Swarm and Evolutionary Computation最新文献

A comprehensive review on deep learning for multi-objective optimization 面向多目标优化的深度学习研究综述

IF 8.5 1区计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Swarm and Evolutionary Computation

Pub Date : 2026-02-01 DOI: 10.1016/j.swevo.2026.102304

Haiping Ma, Jin Liu, Jiajun Li, Junhan Jia

Over the past decades, multi-objective optimization has established itself as a fundamental and continuously evolving research area within computational intelligence. While traditional methods remain relevant, the integration of deep learning techniques has recently opened up new possibilities for solving complex optimization problems with multiple competing objectives. This trend has led to the development of numerous innovative approaches that leverage the powerful pattern recognition and representation learning capabilities of deep neural networks. This review systematically examines the current landscape of deep learning applications in multi-objective optimization, beginning with essential foundational concepts before progressing to a detailed analysis of how various deep learning architectures have been adapted for optimization tasks. Then the review categorizes these applications across different engineering domains and discusses their practical implementations. Finally, the paper outlines several promising research directions for advancing this rapidly evolving field, including the development of novel network architectures, deeper integration of deep learning with established multi-objective optimization frameworks, the creation of user-oriented interactive systems, the establishment of explainable theoretical foundations, and the reduction of computational costs.

在过去的几十年里，多目标优化已经成为计算智能的一个基础和不断发展的研究领域。虽然传统方法仍然适用，但深度学习技术的集成最近为解决具有多个竞争目标的复杂优化问题开辟了新的可能性。这一趋势导致了许多创新方法的发展，这些方法利用了深度神经网络强大的模式识别和表示学习能力。本综述系统地考察了深度学习在多目标优化中的应用现状，从基本的基础概念开始，然后详细分析了各种深度学习架构是如何适应优化任务的。然后对这些应用程序在不同的工程领域进行分类，并讨论它们的实际实现。最后，本文概述了推进这一快速发展领域的几个有前途的研究方向，包括开发新的网络架构，将深度学习与已建立的多目标优化框架进行更深层次的整合，创建面向用户的交互系统，建立可解释的理论基础，以及降低计算成本。

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引用次数: 0

Experimental survey of L-SHADE and SHADE-based adaptive differential evolution algorithms L-SHADE和基于shade的自适应差分进化算法实验综述

IF 8.5 1区计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Swarm and Evolutionary Computation

Pub Date : 2026-02-01 DOI: 10.1016/j.swevo.2026.102286

Adam P. Piotrowski , Agnieszka E. Piotrowska , Jaroslaw J. Napiorkowski

Adaptive Differential Evolution (DE) methods are currently among the most efficient Evolutionary Algorithms. In the recent years different Success-History-Based Adaptive Differential Evolution algorithms (SHADE), often with linear population size reduction (commonly known as L-SHADE), have won numerous Competitions in Evolutionary Computation. Since 2014, the number and the variety of SHADE or L-SHADE-based algorithms flourished, encompassing novel operators and procedures. However, it is unclear which new SHADE/L-SHADE operators and procedures are the most successful, or efficient, for specific kinds of problems. After more than a decade of rapid development, some large-scale empirical tests are needed to select the best SHADE/L-SHADE-based algorithms for different purposes. This paper aims at a wide-scale inter-comparison between 32 SHADE/L-SHADE-based variants on large sets of various-dimensional benchmarks and on numerous real-world problems. We point at SHADE/L-SHADE-based algorithms that perform best for low-, or for high-dimensional problems. We determine variants that outperform others on simple problems, and those that perform best for more difficult tasks. Finally, we analyze which variants are best-suited for real-world applications, considering different computational budgets. Results indicate that much different SHADE/L-SHADE-based algorithms perform best for real-world problems than for numerical benchmark functions. Also, different algorithms may be recommended for higher, than for lower-dimensional problems, and other methods perform better for difficult problems than for unimodal ones. This discrepancy poses a challenge for choosing the appropriate algorithm for the specific application, and casts doubts on the classical way of justifying the introduction of novel variants.

