Computers & Operations Research最新文献_第3页

Electric vehicle routing with heterogeneous charging stations 具有异构充电站的电动汽车路径

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

Computers & Operations Research

Pub Date : 2026-01-14 DOI: 10.1016/j.cor.2025.107374

Weiquan Wang , Yossiri Adulyasak , Jean-François Cordeau

The routing of an electric vehicle often requires planning stops at charging stations to recharge the vehicle’s battery. At the same time, the price of electricity, the charging technology, and the waiting time at a charging station (CS) can impact routing and charging decisions for a fleet of vehicles. We introduce the Electric Vehicle Routing Problem with Heterogeneous Charging Stations (E-VRP-HC). We simultaneously consider charging functions (which are nonlinear in nature), time-dependent waiting functions, and time-of-use electricity pricing at CSs. The advantage of considering this function explicitly is that we can reduce costs by avoiding peak queuing times at CSs or periods with high charging prices. The objective function is to minimize the sum of the route duration costs, charging costs, and vehicle fixed costs. To solve this problem, we propose a path-based mixed-integer linear programming formulation, which does not require time discretization to track charging costs. The formulation can be solved using a general-purpose solver to find optimal solutions for small-sized instances. However, tackling this large-scale problem is challenging given the fact that determining an optimal vehicle’s time schedule for a given route in this context is already a complex optimization problem. To address this, we propose two methods for the time scheduling problem: (i) an exact method that obtains an optimal schedule but is computationally intensive and (ii) a heuristic method that can provide a high-quality solution in a very short time. Building upon these two optimization subroutines, we develop an effective metaheuristic framework to solve large-scale instances. The proposed model and heuristic are validated on two sets of benchmark instances: a newly designed benchmark set, and a real-world dataset from Beijing. The computational results on benchmark instances demonstrate the performance of our approach in handling the complexity of the E-VRP-HC. Numerical tests on the real-world dataset show that considering the time-of-use pricing function and nonlinear charging function can significantly reduce costs. Finally, we provide valuable managerial insights based on the results of our computational experiments.

电动汽车的路线通常需要在充电站停下来为汽车电池充电。与此同时，电价、充电技术和在充电站（CS）的等待时间会影响车队的路线和充电决策。介绍了具有异构充电站的电动汽车路径问题（E-VRP-HC）。我们同时考虑了充电函数（本质上是非线性的）、时间依赖的等待函数和CSs的分时电价。明确考虑这个函数的好处是，我们可以通过避免CSs的高峰排队时间或高收费时段来降低成本。目标函数是最小化路线持续时间成本、充电成本和车辆固定成本的总和。为了解决这个问题，我们提出了一个基于路径的混合整数线性规划公式，它不需要时间离散来跟踪收费成本。该公式可以使用通用求解器求解，以找到小型实例的最优解。然而，考虑到在这种情况下确定给定路线的最佳车辆时间表已经是一个复杂的优化问题，解决这个大规模问题是具有挑战性的。为了解决这个问题，我们提出了两种时间调度问题的方法：(i)一种精确的方法，它可以获得最优的调度，但计算量很大；（ii）一种启发式方法，可以在很短的时间内提供高质量的解决方案。在这两个优化子程序的基础上，我们开发了一个有效的元启发式框架来解决大规模实例。在新设计的基准集和北京的实际数据集两组基准实例上验证了所提出的模型和启发式算法。在基准实例上的计算结果证明了我们的方法在处理E-VRP-HC的复杂性方面的性能。在实际数据集上的数值测试表明，考虑使用时间定价函数和非线性收费函数可以显著降低成本。最后，基于我们的计算实验结果，我们提供了有价值的管理见解。

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引用次数: 0

Multilevel iterated tabu search for the multi-constraint graph partitioning problem 多约束图划分问题的多级迭代禁忌搜索

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

Computers & Operations Research

Pub Date : 2026-01-13 DOI: 10.1016/j.cor.2026.107389

Zhi Lu , Linlin Chen , Jian Gao , Jin-Kao Hao

The multi-constraint graph partitioning (MCGP) problem involves partitioning a set of vertices into nonempty, pairwise-disjoint subsets such that each subset must satisfy certain bound constraints while minimizing the total cost of edges with both endpoints in the same subset. Arising from an integrated vehicle and pollster problem in a real-world application, MCGP generalizes a number of other well-known graph partitioning problems. Due to its NP-hard nature, solving MCGP is computationally challenging. This work presents the first multilevel iterated tabu search (MITS) algorithm to tackle MCGP. Specifically, the algorithm uses a problem-specific coarsening method to reduce progressively the input graph and relies on a dedicated feasible-and-infeasible iterated tabu search procedure to refine the solution to each reduced graph. Extensive experiments on two sets of 665 benchmark instances demonstrate that MITS significantly outperforms state-of-the-art algorithms by finding 573 new upper bounds, while matching 83 previous best-known upper bounds. We also apply the algorithm to another related graph partitioning problem to demonstrate its broader applicability. Additionally, we conduct analysis studies on key algorithmic components to verify the effectiveness of the proposed ideas and strategies.

