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Leveraging explainable artificial intelligence in understanding public transportation usage rates for sustainable development 利用可解释人工智能了解公共交通使用率,促进可持续发展
IF 6.9 2区 管理学 Q1 MANAGEMENT Pub Date : 2024-04-28 DOI: 10.1016/j.omega.2024.103105
Gorkem Sariyer , Sachin Kumar Mangla , Mert Erkan Sozen , Guo Li , Yigit Kazancoglu

Public transportation usage prediction is valuable for the sustainable development of transportation systems, particularly in crowded megacities. Machine learning technologies are of great interest for predicting public transportation usage. While these technologies outperform many other techniques, they suffer from limited interpretability. Explainable artificial intelligence (XAI) tools and techniques that offer post-hoc explanations of the obtained predictions are gaining popularity. This paper proposes an advanced tree-based ensemble algorithm for public transportation usage rate prediction. We aim to explain the predictions both with the most widely used technique of XAI, Shapley additive explanation (SHAP) and in the light of the rules presented. To predict the total public transportation usage, the proposed model combines all types of public transportation, categorized as ferry, railway, and bus, unlike most existing studies focusing on a single kind of public transport. Besides the sort of transportation, the day of the week, whether the day is special, and the daily ratio of passenger types were identified as model features for predicting the daily usage of each type of public transportation. We tested the proposed model using an open data set from Izmir City, Turkey. While the model had superior prediction performance, the explanations showed that the type of public transportation, weekday, and the ratio of full-fare passengers have the highest SHAP values, and the model features have many interactions. We also validated our results using an online data set showing Google search trends.

公共交通使用率预测对交通系统的可持续发展很有价值,尤其是在拥挤的大城市。机器学习技术在预测公共交通使用率方面备受关注。虽然这些技术优于许多其他技术,但它们的可解释性有限。为预测结果提供事后解释的可解释人工智能(XAI)工具和技术越来越受欢迎。本文针对公共交通使用率预测提出了一种先进的基于树的集合算法。我们的目标是利用最广泛使用的 XAI 技术--夏普利加法解释(SHAP),并根据所提出的规则来解释预测结果。为了预测公共交通的总使用率,我们提出的模型结合了所有类型的公共交通,包括轮渡、铁路和公交车,这与大多数现有研究只关注单一类型的公共交通不同。除了交通工具的种类外,一周中的哪一天、这一天是否特殊以及每天乘客类型的比例也被确定为预测每种公共交通工具每日使用率的模型特征。我们使用土耳其伊兹密尔市的公开数据集对所提出的模型进行了测试。虽然该模型具有出色的预测性能,但解释结果表明,公共交通类型、工作日和全价乘客比例的 SHAP 值最高,而且模型特征之间存在许多交互作用。我们还利用显示谷歌搜索趋势的在线数据集验证了我们的结果。
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引用次数: 0
Increasing schedule reliability in the multiple depot vehicle scheduling problem with stochastic travel time 在具有随机旅行时间的多车厂车辆调度问题中提高调度可靠性
IF 6.9 2区 管理学 Q1 MANAGEMENT Pub Date : 2024-04-26 DOI: 10.1016/j.omega.2024.103100
Léa Ricard , Guy Desaulniers , Andrea Lodi , Louis-Martin Rousseau

The multiple depot vehicle scheduling problem (MDVSP) is one of the most studied problems in public transport service planning. It consists of assigning buses to each timetabled trip while respecting vehicle availability at each depot. Although service quality, and especially reliability, is the core of most transport agencies, the MDVSP is more often than not solved solely in a cost-efficient way. This work introduces a data-driven model to the reliable MDVSP with stochastic travel time (R-MDVSP-STT). The reliability of a schedule is assessed and accounted for by propagating delays using the probability mass function of the travel time of each timetabled trip. We propose a heuristic branch-and-price algorithm to solve this problem and a labeling algorithm with a stochastic dominance criterion for the associated subproblems. The solutions obtained are compared based on three metrics — under normal and extraordinary circumstances. Computational results on real-life instances show that our method can efficiently find good trade-offs between operational costs and reliability, improving the reliability of the solutions with little cost increase.