自适应差分进化（DE）方法是目前最有效的进化算法之一。近年来，不同的基于成功历史的自适应差分进化算法（SHADE）在进化计算中赢得了许多竞争，这些算法通常采用线性种群大小缩减（通常称为L-SHADE）。自2014年以来，基于SHADE或l -SHADE的算法的数量和种类蓬勃发展，包括新的运算符和程序。然而，对于特定类型的问题，目前尚不清楚哪种新的SHADE/L-SHADE操作器和程序是最成功或最有效的。经过十多年的快速发展，需要进行一些大规模的实证测试，以选择最适合不同用途的基于SHADE/ l -SHADE的算法。本文旨在对32种基于SHADE/ l- SHADE的变体在各种维度的大型基准测试集和许多现实世界问题上进行大规模的相互比较。我们指出基于SHADE/ l -SHADE的算法在低维或高维问题上表现最好。我们确定哪些变体在简单问题上比其他变体表现更好，哪些变体在更困难的任务上表现最好。最后，考虑到不同的计算预算，我们分析哪些变体最适合实际应用。结果表明，与数值基准函数相比，基于SHADE/ l- SHADE的算法在实际问题中表现得更好。此外，对于高维问题，可能会推荐不同的算法，而不是低维问题，并且其他方法在困难问题上比单峰问题表现得更好。这种差异对选择适合特定应用的算法提出了挑战，并对证明引入新变体的经典方法提出了质疑。

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引用次数: 0

An efficient new method for traveling salesman problem using discrete evolutionary algorithm with special encoding and novel optimization strategy 采用特殊编码和新颖优化策略的离散进化算法，提出了求解旅行商问题的有效新方法

IF 8.5 1区计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Swarm and Evolutionary Computation

Pub Date : 2026-02-01 DOI: 10.1016/j.swevo.2026.102306

Yichao He , Guoxin Chen , Xizhao Wang , Haibin Ouyang , Manman Meng , Ju Chen

In order to overcome the limitations of existing methods for solving traveling salesman problem (TSP) using evolutionary algorithms, this paper proposes a novel method for solving TSP based on group theory-based optimization algorithm (GTOA) and special encoding. Firstly, a new encoding method using special integer vector as individual encoding to represent TSP solution is proposed, which is proven to be completely equivalent to using permutation as TSP solution. It solves the bottleneck problem in which basic mathematical operations cannot be used to build evolution equations when using evolutionary algorithms to solve TSP. Secondly, by limiting the range of each component, an improved random mutation operator is proposed, which makes GTOA very suitable for solving TSP by using the new encoding method. Thirdly, a novel optimization method, fixed fragment exchange method (FFEM), is proposed to improve the structure of TSP solution. The combination of FFEM and 3-Opt can greatly improve the performance of the algorithm by simply optimizing the current best solution. Finally, a discrete evolutionary algorithm IGTOA is proposed based on GTOA to solve TSP. To verify the efficiency of IGTOA, it is used to solve 65 benchmark instances in TSPLIB. Based on the calculation results, the necessity of combining FFEM with 3-Opt is first analyzed. Then, by comparing IGTOA with 7 state-of-the-art evolutionary algorithms for solving TSP, it is shown that IGTOA has excellent ability to obtain the optimal solution, higher stability, and faster solving speed, and it is more competitive in solving TSP.