多约束图划分（MCGP）问题涉及将一组顶点划分为非空的、两两不相交的子集，使得每个子集必须满足一定的边界约束，同时最小化具有同一子集中两个端点的边的总代价。MCGP产生于实际应用程序中的集成车辆和民意调查问题，它推广了许多其他著名的图划分问题。由于其NP-hard性质，解决MCGP在计算上具有挑战性。这项工作提出了第一个多层迭代禁忌搜索（MITS）算法来解决MCGP。具体而言，该算法使用针对特定问题的粗化方法逐步约简输入图，并依赖于专用的可行和不可行迭代禁忌搜索过程来细化每个约简图的解。在两组665个基准实例上进行的大量实验表明，MITS通过找到573个新的上界，同时匹配83个已知的上界，显著优于最先进的算法。我们还将该算法应用于另一个相关的图划分问题，以证明其更广泛的适用性。此外，我们对关键算法组件进行分析研究，以验证所提出的想法和策略的有效性。

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引用次数: 0

A hybrid genetic search for the inventory routing problem 一种针对库存路径问题的混合遗传搜索

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

Computers & Operations Research

Pub Date : 2026-01-13 DOI: 10.1016/j.cor.2025.107376

Bruno Castro , Marcus Poggi , Rafael Martinelli

The Inventory Routing Problem (IRP), an essential component of supply chain management, involves efficiently managing deliveries from a depot to clients using a fleet of vehicles. Recognized in a recent international challenge, the IRP requires innovative approaches. This paper presents a Hybrid Genetic Search (HGS) algorithm, with a distinctive crossover operation tailored for IRP and a fast way to calculate optimal inventory levels using network flows on an auxiliary graph. Our method integrates HGS with the Network Simplex IRP decoder, combined with a refined solution constructor, efficient IRP and Capacitated Vehicle Routing Problem local searches, and several components that make the hybrid framework effective for the IRP. We provide an extensive computational evaluation, showing that our algorithm outperforms 22 recent methods from the literature, providing 137 new best-known solutions for a classical instance set and 180 new best-known solutions for a recent larger instance set. Moreover, according to the rules of the recent international challenge, our method would rank first.

库存路径问题（IRP）是供应链管理的一个重要组成部分，涉及到使用车队有效地管理从仓库到客户的交付。在最近的国际挑战中认识到，IRP需要创新的方法。本文提出了一种混合遗传搜索（HGS）算法，该算法为IRP定制了独特的交叉操作，并在辅助图上使用网络流快速计算最优库存水平。我们的方法将HGS与网络单纯形IRP解码器集成在一起，结合了一个精细的解构造器、高效的IRP和有能力车辆路径问题的局部搜索，以及使混合框架有效地用于IRP的几个组件。我们提供了广泛的计算评估，表明我们的算法优于文献中的22种最新方法，为经典实例集提供了137个新的最知名解决方案，为最近的更大实例集提供了180个新的最知名解决方案。此外，根据最近国际挑战赛的规则，我们的方法将排名第一。

引用次数: 0

Numerical methods for stochastic optimization problems with decision-dependent distributions under large delays 大时滞下决策依赖分布随机优化问题的数值方法

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

Computers & Operations Research

Pub Date : 2026-01-13 DOI: 10.1016/j.cor.2026.107392

Licheng Deng, Yongchao Liu

In this paper, we aim to seek the performative stable solution and the stationary point of the stochastic optimization problem with decision-dependent distributions in a centralized communication setting. We focus on the scenario where there are linearly growing delays in the system with a centralized communication protocol and propose two distributed asynchronous algorithms. For the performative stable solution, we provide a distributed asynchronous algorithm, DASGD-GD, which integrates the distributed asynchronous stochastic gradient descent method with the greedy deployment. We show that the iterates generated by DASGD-GD converge to the performative stable solution with rate

O (k^{- α})

, where

α \in (0, 1)

and depends on the setting of the stochastic optimization problem under large delays. For the stationary point, we provide a distributed asynchronous algorithm, DASGD-AG, which combines the distributed asynchronous stochastic gradient descent method with the adaptive gradient scheme. We show that the iterates generated by DASGD-AG converge to a stationary point with rate

O (\frac{1}{ln k})

. The effectiveness of DASGD-GD and DASGD-AG is further demonstrated numerically with synthetic and real-world data.