多车厂车辆调度问题(MDVSP)是公共交通服务规划中研究最多的问题之一。它包括为每个定时班次分配公共汽车,同时保证每个车厂的车辆可用性。虽然服务质量,尤其是可靠性,是大多数运输机构的核心问题,但 MDVSP 通常只是以成本效益的方式来解决。这项工作为具有随机旅行时间的可靠 MDVSP(R-MDVSP-STT)引入了一个数据驱动模型。通过使用每个定时行程的旅行时间的概率质量函数来传播延迟,从而评估和计算时间表的可靠性。我们提出了一种启发式分支-价格算法来解决这一问题,并针对相关子问题提出了一种带有随机优势准则的标记算法。我们根据正常和特殊情况下的三个指标对所获得的解决方案进行了比较。在实际案例中的计算结果表明,我们的方法可以有效地在运营成本和可靠性之间找到良好的折衷方案,在几乎不增加成本的情况下提高解决方案的可靠性。
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引用次数: 0
Assessing the performance of banks through an improved sigma-mu multicriteria analysis approach 通过改进的西格玛-穆多标准分析法评估银行绩效
IF 6.9 2区 管理学 Q1 MANAGEMENT Pub Date : 2024-04-24 DOI: 10.1016/j.omega.2024.103099
Silvia Angilella , Michalis Doumpos , Maria Rosaria Pappalardo , Constantin Zopounidis

The σ-μ efficiency methodology has been recently introduced for multicriteria evaluation problems, based on the framework of Stochastic Multi-Attribute Acceptability analysis (SMAA), to address the uncertainty in the performance of a set of decision alternatives. The methodology builds, iteratively, a set of Pareto-Koopmans efficiency frontiers, which are used to assess the alternatives with respect to their expected performance and its variability, measured across different scenarios for the weights of the evaluation criteria. This paper presents an improved algorithmic implementation of this methodology that provides results that are consistent with the Pareto dominance relation between the alternatives. The proposed approach is employed to evaluate the performance of a sample of European banks which participated in the European stress tests conducted by the European Banking Authority, over the last five years available (2017–2021). The performance and efficiency of the banks is analyzed using financial criteria along with environmental, social, and governance (ESG) factors. Results from comprehensive and disaggregated analysis reveal performance disparities among banks in financial and ESG factors, highlighting the influence of country-specific green policies and individual bank practices. Valuable for the banking sector and regulators, the findings help identify operational inefficiencies and propose areas for performance enhancement, operational improvement, and innovation, with a focus on green practices.

最近,在随机多属性可接受性分析(SMAA)框架的基础上,针对多标准评价问题引入了 σ-μ 效率方法,以解决一组决策备选方案性能的不确定性问题。该方法通过迭代建立了一组帕累托-库普曼斯效率前沿,用于评估备选方案的预期绩效及其可变性,并在不同情况下衡量评价标准的权重。本文介绍了这一方法的改进算法实施,其结果与备选方案之间的帕累托优势关系相一致。本文采用所提出的方法,对参加欧洲银行管理局进行的欧洲压力测试的欧洲银行样本在过去五年(2017-2021 年)的表现进行了评估。分析银行的绩效和效率时使用了财务标准以及环境、社会和治理(ESG)因素。综合和分类分析的结果显示了银行在财务和 ESG 因素方面的绩效差异,凸显了特定国家绿色政策和个别银行实践的影响。这些研究结果对银行业和监管机构很有价值,有助于发现运营效率低下的问题,并提出提高绩效、改善运营和创新的领域,重点关注绿色实践。
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引用次数: 0
Optimal decision-making of post-disaster emergency material scheduling based on helicopter–truck–drone collaboration 基于直升机-卡车-无人机协作的灾后应急物资调度优化决策
IF 6.9 2区 管理学 Q1 MANAGEMENT Pub Date : 2024-04-24 DOI: 10.1016/j.omega.2024.103104
Yong Shi , Junhao Yang , Qian Han , Hao Song , Haixiang Guo

In the last decades, natural disasters, such as earthquakes and landslides, have occurred frequently, seriously threatening the safety of people’s lives and property. How emergency material is scheduled and delivered efficiently to the affected sites after a disaster has become a critical issue in emergency management. Current studies on emergency material scheduling mainly focus on truck or helicopter transport. Inspired by the success of employing drones in commercial logistics, this work investigates the emergency material scheduling issue based on the cooperative transport of drones, helicopters, and trucks. Specifically, this paper considers the limited transport capacity, road conditions in the early stage of the disaster rescue, and affected sites restricted by road conditions that can only be served by helicopters or drones. The studied problem is formulated as a mixed integer programming model, and a two-stage heuristic algorithm is developed to solve the model. For the proposed model, instances of different sizes are generated, and extensive experiments are performed to test the efficiency of the proposed algorithm. The comparison between the solutions obtained by the two-stage algorithm and Gurobi Solver for the small instances validates the effectiveness of the proposed heuristic algorithm. Experimental results for the larger instances show that the proposed two-stage algorithm can effectively solve the problem of emergency material scheduling. Sensitivity analysis of ten typical instances is performed to provide managerial insights. Finally, a case study of the Sichuan earthquake and the visualization of transport routes are presented. The model and solving approach proposed in this work can provide essential decision references for emergency management decision-making.

