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RBSS: A fast subset selection strategy for multi-objective optimization RBSS:多目标优化的快速子集选择策略
IF 8.2 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2024-07-25 DOI: 10.1016/j.swevo.2024.101659
Hainan Zhang , Jianhou Gan , Juxiang Zhou , Wei Gao

Multi-objective optimization problems (MOPs) aim to obtain a set of Pareto-optimal solutions, and as the number of objectives increases, the quantity of these optimal solutions grows exponentially. However, a plethora of optimal solutions can impose significant decision stress on decision-makers. Subset selection, as the extension of a model, can extract a representative set of solutions, thereby alleviating the decision-makers’ choice pressure. In addition, extending a model undoubtedly incurs additional time costs. To cope with the foregoing issues, a fast subset selection method named ranking-based subset selection (RBSS) is proposed in this paper. It can efficiently select a small number of optimal solutions within an unbounded external archive and can be directly applied to any multi-objective evolutionary algorithm. This allows it to maintain good distribution and diversity with very little time investment. We employed a ranking-based approach to map the objective space to a ranking space (an integer space) defined by us and then selected the corresponding subset in the ranking space. The well-behaved mathematical properties of the ranking space and the advantages of using integer calculations accelerated the subset selection process. Experimental results indicate that compared to several state-of-the-art subset selection methods, RBSS is capable of selecting a set of representative and diverse solutions across different types of MOPs, while consuming significantly less time. Specifically, for problems where the Pareto front is a two-dimensional manifold and a one-dimensional manifold, the time consumption of RBSS is approximately only 0.028% to 27.5% and 4.6e−4% to 0.15% of that required by other algorithms, respectively.

多目标优化问题(MOPs)旨在获得一组帕累托最优解,随着目标数量的增加,这些最优解的数量也会呈指数级增长。然而,过多的最优解会给决策者带来巨大的决策压力。子集选择作为模型的扩展,可以提取具有代表性的解集,从而减轻决策者的选择压力。此外,扩展模型无疑会产生额外的时间成本。针对上述问题,本文提出了一种名为基于排序的子集选择(RBSS)的快速子集选择方法。它能在无限制的外部档案中有效地选择少量最优解,并可直接应用于任何多目标进化算法。这使得它能以极少的时间投入保持良好的分布和多样性。我们采用了基于排序的方法,将目标空间映射到我们定义的排序空间(整数空间),然后在排序空间中选择相应的子集。排序空间良好的数学特性和使用整数计算的优势加速了子集选择过程。实验结果表明,与几种最先进的子集选择方法相比,RBSS 能够在不同类型的澳门威尼斯人官网程中选择出一组具有代表性的多样化解决方案,同时耗时大大减少。具体来说,对于帕累托前沿是二维流形和一维流形的问题,RBSS 的耗时分别仅为其他算法的 0.028% 到 27.5% 和 4.6e-4% 到 0.15%。
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引用次数: 0
A Q-learning-based biology migration algorithm for energy-saving flexible job shop scheduling with speed adjustable machines and transporters 基于 Q 学习的生物迁移算法,适用于具有速度可调机器和运输机的节能型灵活作业车间调度
IF 8.2 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2024-07-25 DOI: 10.1016/j.swevo.2024.101655
Tianhua Jiang, Lu Liu, Huiqi Zhu

Due to the increasing demand for green manufacturing, energy-saving scheduling problems have garnered significant attention. These problems aim to reduce energy consumption at the production system level within workshops. To simulate a realistic production environment, this study addresses an energy-saving flexible job shop scheduling problem that considers two types of speed-adjustable resources, namely machines and transporters. The optimization objective is to minimize the comprehensive energy consumption of the workshop. A novel mathematical model is initially constructed based on the specific characteristics of the problem at hand. Given its NP-hard nature, a new Q-learning-based biology migration algorithm (QBMA) is proposed, which encompasses diverse search strategies and employs a Q-learning algorithm to dynamically select search strategies, thereby preventing blind search during the evolutionary process. The experimental results of our study demonstrate the promising efficacy of QBMA in effectively addressing the aforementioned problem, while also highlighting the positive impact of considering resources with adjustable speed.