本文的目的是寻求具有决策依赖分布的随机优化问题在集中通信环境下的性能稳定解和平稳点。针对集中式通信协议下系统延迟线性增长的情况，提出了两种分布式异步算法。对于性能稳定的解决方案，我们提出了一种分布式异步算法DASGD-GD，它将分布式异步随机梯度下降法与贪婪部署相结合。我们证明了DASGD-GD生成的迭代收敛于速率为O（k−α）的性能稳定解，其中α∈(0,1)，并且依赖于大延迟下随机优化问题的设置。对于平稳点，我们提出了一种将分布式异步随机梯度下降法与自适应梯度方案相结合的分布式异步算法DASGD-AG。我们证明了DASGD-AG生成的迭代收敛到一个速率为0 （1link）的驻点。用合成数据和实际数据进一步验证了DASGD-GD和DASGD-AG的有效性。

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引用次数: 0

Stochastic dynamic inventory-routing: A comprehensive review 随机动态库存路径：综述

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

Computers & Operations Research

Pub Date : 2026-01-12 DOI: 10.1016/j.cor.2026.107383

Francisco Maia , Gonçalo Figueira , Fábio Neves-Moreira

The stochastic dynamic inventory-routing problem (SDIRP) is a fundamental problem within supply chain operations that integrates inventory management and vehicle routing while handling the stochastic and dynamic nature of exogenous factors unveiled over time, such as customer demands, inventory supply and travel times. While practical applications require dynamic and stochastic decision-making, research in this field has only recently experienced significant growth, with most inventory-routing literature focusing on static variants. This paper reviews the current state of research on SDIRPs, identifying critical gaps and highlighting emerging trends in problem settings and decision policies. We extend the existing inventory-routing taxonomies by incorporating additional problem characteristics to better align models with real-world contexts. As a result, we highlight the need to account for further sources of uncertainty, multiple-supplier networks, perishability, multiple objectives, and pickup and delivery operations. We further categorize each study based on its policy design, investigating how different problem aspects shape decision policies. To conclude, we emphasize that large-scale and real-time problems require more attention and can benefit from decomposition approaches and learning-based methods.

随机动态库存路径问题（SDIRP）是供应链运营中的一个基本问题，它集成了库存管理和车辆路径，同时处理随时间变化的随机和动态的外部因素，如客户需求、库存供应和旅行时间。虽然实际应用需要动态和随机决策，但该领域的研究直到最近才经历了显著的增长，大多数库存路由文献都集中在静态变量上。本文回顾了sdirp的研究现状，确定了关键差距，并强调了问题设置和决策政策方面的新趋势。我们通过合并其他问题特征来扩展现有的库存路由分类法，以便更好地将模型与现实环境结合起来。因此，我们强调需要考虑不确定性的进一步来源、多供应商网络、易腐性、多目标以及取货和交付操作。我们进一步根据其政策设计对每个研究进行分类，调查不同的问题方面如何影响决策政策。总之，我们强调大规模和实时问题需要更多的关注，并且可以从分解方法和基于学习的方法中受益。

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引用次数: 0

Hybrid action space approach to traffic signal optimization using deep reinforcement learning 基于深度强化学习的混合行动空间交通信号优化方法

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

Computers & Operations Research

Pub Date : 2026-01-12 DOI: 10.1016/j.cor.2026.107391

Jihong Jin , Shangming Wu , Pengwei Zhang , Xiaorui Zhang , Chaoen Yin , Changyin Dong

