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A literature review of reinforcement learning methods applied to job-shop scheduling problems 强化学习方法应用于作业车间调度问题的文献综述
IF 4.1 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-27 DOI: 10.1016/j.cor.2024.106929
Xiehui Zhang, Guang-Yu Zhu
The job-shop scheduling problem (JSP) is one of the most famous production scheduling problems, and it is an NP-hard problem. Reinforcement learning (RL), a machine learning method capable of feedback-based learning, holds great potential for solving shop scheduling problems. In this paper, the literature on applying RL to solve JSPs is taken as the review object and analyzed in terms of RL methods, the number of agents, and the agent upgrade strategy. We discuss three major issues faced by RL methods for solving JSPs: the curse of dimensionality, the generalizability and the training time. The interconnectedness of the three main issues is revealed and the main factors affecting them are identified. By discussing the current solutions to the above issues as well as other challenges that exist, suggestions for solving these problems are given, and future research trends are proposed.
车间作业调度问题(JSP)是最著名的生产调度问题之一,属于np困难问题。强化学习(RL)是一种基于反馈学习的机器学习方法,在解决车间调度问题方面具有很大的潜力。本文以应用强化学习解决jsp的文献为综述对象,从强化学习方法、agent数量、agent升级策略等方面进行分析。我们讨论了RL方法在解决jsp时面临的三个主要问题:维度的诅咒、泛化性和训练时间。揭示了三个主要问题的相互联系,并确定了影响它们的主要因素。通过讨论目前解决上述问题的方法以及存在的其他挑战,提出了解决这些问题的建议,并提出了未来的研究趋势。
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引用次数: 0
An accelerated Benders decomposition method for distributionally robust sustainable medical waste location and transportation problem 分布式稳健可持续医疗废物定位与运输问题的加速Benders分解方法
IF 4.1 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-26 DOI: 10.1016/j.cor.2024.106895
Zihan Quan , Yankui Liu , Aixia Chen
This study addresses the sustainable medical waste location and transportation (SMWLT) problem from the viewpoint of social risk, environmental impact, and economic performance, where model uncertainty includes risk and transportation costs. In practice, it is usually hard to obtain the exact probability distribution of uncertain parameters. To address this challenge, this study first constructs an ambiguity set to model the partial distribution information of uncertain parameters. Based on the constructed ambiguity set, this study develops a new multi-objective distributionally robust chance-constrained (DRCC) model for the SMWLT problem. Subsequently, this study adopts the robust counterpart (RC) approximation method to reformulate the proposed DRCC model as a computationally tractable mixed-integer linear programming (MILP) model. Furthermore, an accelerated Benders decomposition (BD) enhanced by valid inequalities is designed to solve the resulting MILP model, which significantly improves the solution efficiency compared with the classical BD algorithm and CPLEX solver. Finally, a practical case in Chongqing, China, is addressed to illustrate the effectiveness of our DRCC model and the accelerated BD solution method.
本研究从社会风险、环境影响和经济效益的角度探讨医疗废弃物永续安置与运输问题,其中模型不确定性包括风险和运输成本。在实际应用中,通常很难得到不确定参数的精确概率分布。为了解决这一挑战,本研究首先构建了一个模糊集来模拟不确定参数的部分分布信息。基于构建的模糊集,本文提出了一种新的SMWLT问题的多目标分布鲁棒机会约束(DRCC)模型。随后,本文采用鲁棒对应(RC)近似方法将所提出的DRCC模型重新表述为可计算的混合整数线性规划(MILP)模型。在此基础上,设计了一种基于有效不等式的加速Benders分解(Benders decomposition, BD)来求解MILP模型,与传统的Benders分解算法和CPLEX求解器相比,显著提高了求解效率。最后,以中国重庆的一个实际案例为例,说明了我们的DRCC模型和加速BD解决方法的有效性。
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引用次数: 0
A VNS method for the conditional p-next center problem 条件p-下一中心问题的VNS方法
IF 4.1 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-26 DOI: 10.1016/j.cor.2024.106916
Jelena Tasić, Zorica Dražić, Zorica Stanimirović