由于对绿色制造的需求日益增长,节能调度问题备受关注。这些问题旨在降低车间内生产系统层面的能耗。为了模拟真实的生产环境,本研究探讨了一个节能灵活作业车间调度问题,该问题考虑了两类速度可调的资源,即机器和运输机。优化目标是最大限度地降低车间的综合能耗。根据当前问题的具体特点,我们初步构建了一个新颖的数学模型。该算法包含多种搜索策略,并采用 Q-learning 算法动态选择搜索策略,从而避免了进化过程中的盲目搜索。我们的研究实验结果表明,QBMA 在有效解决上述问题方面具有良好的效果,同时也凸显了考虑可调节速度的资源所带来的积极影响。
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引用次数: 0
Co-evolution genetic programming-based hyper-heuristics for the stochastic project scheduling problem with resource transfer and idle costs 基于协同进化遗传编程的超启发式算法,用于具有资源转移和闲置成本的随机项目调度问题
IF 8.2 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2024-07-24 DOI: 10.1016/j.swevo.2024.101678
Haohua Zhang , Lubo Li , Sijun Bai , Jingwen Zhang

In this paper, we study the stochastic resource-constrained project scheduling problem with transfer and idle costs (SRCPSP-TIC) under uncertain environments, where the resource transfer and idle take time and costs. Priority rule (PR) based heuristics are the most commonly used approaches for project scheduling under uncertain environments due to their simplicity and efficiency. For PR-based heuristics of the SRCPSP-TIC, activity priority rules (APRs) and transfer priority rules (TPRs) are necessary to decide the activity sequence and resource transfer. Traditionally, APRs and TPRs need to be manually designed, which is time-consuming and difficult to adapt to different scheduling scenarios. Therefore, based on two individual representation methods, we propose two co-evolution genetic programming (CGP) based hyper-heuristics to evolve APRs and TPRs automatically. Furthermore, a fitness function surrogate-assisted method and a transfer learning mechanism are designed to improve the efficiency and solution quality of the CGP. Based on the instances with different stochastic activity duration distributions, we test the performance of different CGP-based hyper-heuristics and compare the evolved PRs with the classical PRs to demonstrate the effectiveness of evolved PRs. Experimental results show that the proposed algorithms can automatically evolve efficient PRs for the SRCPSP-TIC.

本文研究了不确定环境下带有转移和闲置成本的随机资源受限项目调度问题(SRCPSP-TIC),其中资源的转移和闲置需要时间和成本。基于优先级规则(PR)的启发式方法因其简单高效而成为不确定环境下最常用的项目调度方法。对于基于 PR 的 SRCPSP-TIC 启发式算法,活动优先规则(APR)和资源转移优先规则(TPR)是决定活动顺序和资源转移的必要条件。传统上,活动优先规则和转移优先规则需要人工设计,既费时又难以适应不同的调度场景。因此,我们在两种单独表示方法的基础上,提出了两种基于共同进化遗传编程(CGP)的超启发式方法,以自动演化 APR 和 TPR。此外,为了提高 CGP 的效率和求解质量,我们还设计了一种适合度函数辅助方法和一种迁移学习机制。基于不同随机活动持续时间分布的实例,我们测试了不同基于 CGP 的超启发式算法的性能,并将进化 PR 与经典 PR 进行了比较,以证明进化 PR 的有效性。实验结果表明,所提出的算法可以自动为 SRCPSP-TIC 演化出高效的 PR。
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引用次数: 0
When large language model meets optimization 当大型语言模型遇到优化
IF 8.2 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2024-07-24 DOI: 10.1016/j.swevo.2024.101663
Sen Huang , Kaixiang Yang , Sheng Qi , Rui Wang

Optimization algorithms and large language models (LLMs) enhance decision-making in dynamic environments by integrating artificial intelligence with traditional techniques. LLMs, with extensive domain knowledge, facilitate intelligent modeling and strategic decision-making in optimization, while optimization algorithms refine LLM architectures and output quality. This synergy offers novel approaches for advancing general AI, addressing both the computational challenges of complex problems and the application of LLMs in practical scenarios. This review outlines the progress and potential of combining LLMs with optimization algorithms, providing insights for future research directions.