为了克服现有进化算法求解旅行商问题（TSP）方法的局限性，提出了一种基于群理论优化算法（GTOA）和特殊编码的旅行商问题求解方法。首先，提出了一种用特殊整数向量作为个体编码来表示TSP解的新编码方法，并证明了这种编码方法完全等价于用置换来表示TSP解。它解决了用进化算法求解TSP时不能用基本数学运算建立进化方程的瓶颈问题。其次，通过限制各分量的取值范围，提出了一种改进的随机变异算子，使得GTOA非常适合用新的编码方法求解TSP。再次，提出了一种新的优化方法——固定片段交换法（FFEM）来改进TSP解的结构。FFEM和3-Opt的结合可以通过简单地优化当前最优解来大大提高算法的性能。最后，提出了基于GTOA的离散进化算法IGTOA来求解TSP问题。为了验证IGTOA算法的有效性，在TSPLIB中对65个基准实例进行了求解。根据计算结果，首先分析了FFEM与3-Opt相结合的必要性。然后，将IGTOA算法与7种最先进的求解TSP的进化算法进行比较，结果表明，IGTOA算法获得最优解的能力优异，稳定性高，求解速度快，在求解TSP时更具竞争力。

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引用次数: 0

A large-scale multi-objective evolutionary neural network model considering robustness for short-term wind power prediction 一种考虑鲁棒性的大规模多目标进化神经网络模型用于风电短期预测

IF 8.5 1区计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Swarm and Evolutionary Computation

Pub Date : 2026-02-01 DOI: 10.1016/j.swevo.2026.102308

Jianhua Zhu , Yaoyao He

Accurate prediction of wind power generation plays an essential role in the efficient operation of wind farms and power system. However, traditional deep learning-based models fail to fully utilize the temporal information and lack consideration of prediction robustness. This paper proposes a novel multi-objective evolutionary neural network model considering robustness to obtain high-quality wind power prediction results. In this approach, a dynamic temporal neural network (DTNN) that divides multiple time steps is proposed to extract critical temporal information of wind power while avoiding redundant information. Then, a multi-objective optimization (MOO) framework considering both accuracy and robustness is designed to drive the training of DTNN, which directly improves the ability of model to face highly volatile scenarios in an internally updated way. Finally, given the excessive dimensionality of the decision variables, we propose a novel large-scale multi-objective evolutionary algorithm to solve this MOO. Large-scale multi-objective multi-evolutionary state competitive swarm optimizer (LMMSCSO) adaptively implements convergence and diversity-based competitive learning strategies to improve global search and escape local optimality by quantifying evolutionary states. Experiments on real world datasets demonstrate that the proposed method effectively reduces the average forecasting error by 12.5% compared to existing benchmarks.

准确的风力发电预测对风电场和电力系统的高效运行起着至关重要的作用。然而，传统的基于深度学习的模型未能充分利用时间信息，且缺乏对预测鲁棒性的考虑。为了获得高质量的风电预测结果，提出了一种考虑鲁棒性的多目标进化神经网络模型。该方法提出了一种多时间步长的动态时间神经网络（DTNN）来提取风电的关键时间信息，同时避免冗余信息。然后，设计了兼顾准确性和鲁棒性的多目标优化（MOO）框架来驱动DTNN的训练，以内部更新的方式直接提高了模型面对高度多变场景的能力。最后，针对决策变量维数过高的问题，提出了一种新的大规模多目标进化算法。大规模多目标多进化状态竞争群优化器（LMMSCSO）通过对进化状态进行量化，实现基于收敛性和多样性的竞争学习策略，提高全局搜索能力，避免局部最优。在实际数据集上的实验表明，与现有基准相比，该方法有效地将平均预测误差降低了12.5%。

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引用次数: 0

An adaptive VNS-based evolutionary optimization for hybrid flowshop scheduling with consistent sublots 具有一致子批的混合流水车间调度的自适应vns进化优化

IF 8.5 1区计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Swarm and Evolutionary Computation