Traffic intersections with time-varying demand encounter persistent challenges in achieving adaptive signal timing optimization and dynamic traffic equilibrium. Existing deep reinforcement learning methodologies predominantly adopt discrete action spaces, which constrain the capacity of such approaches to address complex spatiotemporal traffic dynamics. This research proposes a hybrid action space-based Deep Q-Network (H-DQN) framework for traffic signal control, evaluating its optimization effects through multi-dimensional performance metrics under dynamic traffic conditions. Firstly, this study treats phase policy selection and duration setting as two-level synergistic optimization, thereby proposing a refined hybrid action decision-making mechanism that integrates a dual-layer architecture for joint decision-making on signal phases and green durations. Secondly, the state space is defined by integrating lane saturation levels, queuing lengths, and current green phases across all intersection lanes. At the same time, the reward function is constructed based on the temporal variation in vehicle counts between consecutive sampling intervals, enabling dynamic adaptation to real-time traffic changes while ensuring computational efficiency through optimized design. Finally, this study validates the model in the Simulation of Urban MObility (SUMO) simulation environment across three traffic scenarios, which are uniform traffic with stable speed, non-uniform traffic with stable speed, and complex traffic with varying arrival rates. The results show that the proposed H-DQN model significantly improved intersection throughput efficiency across all three traffic scenarios compared to the DQN method, reducing average queue lengths by 21.58%, 49.43%, and 44.92%, respectively. Compared to Q-learning, the reductions in average queue lengths improved by 86.32%, 87.61%, and 84.51%. Meanwhile, the H-DQN model strengthens average vehicle speeds while minimizing delays, fuel consumption, and lane occupancy, thereby achieving substantial improvements in intersection operational efficiency and traffic throughput.

具有时变需求的交通交叉口在实现自适应信号配时优化和动态交通平衡方面面临着长期的挑战。现有的深度强化学习方法主要采用离散动作空间，这限制了此类方法处理复杂时空交通动态的能力。本研究提出了一种基于混合动作空间的交通信号控制Deep Q-Network （H-DQN）框架，通过动态交通条件下的多维性能指标评估其优化效果。首先，本文将相位策略选择和绿灯持续时间设置视为两级协同优化，提出了一种融合信号相位和绿灯持续时间联合决策双层架构的精细化混合行动决策机制。其次，通过整合车道饱和水平、排队长度和所有交叉口车道的当前绿色相位来定义状态空间。同时，基于连续采样间隔间车辆数量的时间变化构造奖励函数，在优化设计保证计算效率的同时，动态适应实时交通变化。最后，在城市交通仿真（SUMO）仿真环境中，对模型进行了三种交通场景的验证，分别是匀速交通、匀速非匀速交通和不同到达率的复杂交通。结果表明，与DQN方法相比，提出的H-DQN模型显著提高了三种交通场景下的交叉口吞吐效率，平均排队长度分别减少21.58%、49.43%和44.92%。与Q-learning相比，平均队列长度的减少分别提高了86.32%、87.61%和84.51%。同时，H-DQN模型在提高平均车速的同时，最大限度地减少延误、燃油消耗和车道占用，从而大幅提高交叉口运营效率和交通吞吐量。

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引用次数: 0

Optimizing order bundling and dispatching in online food delivery for enhanced delivery efficiency 优化网上外卖的订单捆绑和配送，提高配送效率

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

Computers & Operations Research

Pub Date : 2026-01-09 DOI: 10.1016/j.cor.2026.107387

Shan Zhu , Xiangpei Hu , Yanling Zhuang , Yufei Yuan , Wenjie Wang , Zheng Wang

The online food delivery industry is undergoing a rapid global expansion, making it an easily accessible service for a growing number of consumers. With a simple swipe on a smartphone, customers can conveniently order food from a wide range of restaurants through online food delivery platforms such as Uber Eats, Grubhub, Meituan, and Eleme. The core functionality of these platforms is their algorithmic approach to order dispatching, which is the focus of our study. The objective is to optimize the courier-order matching process, thereby minimizing delivery time and distance, enhancing the efficiency and effectiveness of the service. In contrast to the conventional approach of matching a single order to each courier, our study explores a one-to-many courier-order matching process, which we term a concurrent order dispatching process optimizing order bundling, courier matching and route planning jointly. Our study proposes a comprehensive framework that intricately models the concurrent order dispatching process in great detail. Specifically, we construct a mixed-integer programming model and develop a hybrid heuristic algorithm to address the issue in an efficient manner. We introduce a novel order-bundling closeness measurement value to strategically dispatch multiple orders concurrently to each single courier during a designated decision time window. To assess the model’s and algorithm’s efficacy, we conducted experiments on both small-scale synthetic instances and large-scale real cases, utilizing data from a prominent online food delivery platform in China. The computational results demonstrate that our proposed approach yields solutions that are very close to the optimum in small-scale cases, and achieves significant improvements in terms of average delay time reduction and average distance savings in large-scale cases. In particular, our approach can save the average distance per order by 1.8 km and reduce the average delay time per order from 35 min to 10 min, in comparison to existing policies. We seek to ensure that a significant portion of orders are delivered on time, even with a limited number of couriers.