优化算法和大型语言模型(LLM)通过将人工智能与传统技术相结合,增强了动态环境中的决策能力。LLM 具有广泛的领域知识,可促进优化过程中的智能建模和战略决策,而优化算法则可完善 LLM 架构和提高输出质量。这种协同作用为推进通用人工智能提供了新方法,既能解决复杂问题的计算挑战,又能将 LLM 应用于实际场景。本综述概述了 LLM 与优化算法相结合的进展和潜力,为未来的研究方向提供了启示。
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引用次数: 0
An Adaptive Multi-Meme Memetic Algorithm for the prize-collecting generalized minimum spanning tree problem 奖品收集广义最小生成树问题的自适应多主题记忆算法
IF 8.2 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2024-07-24 DOI: 10.1016/j.swevo.2024.101664
Chenwei Zhu, Yu Lin, Fuyuan Zheng, Juan Lin, Yiwen Zhong

In this paper, we address the prize-collecting generalized minimum spanning tree problem (PC-GMSTP) which aims to find a minimum spanning tree to connect a network of clusters using exactly one vertex per cluster, minimizing the total cost of connecting the clusters while considering both the costs of edges and the prizes offered by the vertices. An Adaptive Multi-meme Memetic Algorithm (AMMA) is proposed to tackle PC-GMSTP, which combines an adaptive reproduction procedure and a collaborated local search procedure. The adaptive reproduction procedure uses either crossover or mutation to produce offspring to maintain a good balance between exploration and exploitation of the search space, and the probability to use crossover or mutation is adaptively adjusted based on the diversity of population. The collaborated local search procedure, which includes two efficient local search operators, can effectively enhance the intensification ability of AMMA due to their complementary features. Extensive computational experiments on 126 challenging instances demonstrate the superiority of AMMA, outperforming 23 best-known solutions from existing literature while achieving similar solutions for the remaining 103 instances. Wilcoxon’s signed rank test confirms that the performance of AMMA is significantly better than the state-of-the-art algorithms.

本文探讨了奖金收集广义最小生成树问题(PC-GMSTP),该问题旨在找到一棵最小生成树来连接一个簇网络,每个簇使用一个顶点,在考虑边的成本和顶点提供的奖金的同时,使连接簇的总成本最小。为解决 PC-GMSTP 问题,提出了一种自适应多主题记忆算法(AMMA),它结合了自适应复制程序和协作局部搜索程序。自适应繁殖过程使用交叉或突变来产生后代,以保持搜索空间的探索和开发之间的良好平衡,并根据种群的多样性自适应地调整使用交叉或突变的概率。协同局部搜索程序包括两个高效的局部搜索算子,由于它们的互补性,可以有效提高 AMMA 的强化能力。在 126 个具有挑战性的实例上进行的大量计算实验证明了 AMMA 的优越性,其性能优于现有文献中最著名的 23 种解决方案,同时在其余 103 个实例上也取得了类似的解决方案。Wilcoxon 符号秩检验证实,AMMA 的性能明显优于最先进的算法。
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引用次数: 0
Formulating approximation error as noise in surrogate-assisted multi-objective evolutionary algorithm 将近似误差表述为代理辅助多目标进化算法中的噪声
IF 8.2 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2024-07-24 DOI: 10.1016/j.swevo.2024.101666
Nan Zheng , Handing Wang , Jialin Liu

Many real multi-objective optimization problems with 20-50 decision variables often have only a small number of function evaluations available, because of their heavy time/money burden. Therefore, surrogate models are often utilized as alternatives for expensive function evaluations. However, the approximation error of the surrogate model is inevitable compared to the real function evaluation. The approximation error has a similar impact on the algorithm as noise, i.e., different optimization stages suffer from various impacts. Therefore, the current optimization stage can be indirectly detected via measuring the impact of the noise formulated by the approximation error. In addition, the rising dimension of the search space leads to an increase in the approximation errors of the surrogate models, which poses a huge challenge for existing surrogate-assisted multi-objective evolutionary algorithms. In this work, we propose a stage-adaptive surrogate-assisted multi-objective evolutionary algorithm to solve the medium-scale optimization problems. In the proposed algorithm, the ensemble model consisting of the latest and historical models is used as the surrogate model, on the basis of which a set of potential candidates can be discovered. Then, a stage-adaptive infill sampling strategy selects the most suitable sampling strategy by analyzing the demand of the current optimization stage on convergence, diversity, model accuracy to sample from the candidates. As for the current optimization stage, it is detected by a noise impact indicator, where the approximation errors of surrogate models are formulated as noise. The experimental results on a series of medium-scale expensive test problems demonstrate the superiority of the proposed algorithm over six state-of-the-art compared algorithms.