This paper considers the conditional p-next center problem (CPNCP) and proposes a metaheuristic method as a solution approach. The p-next center problem (PNCP) is an extension of the classical p-center problem that captures real-life situations when centers suddenly fail due to an accident or some other problem. When the center failure happens, the customers allocated to the closed center are redirected to the center closest to the closed one, called the backup center. On the other hand, when a service network expands, some of the existing centers are usually retained and a number of new centers are opened. The conditional p-next center problem involves both of these two aspects that arise in practice and, to the best of our knowledge, has not been considered in the literature so far. Since the CPNCP is NP-hard, a metaheuristic algorithm based on the Variable Neighborhood Search is developed. The proposed VNS includes an efficient implementation of the Fast Interchange heuristic which enables the VNS to tackle with real-life problem dimensions. The exhaustive computational experiments were performed on the modified PNCP test instances from the literature with up to 900 nodes. The obtained results are compared with the results of the exact solver CPLEX. It is shown that the proposed VNS reaches optimal solutions or improves the feasible ones provided by CPLEX in a significantly shorter CPU time. The VNS also quickly returns its best solutions when CPLEX failed to provide a feasible one. In order to investigate the effects of two different approaches in service network planning, the VNS solutions of the CPNCP are compared with the optimal or best-known solutions of the p-next center problem. In addition, the conducted computational study includes direct comparisons of the results obtained when the proposed SVNS is applied to PNCP (by setting the number of existing centers to 0) with the results of recent solution methods proposed for the PNCP.
本文考虑了条件p-下一中心问题(CPNCP),提出了一种元启发式求解方法。下一个p中心问题(PNCP)是经典p中心问题的扩展,它捕获了由于事故或其他问题导致中心突然失效的现实情况。当中心发生故障时,分配到关闭中心的客户被重定向到离关闭中心最近的中心,称为备份中心。另一方面,当一个服务网络扩大时,通常会保留一些现有的中心,并开设一些新的中心。条件p-下一中心问题涉及到实践中出现的这两个方面,据我们所知,迄今为止还没有在文献中得到考虑。针对CPNCP的np困难特性,提出了一种基于变邻域搜索的元启发式算法。提出的VNS包括快速交换启发式的有效实现,使VNS能够处理现实生活中的问题维度。在文献中改进的PNCP测试实例上进行了详尽的计算实验,其节点数高达900个。所得结果与精确求解器CPLEX的结果进行了比较。结果表明,所提出的VNS在较短的CPU时间内达到了最优解或改进了CPLEX提供的可行解。当CPLEX无法提供可行的解决方案时,VNS也会迅速返回最佳解决方案。为了研究两种不同方法在业务网络规划中的效果,将CPNCP的VNS解与p-next中心问题的最优解或最知名解进行了比较。此外,所进行的计算研究包括将所提出的SVNS应用于PNCP(通过将现有中心数量设置为0)时获得的结果与最近提出的PNCP解决方法的结果进行直接比较。
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引用次数: 0
Lexicographic optimization-based approaches to learning a representative model for multi-criteria sorting with non-monotonic criteria 基于词典优化的非单调标准多准则排序代表性模型学习方法
IF 4.1 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-26 DOI: 10.1016/j.cor.2024.106917
Zhen Zhang , Zhuolin Li , Wenyu Yu
Deriving a representative model using value function-based methods from the perspective of preference disaggregation has emerged as a prominent and growing topic in multi-criteria sorting (MCS) problems. A noteworthy observation is that many existing approaches to learning a representative model for MCS problems traditionally assume the monotonicity of criteria, which may not always align with the complexities found in real-world MCS scenarios. Consequently, this paper proposes some approaches to learning a representative model for MCS problems with non-monotonic criteria through the integration of the threshold-based value-driven sorting procedure. To do so, we first define some transformation functions to map the marginal values and category thresholds into a UTA-like functional space. Subsequently, we construct constraint sets to model non-monotonic criteria in MCS problems and develop optimization models to check and rectify the inconsistency of the decision maker’s assignment example preference information. By simultaneously considering the complexity and discriminative power of the models, two distinct lexicographic optimization-based approaches are developed to derive a representative model for MCS problems with non-monotonic criteria. Eventually, we offer an illustrative example and conduct comprehensive simulation experiments to elaborate the feasibility and validity of the proposed approaches.