在线送餐行业正在全球迅速扩张，为越来越多的消费者提供了一项便捷的服务。顾客只需在智能手机上轻轻一刷，就可以通过Uber Eats、Grubhub、美团和饿了么等在线送餐平台，方便地从各种餐厅点餐。这些平台的核心功能是它们的订单调度算法，这是我们研究的重点。目标是优化快递订单匹配过程，从而最大限度地缩短交货时间和距离，提高服务的效率和效果。与传统的单个订单与每个快递员匹配的方法不同，我们探索了一对多快递员-订单匹配过程，我们称之为并行订单调度过程，该过程共同优化了订单捆绑、快递员匹配和路线规划。我们的研究提出了一个全面的框架，对并发订单调度过程进行了复杂的详细建模。具体而言，我们构建了一个混合整数规划模型，并开发了一种混合启发式算法来有效地解决这一问题。我们引入了一种新的订单捆绑紧密度测量值，以便在指定的决策时间窗口内战略性地将多个订单并发地分配给每个快递员。为了评估模型和算法的有效性，我们利用中国一家著名的在线外卖平台的数据，对小规模的合成实例和大规模的真实案例进行了实验。计算结果表明，我们提出的方法在小规模情况下产生的解非常接近最优，并且在大规模情况下在平均延迟时间减少和平均距离节省方面取得了显着改进。特别是，与现有政策相比，我们的方法可以将每笔订单的平均距离节省1.8公里，将每笔订单的平均延迟时间从35分钟减少到10分钟。即使快递员数量有限，我们也力求确保大部分订单准时送达。

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引用次数: 0

Enhancing matheuristics for a thermal unit commitment problem through kernel search and local branching 利用核搜索和局部分支增强热单元承诺问题的数学性质

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

Computers & Operations Research

Pub Date : 2026-01-09 DOI: 10.1016/j.cor.2026.107385

Uriel I. Lezama-Lope , Roger Z. Ríos-Mercado , Diana L. Huerta-Muñoz

The unit commitment problem is an important problem arising in the planning and optimization of power system operations. The problem is characterized by the need to determine the optimal scheduling of electrical generators to meet fluctuating demand while minimizing production costs. In this study, we address a thermal unit commitment problem under a staircase cost structure. Despite the encouraging outcomes from the reformulation strategies to the mathematical model, this problem still presents significant challenges. Despite the encouraging outcomes from the reformulation strategies to the mathematical model, the unit commitment problem still presents significant challenges. We propose a novel two-phase matheuristic framework that first employs a constructive heuristic to generate high-quality initial solutions, followed by an enhancement phase that leverages mechanisms such as local branching and kernel search. The proposed methods form a hybrid approach, working alongside off-the-shelf solvers on the same mathematical formulation to accelerate the search and obtain solutions near optimality. Experimental results on well-known, highly challenging instances demonstrate the effectiveness and value of each matheuristic component and show that the proposed hybrid approach consistently outperforms solvers working alone as well as existing heuristics, particularly for large-scale instances.

机组承诺问题是电力系统运行规划与优化中的一个重要问题。该问题的特点是需要确定发电机的最佳调度，以满足波动的需求，同时最大限度地降低生产成本。在本研究中，我们讨论了阶梯成本结构下的热单位承诺问题。尽管对数学模型的重新制定策略取得了令人鼓舞的成果，但这一问题仍然提出了重大挑战。尽管对数学模型的重新制定策略取得了令人鼓舞的成果，但机组承诺问题仍然提出了重大挑战。我们提出了一个新的两阶段数学框架，首先采用建设性启发式来生成高质量的初始解，然后是利用局部分支和内核搜索等机制的增强阶段。所提出的方法形成了一种混合方法，与现成的求解器一起使用相同的数学公式来加速搜索并获得接近最优解。在众所周知的、极具挑战性的实例上的实验结果证明了每个数学组件的有效性和价值，并表明所提出的混合方法始终优于单独工作的求解器以及现有的启发式方法，特别是对于大规模实例。

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引用次数: 0

Spatial decomposition-based variable neighborhood search algorithm for the integrated semiconductor backend production and distribution scheduling problem 基于空间分解的半导体后端生产配送调度问题的变邻域搜索算法