许多包含 20-50 个决策变量的实际多目标优化问题,由于时间/金钱负担沉重,往往只有少量的函数评估可用。因此,代用模型常常被用来替代昂贵的函数评估。然而,与实际函数评估相比,代用模型的近似误差是不可避免的。近似误差对算法的影响类似于噪声,即不同的优化阶段会受到不同的影响。因此,可以通过测量由近似误差形成的噪声的影响来间接检测当前的优化阶段。此外,搜索空间维度的增加导致代用模型的近似误差增大,这对现有的代用辅助多目标进化算法提出了巨大挑战。在这项工作中,我们提出了一种阶段自适应的代型辅助多目标进化算法来解决中等规模的优化问题。在所提出的算法中,由最新模型和历史模型组成的集合模型被用作代用模型,在此基础上可以发现一组潜在的候选模型。然后,阶段自适应填充采样策略通过分析当前优化阶段对收敛性、多样性、模型精度的需求,选择最合适的采样策略,从候选模型中进行采样。至于当前优化阶段,则通过噪声影响指标来检测,将代用模型的近似误差作为噪声。在一系列中等规模的昂贵测试问题上的实验结果表明,所提出的算法优于六种最先进的比较算法。
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引用次数: 0
Evolutionary computation for feature selection in classification: A comprehensive survey of solutions, applications and challenges 用于分类中特征选择的进化计算:关于解决方案、应用和挑战的全面调查
IF 8.2 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2024-07-22 DOI: 10.1016/j.swevo.2024.101661
Xianfang Song , Yong Zhang , Wanqiu Zhang , Chunlin He , Ying Hu , Jian Wang , Dunwei Gong

Feature selection (FS), as one of the most significant preprocessing techniques in the fields of machine learning and pattern recognition, has received great attention. In recent years, evolutionary computation has become a popular technique for handling FS problems due to its superior global search performance. In this paper, a comprehensive review of evolutionary computation research on the FS problems is presented. Firstly, a new taxonomy for the basic components of evolutionary feature selection algorithms (EFSs) is proposed, including encoding strategy, population initialization, population updating, local search, multi-FS hybrid and ensemble. Secondly, we summarize the latest research progress of EFSs on some new and complex scenarios, including large-scale high-dimensional data, multi-objective/metric scenario, multi-label data, distributed storage data, multi-task scenario, multi-modal scenario, interpretable FS and stable FS, etc. Moreover, this survey provides also an in-depth analysis of real-world applications of EFSs, such as hyperspectral band selection, bioinformatics gene selection, text classification and fault detection, etc. Finally, several opportunities for future work are pointed out.

特征选择(FS)作为机器学习和模式识别领域最重要的预处理技术之一,受到了广泛关注。近年来,进化计算以其优越的全局搜索性能成为处理 FS 问题的热门技术。本文全面回顾了进化计算在金融服务问题上的研究。首先,本文提出了进化特征选择算法(EFS)基本组成部分的新分类法,包括编码策略、种群初始化、种群更新、局部搜索、多 FS 混合和集合。其次,总结了进化特征选择算法在一些新的复杂场景下的最新研究进展,包括大规模高维数据、多目标/度量场景、多标签数据、分布式存储数据、多任务场景、多模态场景、可解释特征选择算法和稳定特征选择算法等。此外,本研究还深入分析了 EFS 在现实世界中的应用,如高光谱波段选择、生物信息学基因选择、文本分类和故障检测等。最后,还指出了未来工作的几个机会。
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引用次数: 0
Dynamic variable analysis guided adaptive evolutionary multi-objective scheduling for large-scale workflows in cloud computing 动态变量分析引导的自适应进化多目标调度,适用于云计算中的大规模工作流
IF 8.2 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2024-07-20 DOI: 10.1016/j.swevo.2024.101654
Yangkun Xia , Xinran Luo , Wei Yang , Ting Jin , Jun Li , Lining Xing , Lijun Pan