从偏好分解的角度出发,利用基于价值函数的方法推导具有代表性的模型,已成为多准则排序问题中一个突出而日益增长的课题。一个值得注意的观察是,许多现有的学习MCS问题的代表性模型的方法传统上假设标准的单调性,这可能并不总是与现实世界MCS场景中的复杂性相一致。因此,本文提出了一些通过整合基于阈值的值驱动排序过程来学习具有非单调准则的MCS问题的代表性模型的方法。为此,我们首先定义一些转换函数,将边际值和类别阈值映射到一个类似uta的功能空间。随后,我们构建约束集来模拟MCS问题中的非单调准则,并建立优化模型来检查和纠正决策者分配示例偏好信息的不一致性。通过同时考虑模型的复杂性和判别能力,提出了两种不同的基于词典学的优化方法,推导出具有非单调准则的MCS问题的代表性模型。最后,我们提供了一个说明性的例子,并进行了全面的仿真实验来阐述所提出方法的可行性和有效性。
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引用次数: 0
Portfolio optimisation: Bridging the gap between theory and practice 投资组合优化:弥合理论与实践之间的差距
IF 4.1 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-26 DOI: 10.1016/j.cor.2024.106918
Cristiano Arbex Valle
Portfolio optimisation is essential in quantitative investing, but its implementation faces several practical difficulties. One particular challenge is converting optimal portfolio weights into real-life trades in the presence of realistic features, such as transaction costs and integral lots. This is especially important in automated trading, where the entire process happens without human intervention.
Several works in literature have extended portfolio optimisation models to account for these features. In this paper, we highlight and illustrate difficulties faced when employing the existing literature in a practical setting, such as computational intractability, numerical imprecision and modelling trade-offs. We then propose a two-stage framework as an alternative approach to address this issue. Its goal is to optimise portfolio weights in the first stage and to generate realistic trades in the second. Through extensive computational experiments, we show that our approach not only mitigates the difficulties discussed above but also can be successfully employed in a realistic scenario.
By splitting the problem in two, we are able to incorporate new features without adding too much complexity to any single model. With this in mind we model two novel features that are critical to many investment strategies: first, we integrate two classes of assets, futures contracts and equities, into a single framework, with an example illustrating how this can help portfolio managers in enhancing investment strategies. Second, we account for borrowing costs in short positions, which have so far been neglected in literature but which significantly impact profits in long/short strategies. Even with these new features, our two-stage approach still effectively converts optimal portfolios into actionable trades.
投资组合优化在量化投资中是必不可少的,但其实施面临着一些实际困难。其中一个特别的挑战是,在交易成本和整手等现实特征存在的情况下,将最优投资组合权重转换为现实交易。这在自动交易中尤其重要,因为整个过程都是在没有人为干预的情况下进行的。文献中的一些作品扩展了投资组合优化模型来解释这些特征。在本文中,我们强调并说明了在实际环境中使用现有文献时面临的困难,例如计算难解性、数值不精确和建模权衡。然后,我们提出了一个两阶段框架作为解决这个问题的替代方法。它的目标是在第一阶段优化投资组合权重,在第二阶段产生现实的交易。通过大量的计算实验,我们表明我们的方法不仅减轻了上述困难,而且可以成功地应用于现实场景。通过将问题一分为二,我们能够在不给任何单一模型增加太多复杂性的情况下合并新的特征。考虑到这一点,我们对两个对许多投资策略至关重要的新特征进行了建模:首先,我们将两类资产,期货合约和股票,整合到一个单一的框架中,并举例说明这如何帮助投资组合经理提高投资策略。其次,我们考虑了空头头寸的借贷成本,这一点迄今为止在文献中被忽视,但它对多头/空头策略的利润产生了重大影响。即使有了这些新功能,我们的两阶段方法仍然有效地将最佳投资组合转化为可操作的交易。
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引用次数: 0
A Q-learning driven multi-objective evolutionary algorithm for worker fatigue dual-resource-constrained distributed hybrid flow shop 基于q学习驱动的工人疲劳双资源约束分布式混合流水车间多目标进化算法
IF 4.1 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-26 DOI: 10.1016/j.cor.2024.106919
Haonan Song , Junqing Li , Zhaosheng Du , Xin Yu , Ying Xu , Zhixin Zheng , Jiake Li
In practical industrial production, workers are often critical resources in manufacturing systems. However, few studies have considered the level of worker fatigue when assigning resources and arranging tasks, which has a negative impact on productivity. To fill this gap, the distributed hybrid flow shop scheduling problem with dual-resource constraints considering worker fatigue (DHFSPW) is introduced in this study. Due to the complexity and diversity of distributed manufacturing and multi-objective, a Q-learning driven multi-objective evolutionary algorithm (QMOEA) is proposed to optimize both the makespan and total energy consumption of the DHFSPW at the same time. In QMOEA, solutions are represented by a four-dimensional vector, and a decoding heuristic that accounts for real-time worker productivity is proposed. Additionally, three problem-specific initialization heuristics are developed to enhance convergence and diversity capabilities. Moreover, encoding-based crossover, mirror crossover and balanced mutation methods are presented to improve the algorithm’s exploitation capabilities. Furthermore, a Q-learning based local search is employed to explore promising nondominated solutions across different dimensions. Finally, the QMOEA is assessed using a set of randomly generated instances, and a detailed comparison with state-of-the-art algorithms is performed to demonstrate its efficiency and robustness.
