位置分配模型。然而,这个公式是非凸的,很难求解。因此,我们提出了一个合适的离散化程序,以在合适的时间内找到高质量的解决方案。离散化过程在使用随机生成的场景的各种计算实验中显示出强大的性能,在客观值和整体解决方案质量方面保持鲁棒性。这个解决方案的一部分进入了第15届AIMMS-MOPTA优化建模比赛。
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引用次数: 0
Maximum capture location problem with random utilities and overflow penalties 随机实用程序和溢出惩罚的最大捕获位置问题
IF 4.3 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-09-26 DOI: 10.1016/j.cor.2025.107285
Gonzalo Méndez-Vogel , Sebastián Dávila-Gálvez , Pedro Jara-Moroni , Jorge Zamorano , Vladimir Marianov
This paper extends the maximum capture location problem with random utilities by incorporating the facility capacity and introducing penalties for overflows into the objective function. We propose a method that combines the key features of two state-of-the-art approaches for the uncapacitated case, which are adapted to solve the problem at hand. The first approach is a linear reformulation that extends the best-known linearization in the literature, which is based on variable substitution. The second approach is a reformulation that incorporates outer-approximation cuts and enhanced submodular cuts, solving the problem via a branch-and-cut approach. We tested the performance of the three approaches on several instances and show that the combined method outperforms each of the preceding techniques. The optimal location patterns of the model are also analysed, and it is found that considering the overflow and overflow penalties in the objective function affects the location decisions. The resulting optimal locations align more closely with practical scenarios.
本文通过在目标函数中引入设施容量和溢出惩罚,扩展了具有随机效用的最大捕获位置问题。我们提出了一种方法,结合了两种最先进的方法的关键特征,用于无行为能力的情况下,这是适合解决手头的问题。第一种方法是线性重构,扩展了文献中最著名的线性化,它是基于变量替换的。第二种方法是将外部近似切割和增强的子模块切割结合起来,通过分支切割方法解决问题。我们在几个实例上测试了这三种方法的性能,并表明组合方法优于前面的每一种技术。分析了模型的最优选址模式,发现在目标函数中考虑溢出惩罚和溢出惩罚会影响选址决策。最终的最佳位置与实际场景更加接近。
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引用次数: 0
Modeling and algorithm for job shop scheduling with batch operations in semiconductor fabs 半导体晶圆厂批量作业车间调度建模与算法
IF 4.3 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-09-24 DOI: 10.1016/j.cor.2025.107287
Wen Ma , Gedong Jiang , Nuogang Sun , Chaoqing Min , Xuesong Mei
Semiconductor manufacturing presents a highly complex Job Shop Scheduling Problem (JSP) due to the diversity and large number of processing machines, as well as the intricate manufacturing processes including batch and non-batch operations. Existing studies often either overlook batching problems or address them in oversimplified ways, failing to provide effective solutions for large-scale scheduling challenges with batch operations. For this problem, a model for the JSP involving both batching and non-batching processes in semiconductor fabs is first developed. Then, the First Come First Served (FCFS) approach, as an effective rule-based method, is employed to generate high-quality initial solutions. A tailored Constrained Genetic Algorithm (CGA) by embedding constraints to the stages of genetic algorithms is proposed to further optimize the solution. The CGA incorporates batch grouping, constrained encoding, constrained crossover and constrained mutation to effectively handle the sequential constraints of batch and non-batch processes, ensuring the generation of valid solutions. The CGA is validated using the SMT2020 and SMAT2022 datasets across various scales and scenarios. Experimental results demonstrate that the CGA outperforms FCFS, backward simulation and reinforcement learning. These results highlight the CGA’s effectiveness and robustness in solving complex scheduling problems in semiconductor manufacturing.
半导体制造业由于加工机器的多样性和数量多,以及包括批量和非批量操作在内的复杂制造过程,提出了一个高度复杂的作业车间调度问题(JSP)。现有的研究往往忽视了批处理问题,或者以过于简化的方式处理批处理问题,无法为大规模的批处理调度挑战提供有效的解决方案。针对这一问题,首先建立了涉及半导体晶圆厂中批处理和非批处理的JSP模型。然后,采用先到先得(FCFS)方法作为一种有效的基于规则的方法,生成高质量的初始解。提出了一种定制约束遗传算法(CGA),将约束嵌入到遗传算法的各个阶段,进一步优化求解。该算法结合批量分组、约束编码、约束交叉和约束突变等方法,有效地处理了批量和非批量过程的序列约束,保证了有效解的生成。CGA使用SMT2020和SMAT2022数据集跨各种尺度和场景进行验证。实验结果表明,CGA优于FCFS、后向仿真和强化学习。这些结果突出了CGA在解决半导体制造中复杂调度问题方面的有效性和鲁棒性。
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引用次数: 0
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Computers & Operations Research
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