Energy consumption and makespan of workflow execution are two core performance indicators in operating cloud platforms. But, simultaneously optimizing these two indicators encounters various challenges, such as elastic resources, large-scale decision variables, and sophisticated workflow structures. To handle these challenges, we design an adaptive evolutionary scheduling algorithm, namely AESA, with three innovative strategies. First, a heuristic population initialization strategy is devised to gather workflow tasks onto limited potential resources, thereby alleviating the negative impact of redundant cloud resources on evolutionary search efficiency. Then, a variable analysis strategy is designed to dynamically measure the contribution of each decision variable in pushing the population towards Pareto-optimal fronts. Moreover, AESA embraces an adaptive strategy to reward more evolutionary opportunities for decision variables with higher contributions to handle large-scale decision variables in a targeted manner, further improving the efficiency of evolutionary search. Finally, extensive experiments are performed based on real-world cloud platforms and workflow traces to verify the effectiveness of the proposed AESA. The comparison results validate its superior performance by significantly outperforming five representative baselines in optimizing makespan and energy consumption. Also, the results of ablation experiments demonstrate that all three components contribute to AESA’s overall performance, with the adaptive reward mechanism being the most significant.

工作流执行的能耗和时间跨度是云平台运行的两个核心性能指标。但是,同时优化这两个指标会遇到各种挑战,如弹性资源、大规模决策变量和复杂的工作流结构。为了应对这些挑战,我们设计了一种自适应进化调度算法,即AESA,其中包含三种创新策略。首先,设计了启发式种群初始化策略,将工作流任务聚集到有限的潜在资源上,从而减轻冗余云资源对进化搜索效率的负面影响。然后,设计了一种变量分析策略,用于动态测量每个决策变量在推动群体实现帕累托最优前沿方面的贡献。此外,AESA 还采用自适应策略,为贡献度较高的决策变量提供更多的进化机会,从而有针对性地处理大规模决策变量,进一步提高进化搜索的效率。最后,我们基于真实的云平台和工作流痕迹进行了大量实验,以验证所提出的 AESA 的有效性。对比结果验证了其优越性能,在优化时间跨度和能源消耗方面明显优于五种代表性基线。此外,消融实验结果表明,所有三个组件都对 AESA 的整体性能做出了贡献,其中自适应奖励机制的作用最大。
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引用次数: 0
A hierarchical reinforcement learning-aware hyper-heuristic algorithm with fitness landscape analysis 分层强化学习感知超启发式算法与适应性景观分析
IF 8.2 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2024-07-20 DOI: 10.1016/j.swevo.2024.101669
Ningning Zhu , Fuqing Zhao , Yang Yu , Ling Wang

The automation of meta-heuristic algorithm configuration holds the utmost significance in evolutionary computation. A hierarchical reinforcement learning-aware hyper-heuristic algorithm with fitness landscape analysis (HRLHH) is proposed to flexibly configure the suitable algorithms under various optimization scenarios. Two kinds of fitness landscape analysis techniques improved based on specific problem characteristics construct the state spaces for hierarchical reinforcement learning. Among them, an adaptive classification based on dynamic ruggedness of information entropy is designed to discern the complexity of problems, which serves as the basis for decision-making actions in upper-layer space. Additionally, an online dispersion metric based on knowledge is further presented to distinguish the precise landscape features in lower-layer space. In light of the characteristics of the state spaces, the hierarchical action spaces composed of meta-heuristics with disparate exploration and exploitation are designed, and various action selection strategies are introduced. Taking into account the real-time environment and algorithm evolution behavior, dynamic reward mechanisms based on evolutionary success rate and population convergence rate are utilized to enhance search efficiency. The experimental results on the IEEE Congress on Evolutionary Computation (CEC) 2017, CEC 2014, and large-scale CEC 2013 test suites demonstrate that the proposed HRLHH exhibits superiority in terms of accuracy, stability, and convergence speed, and possesses strong generalization.