在实际的工业生产中,工人往往是制造系统的关键资源。然而,很少有研究在分配资源和安排任务时考虑到工人的疲劳程度,这对生产力有负面影响。为了填补这一空白,本文引入了考虑工人疲劳的双资源约束的分布式混合流水车间调度问题。针对分布式制造的复杂性、多样性和多目标特性,提出了一种q学习驱动的多目标进化算法(QMOEA)来同时优化DHFSPW的完工时间和总能耗。在QMOEA中,解由一个四维向量表示,并提出了一种考虑实时工人生产率的解码启发式。此外,本文还开发了三种针对特定问题的初始化启发式方法,以增强收敛性和多样性能力。提出了基于编码的交叉、镜像交叉和平衡突变方法,提高了算法的利用能力。此外,采用基于q学习的局部搜索来探索跨不同维度的有前途的非主导解决方案。最后,使用一组随机生成的实例对QMOEA进行了评估,并与最先进的算法进行了详细的比较,以证明其效率和鲁棒性。
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引用次数: 0
Understand your decision rather than your model prescription: Towards explainable deep learning approaches for commodity procurement 了解您的决策,而不是您的模型处方:为商品采购开发可解释的深度学习方法
IF 4.1 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-22 DOI: 10.1016/j.cor.2024.106905
Moritz Rettinger , Stefan Minner , Jenny Birzl
Hedging against price increases is particularly important in times of significant market uncertainty and price volatility. For commodity procuring firms, futures contracts are a widespread means of financially hedging price risks. Recently, digital data-driven decision-support approaches have been developed, with deep learning-based methods achieving outstanding results in capturing non-linear relationships between external features and price trends. Digital procurement systems leverage targeted purchasing decisions of these optimization models, yet the decision-mechanisms are opaque. We employ a prescriptive deep-learning approach modeling hedging decisions as a multi-label time series classification problem. We backtest the performance in two evaluation periods, i. e., 2018–2020 and 2021–2023, for natural gas, crude oil, nickel, and copper. The approach performs well in the first evaluation period of the testing framework yet fails to capture market disruptions (pandemic, geopolitical developments) in the second evaluation period, yielding significant hedging losses or degenerating into a simple hand-to-mouth procurement policy. We employ explainable artificial intelligence to analyze the performance for both periods. The results show that the models cannot handle market regime switches and disruptive events within the considered feature set.