Pub Date : 2026-02-01 DOI: 10.1016/j.swevo.2026.102299

Li Yuan , Hong-Yan Sang , Lei-Lei Meng , Biao Zhang

Lot streaming technology plays a critical role in shortening production cycles, reducing waiting times, and enhancing production capacity. This paper addresses the hybrid flowshop scheduling problem with consistent sublots (HFSP_CS) and proposes an adaptive VNS-based evolutionary algorithm (AVNSEA) to minimize the total flow time. HFSP_CS involves multiple interdependent subproblems that need to be solved simultaneously, including lot splitting, lot sequencing, and machine allocation. To address this, a mixed integer linear programming (MILP) model is formulated. The proposed AVNSEA algorithm employs an adaptive perturbation strategy to diversify the search and explore potentially promising regions in the solution space, while embedding a variable neighborhood search (VNS)-based local search to intensify the refinement of high-quality solutions. Furthermore, a dynamic acceptance criterion is introduced to balance exploration and exploitation during the evolutionary process. Extensive tests confirm that the proposed AVNSEA algorithm offers significant advantages in solving the HFSP_CS.

批量流技术在缩短生产周期、减少等待时间、提高生产能力等方面发挥着至关重要的作用。研究了具有一致子批的混合流水车间调度问题，提出了一种基于vns的自适应进化算法（AVNSEA），使总流时间最小化。HFSP_CS涉及多个相互依赖的子问题，这些子问题需要同时解决，包括批次拆分、批次排序和机器分配。为了解决这个问题，我们建立了一个混合整数线性规划（MILP）模型。提出的AVNSEA算法采用自适应摄动策略使搜索多样化，并在解空间中探索有潜力的区域，同时嵌入基于可变邻域搜索（VNS）的局部搜索，以加强对高质量解的细化。在演化过程中引入动态接受准则来平衡勘探和开发。大量的测试证实了AVNSEA算法在求解HFSP_CS方面具有显著的优势。

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引用次数: 0

Deep reinforcement learning and heuristic-based dynamic switch migration for Low Earth Orbit satellite networks 基于深度强化学习和启发式的近地轨道卫星网络动态切换迁移

IF 8.5 1区计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Swarm and Evolutionary Computation

Pub Date : 2026-02-01 DOI: 10.1016/j.swevo.2026.102307

Yong Deng , Feng Yao , Jianghan Zhu

The centralized control architecture and programmable features of Software Defined Networking (SDN) present significant opportunities for optimizing Low Earth Orbit (LEO) satellite network performance. Nevertheless, the time-varying topology and non-uniform user distribution characteristics of LEO satellite networks lead to controller load imbalance, which necessitates adaptive controller-switch mapping mechanisms to maintain optimal load distribution between controllers. Most existing migration strategies overlook the overall network performance, resulting in sub-optimal migration quality. Moreover, they fail to address the issue of isolated nodes during migration, which adversely affects network reliability and security. To address these issues, a mathematical optimization model is formulated with the objectives of minimizing latency and achieving controller load balancing, subject to constraints such as controller capacity and intra-domain switch connectivity. To solve this model, we propose a dynamic switch migration algorithm based on deep reinforcement learning and heuristic method (DSM-DH), which comprises two phases: control relationship optimization and connectivity restoration. In the first stage, the deep reinforcement learning (DRL) framework with a multi-neural network architecture is employed, incorporating a dynamic

ϵ

-greedy strategy and a prioritized experience replay mechanism to comprehensively optimize control relationships while satisfying controller capacity constraints. In the second stage, the heuristic approach is used to address the isolated nodes that arise during the migration process. Without violating the controller capacity constraints, isolated switches are prioritized for migration to the controller with the lowest load, so as to minimize the disturbance to the control relationships optimized in the first stage, thereby achieving full connectivity among switches within each domain. Finally, simulation experiments are conducted to compare the DSM-DH algorithm with existing benchmark algorithms across several key performance metrics, including latency and load balancing. The results demonstrate that the DSM-DH algorithm can effectively improve network performance.