元启发式算法配置的自动化在进化计算中具有极其重要的意义。本文提出了一种分层强化学习感知的超启发式算法(HRLHH),该算法具有适配性景观分析(Fitness landscape analysis)功能,可在各种优化场景下灵活配置合适的算法。根据具体问题特征改进的两种适应度景观分析技术构建了分层强化学习的状态空间。其中,基于信息熵动态崎岖度的自适应分类法可以辨别问题的复杂性,作为上层空间决策行动的依据。此外,还进一步提出了一种基于知识的在线分散度量,以区分下层空间的精确景观特征。根据状态空间的特点,设计了由不同探索和利用的元启发式组成的分层行动空间,并引入了各种行动选择策略。考虑到实时环境和算法进化行为,利用基于进化成功率和种群收敛率的动态奖励机制来提高搜索效率。在 2017 年 IEEE 进化计算大会(CEC)、2014 年 CEC 和 2013 年大规模 CEC 测试套件上的实验结果表明,所提出的 HRLHH 在准确性、稳定性和收敛速度方面都表现出优越性,并且具有很强的泛化能力。
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引用次数: 0
Large-scale power system multi-area economic dispatch considering valve point effects with comprehensive learning differential evolution 利用综合学习差分进化考虑阀点效应的大规模电力系统多区域经济调度
IF 8.2 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2024-07-18 DOI: 10.1016/j.swevo.2024.101620
Yang Wang , Guojiang Xiong , Shengping Xu , Ponnuthurai Nagaratnam Suganthan

The role of multi-area economic dispatch (MAED) in power system operation is increasingly significant. It is a non-linear and multi-constraint problem with many local extremes when considering the valve point effects, posing challenges in obtaining a globally optimal solution, especially for large-scale systems. In this study, an improved variant of differential evolution (DE) called CLDE based on comprehensive learning strategy (CLS) is proposed to solve this problem. Three improved strategies are employed to enhance the performance of CLDE. (1) A CLS-based guided mutation strategy is proposed, in which learning exemplars constructed by competent individuals are used to generate mutant vectors to prevent the searching away from global optimum and speed up convergence. (2) A time-varying increasing crossover rate is devised. It can endow CLDE with a larger probability at the later stage to help individuals escape from local extremes. (3) A CLS-based crossover strategy is presented. Trial vectors directly utilize the information from learning exemplars for evolving, which can ensure the search efficiency and population diversity. CLDE is applied to six MAED cases. Compared with DE, it approximately consumes 32 %, 35 %, 10 %, 22 %, 62 %, and 20 % of evaluations to attain comparable results, saves 126.2544$/h, 81.8173$/h, 152.0660$/h, 360.7907$/h, 65.5757$/h, and 1732.8544$/h in fuel costs on average, and exhibits improvements of 34.77 %, 1.80 %, 0.00 %, 76.09 %, 95.15 %, and 16.76 % in robustness, respectively. Moreover, it also outperforms other state-of-the-art algorithms significantly in statistical analysis. Furthermore, the effects of improved strategies on CLDE are thoroughly investigated.

多地区经济调度(MAED)在电力系统运行中的作用越来越重要。它是一个非线性、多约束的问题,在考虑阀点效应时会出现许多局部极值,这给获得全局最优解带来了挑战,尤其是对于大规模系统而言。本研究提出了一种基于综合学习策略(CLS)的微分进化论(DE)改进变体 CLDE 来解决这一问题。(1) 提出了一种基于 CLS 的引导突变策略,即利用有能力的个体构建的学习范例生成突变向量,以防止搜索偏离全局最优并加速收敛。(2) 设计了一种时变递增交叉率。它可以在后期赋予 CLDE 更大的概率,帮助个体摆脱局部极端。(3) 提出了一种基于 CLS 的交叉策略。试验向量直接利用学习典范的信息进行进化,可以确保搜索效率和种群多样性。CLDE 被应用于六个 MAED 案例。与 DE 相比,CLDE 在获得可比结果时大约消耗 32 %、35 %、10 %、22 %、62 % 和 20 % 的评估,平均节省 126.2544 美元/小时、81.8173 美元/小时、152.0660 美元/小时、360.7907 美元/小时、65.5757 美元/小时和 1732.8544 美元/小时的燃料成本,鲁棒性分别提高 34.77 %、1.80 %、0.00 %、76.09 %、95.15 % 和 16.76 %。此外,在统计分析方面,它也明显优于其他最先进的算法。此外,还深入研究了改进策略对 CLDE 的影响。
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引用次数: 0
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Swarm and Evolutionary Computation
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