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

Computers & Operations Research

Pub Date : 2026-01-08 DOI: 10.1016/j.cor.2026.107388

Feng-Shun Zhou , Rong Hu , Wen-Bing Zhang , Bin Qian , Zi-Qi Zhang , Ling Wang

To enhance the supply chain responsiveness of semiconductor enterprises, this study addresses the integrated semiconductor back-end production and distribution scheduling problem (ISBPDSP). To this end, a mixed-integer programming (MIP) model is formulated for the first time to minimize the total cost. Based on the ISBPDSP’s characteristics, four differentiated encoding–decoding schemes are designed to try to reduce both machine idle times and distribution distances, thereby decreasing each solution’s objective value as much as possible. To efficiently solve the considered problem, a novel space decomposition-based variable neighborhood search (SDVNS) algorithm is proposed to perform parallel search in the entire solution space. The SDVNS is a general variable neighborhood search (VNS) framework applicable to any of the above encoding–decoding schemes. In this framework, the space decomposition (SD) method is utilized to reasonably decompose the solution space into multiple subspaces, and an iterative search consisting of small-neighborhood exploration and four-stage large-neighborhood exploitation is developed to execute broad and in-depth search in each subspace. Experimental results demonstrate that the proposed SDVNS outperforms state-of-the-art algorithms in terms of both solution quality and computational efficiency.

为了提高半导体企业的供应链响应能力，本研究探讨了集成半导体后端生产与配送调度问题（ISBPDSP）。为此，首次建立了以总成本最小为目标的混合整数规划模型。根据ISBPDSP的特点，设计了四种不同的编解码方案，尽量减少机器空闲时间和分配距离，从而尽可能降低每种方案的目标值。为了有效地解决所考虑的问题，提出了一种基于空间分解的变量邻域搜索（SDVNS）算法，在整个解空间内进行并行搜索。SDVNS是一种通用的可变邻域搜索（VNS）框架，适用于上述任何一种编解码方案。在该框架中，利用空间分解（SD）方法将解空间合理分解为多个子空间，并提出了由小邻域探索和四阶段大邻域开发组成的迭代搜索，在每个子空间中进行广泛而深入的搜索。实验结果表明，所提出的SDVNS在解质量和计算效率方面都优于当前的算法。

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引用次数: 0

A new job insertion hybrid algorithm for distributed flexible job shop scheduling problems 求解分布式柔性作业车间调度问题的一种新的作业插入混合算法

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

Computers & Operations Research

Pub Date : 2026-01-08 DOI: 10.1016/j.cor.2026.107386

Lin Huang , Changchun Liu , Dunbing Tang , Zequn Zhang , Haihua Zhu , Shikui Zhao

This study focuses on the distributed flexible job shop scheduling problem (DFJSP), which integrates factory assignment, machine selection, and operation sequencing, making it more complex than conventional scheduling. To minimize makespan, we propose a job insertion algorithm based on minimum delay (JIMD) that evaluates insertion positions using delay distance and insertion range for remaining. In the JIMD process, each operation of a job adaptively selects machines and insertion positions to minimize the increase in makespan, ensuring scheduling stability and flexibility. Building on JIMD, three job-level neighborhood structures are developed to optimize both inter- and intra-factory scheduling. For the local search phase, a factory tabu list is designed, and two neighborhood structures are used to achieve scientific search of critical factories. These components are integrated into a job insertion hybrid algorithm (JIHA), which unifies job allocation and operation sequencing to balance global exploration with local exploitation. Extensive experiments on 69 small-scale and 60 large-scale benchmark instances demonstrate that JIHA not only attains all known best solutions but also discovers new ones, confirming its effectiveness and robustness.

本文研究了分布式柔性作业车间调度问题（DFJSP），该问题集成了工厂分配、机器选择和作业排序，使其比传统调度更复杂。为了最小化makespan，我们提出了一种基于最小延迟（JIMD）的作业插入算法，该算法使用延迟距离和剩余插入范围来评估插入位置。在JIMD过程中，作业的每次操作都自适应地选择机器和插入位置，以最大限度地减少完工时间的增加，确保调度的稳定性和灵活性。在JIMD的基础上，开发了三个工作级邻域结构来优化工厂间和工厂内的调度。在局部搜索阶段，设计了工厂禁忌表，采用两个邻域结构实现关键工厂的科学搜索。这些组件集成到作业插入混合算法（JIHA）中，该算法将作业分配和操作排序统一起来，以平衡全局勘探与局部开发。在69个小型和60个大型基准实例上的大量实验表明，JIHA不仅获得了所有已知的最佳解，而且还发现了新的最佳解，证实了它的有效性和鲁棒性。

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引用次数: 0