在市场严重不确定和价格波动时,对冲价格上涨的风险尤为重要。对于大宗商品采购公司来说,期货合约是一种广泛的金融对冲价格风险的手段。最近,数字数据驱动的决策支持方法得到了发展,其中基于深度学习的方法在捕捉外部特征与价格趋势之间的非线性关系方面取得了突出成果。数字采购系统利用这些优化模型做出有针对性的采购决策,但决策机制并不透明。我们采用了一种规范性深度学习方法,将对冲决策建模为多标签时间序列分类问题。我们在两个评估期(即 2018-2020 年和 2021-2023 年)对天然气、原油、镍和铜的性能进行了回溯测试。该方法在测试框架的第一个评估期表现良好,但在第二个评估期未能捕捉到市场干扰(大流行病、地缘政治发展),导致重大对冲损失或沦为简单的手到擒来采购政策。我们采用可解释人工智能来分析这两个时期的表现。结果表明,在所考虑的特征集中,模型无法处理市场制度转换和破坏性事件。
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引用次数: 0
Airline recovery problem under disruptions: A review 中断情况下的航空公司恢复问题:综述
IF 4.1 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-21 DOI: 10.1016/j.cor.2024.106915
Shuai Wu , Enze Liu , Rui Cao , Qiang Bai
Flights are vulnerable to unforeseen factors, such as adverse weather, airport flow control, crew absence, unexpected aircraft maintenance, and pandemic, all of which can cause disruptions in flight schedules. Consequently, managers need to reallocate relevant resources to ensure that the airport can return to normal operations on the basis of minimum cost, a challenge known as the airline recovery problem. Airline recovery is an active research area, with a lot of publications in recent years. To provide a comprehensive overview of airline recovery, first, keywords are selected to search for relevant studies, then existing studies are analyzed in terms of the number of papers, keywords, and sources. The study then delves into an analysis of passenger-oriented airline recovery problems on both traditional and novel recovery strategies. A detailed exploration of novel recovery strategies is conducted to uncover new insights and potential solutions for addressing airline recovery problems. Furthermore, this study investigates recovery strategies for cargo-oriented airline operations, comparing them with those designed for passenger-oriented airline recovery to offer insights for future studies on airline recovery problems. Finally, conclusions are drawn and future study directions are provided. For future studies, it is recommended to conduct more in-depth studies on dynamic and real-time recovery, incorporating human factors into the modeling, multi-modal transportation coupling, optimization of other airport processes, combination of robust scheduling and airline recovery, addressing the stochasticity of parameters, and optimization algorithm improvement.
航班很容易受到不可预见因素的影响,如恶劣天气、机场流量控制、机组人员缺勤、飞机意外维修和大流行病等,所有这些因素都可能导致航班计划中断。因此,管理者需要重新分配相关资源,确保机场能以最低成本恢复正常运营,这就是所谓的航空公司恢复问题。航空公司恢复是一个活跃的研究领域,近年来发表了大量论文。为了全面介绍航空公司恢复问题,首先选择关键词搜索相关研究,然后从论文数量、关键词和来源等方面对现有研究进行分析。然后,研究从传统和新型恢复策略两个方面深入分析了以乘客为导向的航空公司恢复问题。本研究对新型恢复策略进行了详细探讨,以揭示解决航空公司恢复问题的新见解和潜在解决方案。此外,本研究还调查了面向货运的航空公司运营恢复策略,并将其与面向客运的航空公司恢复策略进行了比较,从而为今后研究航空公司恢复问题提供启示。最后,本研究得出了结论,并提供了未来的研究方向。对于未来的研究,建议在动态和实时恢复、将人为因素纳入建模、多式联运耦合、机场其他流程优化、稳健调度与航空公司恢复相结合、解决参数的随机性以及优化算法改进等方面进行更深入的研究。
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引用次数: 0
A decomposition scheme for Wasserstein distributionally robust emergency relief network design under demand uncertainty and social donations 需求不确定和社会捐赠条件下瓦塞尔斯坦分布稳健型紧急救援网络设计的分解方案
IF 4.1 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-19 DOI: 10.1016/j.cor.2024.106913
Weiqiao Wang , Kai Yang , Lixing Yang , Ziyou Gao , Jianjun Dong , Haifeng Zhang
Social donations have played a crucial role in providing effective emergency relief and need to be particularly valued and used wisely. In this study, we address a Wasserstein distributionally robust emergency relief network design problem with demand uncertainty by taking into account the social donations. Specifically, we first formulate the problem into a two-stage stochastic programming model that requires the probability distribution information of the uncertain demand is completely known in advance, where the first stage decides on the location and pre-positioning of resources, and the second stage optimizes the delivery volume of the reserved and donated supplies offered by social organizations and individual. As the probability distribution of the demand cannot be known precisely (i.e., ambiguous) in reality, we further extend the stochastic model to a Wasserstein distributionally robust optimization model, in which the ambiguous demand is captured by the Wasserstein ambiguity set. Theoretically, we derive the tractable deterministic reformulations of the proposed distributionally robust optimization model under Type- and Type-1 Wasserstein metrics. To solve the extensive reformulations, we design a decomposition scheme on the basis of the Benders decomposition framework by adopting aggregated multiple cuts, cut-loop stabilization at root node and stabilized k-opt local branching acceleration strategies. Finally, we carry out numerical experiments to illustrate the computational advantage of the proposed solution method over the single acceleration implementation on hypothetical instances, and demonstrate the superiority of the proposed modeling approach compared with the traditional stochastic programming and robust optimization models on a real case study. The results show that the distributionally robust optimization approach used better trade-offs between cost and risk.