软件定义网络（SDN）的集中控制体系结构和可编程特性为优化低地球轨道（LEO）卫星网络性能提供了重要机会。然而，低轨道卫星网络的时变拓扑和非均匀用户分布特性导致控制器负载不平衡，需要自适应控制器-开关映射机制来保持控制器之间的最优负载分配。大多数现有的迁移策略忽略了整体网络性能，导致迁移质量次优。而且无法解决迁移过程中节点隔离的问题，影响网络的可靠性和安全性。为了解决这些问题，在控制器容量和域内交换机连通性等约束条件下，制定了一个数学优化模型，以最小化延迟和实现控制器负载平衡为目标。为了解决这个模型，我们提出了一种基于深度强化学习和启发式方法的动态开关迁移算法（DSM-DH），该算法包括两个阶段：控制关系优化和连通性恢复。第一阶段，采用多神经网络架构的深度强化学习（DRL）框架，结合动态ϵ-greedy策略和优先体验重放机制，在满足控制器容量约束的前提下，对控制关系进行综合优化。在第二阶段，启发式方法用于处理迁移过程中出现的孤立节点。在不违反控制器容量约束的情况下，将隔离的交换机优先迁移到负载最低的控制器上，使对第一阶段优化的控制关系的干扰最小化，从而实现各域内交换机之间的完全连通性。最后，进行了仿真实验，将DSM-DH算法与现有基准算法在几个关键性能指标（包括延迟和负载平衡）上进行了比较。结果表明，DSM-DH算法可以有效地提高网络性能。

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引用次数: 0

A memetic ant colony optimization algorithm for the large-scale pickup and delivery problem with time windows 带时间窗的大规模取货问题的模因蚁群优化算法

IF 8.5 1区计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Swarm and Evolutionary Computation

Pub Date : 2026-01-23 DOI: 10.1016/j.swevo.2026.102295

Thai Khac Nguyen, Nam Hoai Nguyen, Ngoc Hoang Luong

Hybridizations between metaheuristics and local search methods have gained increasing attention in recent years for solving the Pickup and Delivery Problem with Time Windows (PDPTW), an NP-hard problem with extensive ranges of real-world applications. The primary objective of the PDPTW is to construct scheduling solutions that minimize the number of vehicles used to successfully pick up and deliver all customer requests. When multiple solutions require the same number of vehicles, secondary criteria such as travel cost and service time are used to identify the preferable solution. In this article, we propose a hybrid framework consisting of three key components: 1) the Enhanced Constructive Ant Colony Optimization (EC-ACO) algorithm as a global search method which traverses the schedule search space; 2) the Adaptive Guided Ejection Search (AGES) which focuses on reducing the number of vehicles; and 3) the Large Neighborhood Search (LNS) which aims to optimize the overall solution cost. The experimental results demonstrate the efficacy of this approach on Li and Lim’s benchmarks, showing superior performance over other state-of-the-art methods by achieving better results in 186 out of 354 instances. Notably, the performance gap becomes more significant as the instance size increases. Source code is available at: https://github.com/ELO-Lab/PDPTW-ECACO.

近年来，元启发式算法和局部搜索方法的结合得到了越来越多的关注，用于解决带时间窗的取货问题（PDPTW），这是一个具有广泛实际应用范围的np困难问题。PDPTW的主要目标是构建调度解决方案，以最大限度地减少用于成功拾取和交付所有客户请求的车辆数量。当多个解决方案需要相同数量的车辆时，二级标准（如旅行成本和服务时间）被用来确定优选的解决方案。在本文中，我们提出了一个由三个关键部分组成的混合框架：1)增强建设性蚁群优化（EC-ACO）算法作为一种遍历调度搜索空间的全局搜索方法；2)以减少车辆数量为重点的自适应制导弹射搜索（AGES）；3)旨在优化整体解决方案成本的大邻域搜索（LNS）。实验结果证明了这种方法在Li和Lim的基准上的有效性，在354个实例中的186个实例中取得了更好的结果，显示出优于其他最先进方法的性能。值得注意的是，随着实例大小的增加，性能差距变得更加明显。源代码可从https://github.com/ELO-Lab/PDPTW-ECACO获得。

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引用次数: 0

An ensemble model for high dimensional feature selection based on binary arithmetic optimization algorithm 基于二元算法优化的高维特征选择集成模型

IF 8.5 1区计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Swarm and Evolutionary Computation

Pub Date : 2026-01-22 DOI: 10.1016/j.swevo.2026.102298

Shu-Chuan Chu , Zhongjie Zhuang , Haibin Sun , Jia Zhao , Jeng-Shyang Pan

Traditional feature selection algorithms often face performance degradation or even fail to execute when handling high-dimensional data with over 1000 features. Existing studies predominantly rely on the classical Particle Swarm Optimization (PSO). To investigate the applicability of multigoal strategies to other evolutionary algorithms, this paper extends the binary arithmetic optimization algorithm (BAOA) by incorporating a multigoal framework. The method begins by designing eight distinct yet interrelated goals based on four filter-based algorithms (PCC, CHI2, ReliefF, and NCA) to form goal groups. Furthermore, a sparse initialization method employing a roulette wheel selection strategy is introduced to reduce the number of initially selected features. The proposed Ensemble Binary Arithmetic Optimization Algorithm (EBAOA) integrates a multi-goal optimization mechanism into the original binary arithmetic optimization framework, achieving a significant reduction in error rate. Extensive experiments on 24 high-dimensional datasets demonstrate that EBAOA consistently selects the smallest feature subsets while maintaining the lowest error rates across multiple classifiers, including K-Nearest Neighbors, Support Vector Machine, and Random Forest. The results highlight the effectiveness of the multi-goal strategy, and sparse initialization in enhancing feature selection performance for high-dimensional data. The source code will be released upon acceptance at: https://github.com/zhongjiezhuang/EBAOA.

传统的特征选择算法在处理超过1000个特征的高维数据时，往往面临性能下降甚至无法执行的问题。现有的研究主要依赖于经典的粒子群优化（PSO）。为了研究多目标策略在其他进化算法中的适用性，本文将二元算法优化算法（BAOA）扩展为一个多目标框架。该方法首先基于四种基于滤波器的算法（PCC、CHI2、ReliefF和NCA）设计八个不同但相互关联的目标，形成目标组。此外，引入了一种采用轮盘赌选择策略的稀疏初始化方法来减少初始选择的特征数量。提出的集成二进制算法优化算法（EBAOA）将多目标优化机制集成到原有的二进制算法优化框架中，显著降低了错误率。在24个高维数据集上的大量实验表明，EBAOA在选择最小特征子集的同时，在多个分类器（包括k近邻、支持向量机和随机森林）之间保持最低的错误率。结果表明了多目标策略和稀疏初始化在提高高维数据特征选择性能方面的有效性。源代码将在接受后发布在：https://github.com/zhongjiezhuang/EBAOA。

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引用次数: 0

Cost-optimal analysis of Mn/Mn/1/K retrial queue with N-policy using ABC and QNM 基于ABC和QNM的n策略Mn/Mn/1/K重试队列成本最优分析

IF 8.5 1区计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Swarm and Evolutionary Computation

Pub Date : 2026-01-22 DOI: 10.1016/j.swevo.2026.102296

Vijaykumar Panchal, Sudeep Singh Sanga

This study investigates an

M_{n} / M_{n} / 1 / K

queueing model, incorporating two practical mechanisms: a retrial orbit and a service control N-policy. In this system, customers who find the server busy are directed to a retrial orbit, where they attempt to re-access the server at random intervals. Furthermore, the N-policy regulates the service process by activating it only when the queue size reaches a predetermined threshold N (1

\leq

N

\leq

K). To analyze the model mathematically, Chapman–Kolmogorov (C-K) steady-state equations, based on the birth–death process, are formulated. These equations are subsequently solved using a recursive approach. Further, we derive the time-sharing model (TSM) and the machine repair problem (MRP) as special cases of the proposed model. We develop several key performance measures for the state-dependent model and analyze the impact of various input parameters on these performance measures for both the MRP and TSM. Additionally, a cost function is formulated with decision variables including threshold parameter N and service rate

μ

. For cost optimization, we use the direct search method (DSM), the quasi-Newton method (QNM), and the artificial bee colony (ABC) algorithm. The results are further validated using the Genetic algorithm (GA). Finally, the applicability of the proposed model in the context of TSM and MRP frameworks is demonstrated through real-world examples.