社会捐赠在提供有效的紧急救援方面发挥了至关重要的作用,需要特别重视并合理使用。在本研究中,我们通过考虑社会捐赠,解决了一个具有需求不确定性的 Wasserstein 分布稳健型紧急救援网络设计问题。具体来说,我们首先将该问题表述为一个两阶段随机编程模型,要求事先完全知道不确定需求的概率分布信息,其中第一阶段决定资源的位置和预置,第二阶段优化社会组织和个人提供的预留和捐赠物资的交付量。由于现实中需求的概率分布无法精确获知(即模糊性),我们进一步将随机模型扩展为瓦瑟斯坦分布稳健优化模型,其中模糊需求由瓦瑟斯坦模糊集捕捉。从理论上讲,我们推导出了所提出的分布稳健优化模型在 Type-∞ 和 Type-1 Wasserstein 度量下的可操作性确定性重构。为了解决广泛的重构问题,我们在本德斯分解框架的基础上设计了一种分解方案,采用了聚合多重切割、根节点切割环稳定和稳定的 k-opt 局部分支加速策略。最后,我们进行了数值实验,在假设实例上说明了所提求解方法相对于单一加速实现的计算优势,并在实际案例研究中证明了所提建模方法相对于传统随机编程和鲁棒优化模型的优越性。结果表明,分布稳健优化方法能更好地权衡成本和风险。
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引用次数: 0
Scheduling AMSs with generalized Petri nets and highly informed heuristic search 利用广义 Petri 网和高度知情的启发式搜索安排 AMS
IF 4.1 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-11-18 DOI: 10.1016/j.cor.2024.106912
FengLian Yuan , Bo Huang , JianYong Lv , MeiJi Cui
The design of the heuristic function in a Petri-net(PN)-based A search significantly impacts search efficiency and schedule quality for automated manufacturing systems (AMSs). In Luo et al. (2015), two admissible heuristic functions were formulated for an A search based on place-timed PNs to schedule AMSs. To broaden its application scenarios and enhance search efficiency, this paper proposes a new heuristic function whose calculations take account of multiple resource acquisitions, weighted arcs, redundant resource units, and outdated resources, which are commonly encountered in practical AMSs but usually not considered. The proposed one can deal with generalized PNs, offering broader application scenarios than ordinary PNs. In addition, it is proven to be admissible and more informed than its counterparts, ensuring that the obtained schedules are optimal and making the timed PN-based A search more efficient. To validate the efficacy and efficiency of the proposed method, several benchmark systems are tested.
在基于 Petri 网(PN)的 A∗ 搜索中,启发式函数的设计对自动制造系统(AMS)的搜索效率和排程质量有很大影响。在 Luo 等人(2015 年)的研究中,为基于位置定时 PN 的 A∗ 搜索制定了两个可接受的启发式函数,以调度 AMS。为了拓宽其应用场景并提高搜索效率,本文提出了一种新的启发式函数,其计算考虑了实际 AMS 中经常遇到但通常不考虑的多资源获取、加权弧、冗余资源单元和过时资源。所提出的计算方法可以处理广义 PN,提供比普通 PN 更广泛的应用场景。此外,它还被证明是可接受的,并且比同类算法更有信息量,从而确保获得的计划是最优的,并使基于定时 PN 的 A∗ 搜索更有效率。为了验证所提方法的功效和效率,对几个基准系统进行了测试。
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引用次数: 0
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