本文研究了一个Mn/Mn/1/K排队模型，该模型结合了两种实际机制：重审轨道和服务控制n -策略。在这个系统中，发现服务器繁忙的客户被引导到重试轨道，在那里他们尝试以随机间隔重新访问服务器。此外，N-policy仅在队列大小达到预定阈值N（1≤N≤K）时才激活业务进程，从而对业务进程进行调节。为了对模型进行数学分析，建立了基于出生-死亡过程的Chapman-Kolmogorov （C-K）稳态方程。这些方程随后用递归方法求解。在此基础上，我们推导出了分时模型（TSM）和机器维修问题（MRP）作为该模型的特例。我们为状态依赖模型开发了几个关键的性能度量，并分析了MRP和TSM的各种输入参数对这些性能度量的影响。此外，还构造了包含阈值参数N和服务率μ等决策变量的代价函数。对于成本优化，我们使用了直接搜索法（DSM）、准牛顿法（QNM）和人工蜂群（ABC）算法。利用遗传算法（GA）进一步验证了结果。最后，通过实际实例证明了该模型在TSM和MRP框架中的适用性。

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引用次数: 0

Adaptive neighborhood reduction-based memetic algorithm for the set-union knapsack problem 集并背包问题的自适应邻域约简模因算法

IF 8.5 1区计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Swarm and Evolutionary Computation

Pub Date : 2026-01-21 DOI: 10.1016/j.swevo.2026.102289

Zequn Wei , Jianing Yu , Jin-Kao Hao , Jintong Ren

The set-union knapsack problem (SUKP) is an important NP-hard variant of the knapsack problem, where each item has a profit and is composed of multiple weighted elements. The SUKP aims to select a subset of items that maximizes the total profit while ensuring the union of their associated elements satisfies the capacity constraint. The SUKP is a challenging combinatorial optimization problem that has been widely studied for its theoretical value and practical relevance. In this work, we present a population-based memetic framework specifically designed for solving the SUKP. The proposed approach integrates an adaptive neighborhood reduction based memetic search, which strengthens intensification by embedding a dynamic profit-to-weight ratio scoring method into a solution-based tabu search. To ensure diversification, a diversity-driven greedy crossover operator and an adaptive population updating rule are developed. The algorithm requires no manual parameter tuning and remains effective across instances of widely varying sizes. Computational results on 132 commonly used benchmark instances demonstrate that our method is both competitive and robust compared with state-of-the-art algorithms. The algorithm is further applied to the SUKP-related budgeted maximum coverage problem, confirming its efficiency and generality. We also provide additional analysis on the influences of several key components of the algorithm.

集并背包问题（SUKP）是背包问题的一个重要的NP-hard变体，其中每个项目都有一个利润，并且由多个加权元素组成。SUKP的目标是选择一个项目的子集，使总利润最大化，同时确保其相关元素的联合满足容量约束。SUKP是一个具有挑战性的组合优化问题，因其理论价值和实际意义而被广泛研究。在这项工作中，我们提出了一个基于群体的模因框架，专门设计用于解决SUKP。该方法集成了一种基于自适应邻域约简的模因搜索，通过在基于解的禁忌搜索中嵌入动态利润权重比评分方法来增强搜索强度。为了保证种群的多样化，提出了一种多样性驱动的贪婪交叉算子和自适应种群更新规则。该算法不需要手动调整参数，并且在大小变化很大的实例中仍然有效。在132个常用的基准实例上的计算结果表明，与现有算法相比，我们的方法具有竞争力和鲁棒性。将该算法进一步应用于sukp相关的预算最大覆盖问题，验证了算法的有效性和通用性。我们还对算法的几个关键组件的影响进行了额外的分析。

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引用次数: 0