近几十年来,地震、山体滑坡等自然灾害频发,严重威胁着人们的生命财产安全。如何调度应急物资,并在灾后有效地运送到受灾地点,已成为应急管理的关键问题。目前关于应急物资调度的研究主要集中在卡车或直升机运输方面。受无人机在商业物流中成功应用的启发,本文研究了基于无人机、直升机和卡车协同运输的应急物资调度问题。具体而言,本文考虑了有限的运输能力、灾难救援初期的道路状况,以及受道路状况限制只能由直升机或无人机服务的受灾地点。本文将所研究的问题表述为一个混合整数编程模型,并开发了一种两阶段启发式算法来求解该模型。针对所提出的模型,生成了不同大小的实例,并进行了大量实验来测试所提算法的效率。通过比较两阶段算法和 Gurobi Solver 对小型实例的求解结果,验证了所提出的启发式算法的有效性。对较大实例的实验结果表明,所提出的两阶段算法可以有效地解决紧急材料调度问题。对十个典型实例进行了敏感性分析,以提供管理见解。最后,介绍了四川地震的案例研究和运输路线的可视化。本文提出的模型和求解方法可为应急管理决策提供重要的决策参考。
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引用次数: 0
Multi-period share pledging with sequential three-way proportion decision 多期股票质押与顺序三方比例决策
IF 6.9 2区 管理学 Q1 MANAGEMENT Pub Date : 2024-04-21 DOI: 10.1016/j.omega.2024.103102
Mingwei Wang , Junping Zhang , Decui Liang

Considering the potential loss of decision-making power associated with share pledging, shareholders need to pledge appropriate share proportion based on their own shareholding situation. To assist shareholders in handling this decision-making challenge, we design a share pledging decision-making method with three-way decision, which fully considers the characteristics of share pledging. Firstly, we construct a novel calculation method of conditional probability based on left-tail systemic risk and share return data, which appropriately measures the probability of share price plummeting. Then, we propose a learning method of loss functions with shareholding proportion information, which considers pledged share proportions. To enhance the flexibility of the proposed method in handling practical share pledging issues, we discuss two scenarios including complete shareholding proportion information and limited shareholding proportion information. Furthermore, we design three-way proportion decision (TWPD) through introducing particle swarm optimization algorithm, which can determine the share proportion of pledge and redemption with minimizing the loss of decision-making power, and develop TWPD to sequential three-way proportion decision (STWPD) for solving multi-period share pledging problem. Finally, we apply the proposed method to deal with share pledging problem of a Chinese firm based on real data collected from China Stock Market & Accounting Research Database, and provide implications for shareholders and firms in risk management during share pledging based on the results of comparison experiments and sensitivity analysis.

考虑到股权质押可能带来的决策权损失,股东需要根据自身的持股情况进行适当比例的股权质押。为了帮助股东应对这一决策难题,我们设计了一种股权质押三方决策方法,充分考虑了股权质押的特点。首先,我们基于左尾系统风险和股票收益数据,构建了一种新颖的条件概率计算方法,恰当地度量了股价暴跌的概率。然后,我们提出了一种考虑股权质押比例信息的损失函数学习方法。为了提高所提方法处理实际股权质押问题的灵活性,我们讨论了两种情况,包括完全股权比例信息和有限股权比例信息。此外,我们还通过引入粒子群优化算法设计了三向比例决策(TWPD),该算法可以在决策权损失最小的情况下确定质押和赎回的股份比例,并将 TWPD 发展为顺序三向比例决策(STWPD),用于解决多期股权质押问题。最后,我们基于中国证券市场与会计研究数据库收集的真实数据,将所提出的方法应用于处理一家中国公司的股权质押问题,并根据对比实验和敏感性分析的结果,为股东和公司在股权质押期间的风险管理提供启示。
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引用次数: 0
On-line strategy selection for reducing overcrowding in an Emergency Department 减少急诊室过度拥挤的在线策略选择
IF 6.9 2区 管理学 Q1 MANAGEMENT Pub Date : 2024-04-19 DOI: 10.1016/j.omega.2024.103098
Cristiano Fabbri , Michele Lombardi , Enrico Malaguti , Michele Monaci

Overcrowding is a well-known major issue affecting the behavior of an Emergency Department (ED), as it is responsible for patients’ dissatisfaction and has a negative impact on the quality of workers’ performance. Dealing with overcrowding in an ED is complicated by lack of its precise definition and by exogenous and stochastic nature of requests to be served. In this paper, we present a Decision Support System (DSS) based on the integration of a Deep Neural Network for dealing with the sources of uncertainty and a simulation tool to evaluate how specific management policies affect the ED behavior. The DSS is designed to be run on-line, dynamically suggesting the most suitable policy to be implemented in the ED. We evaluate the performance of the DSS on a specific major ED located in northern Italy. Numerical results show that overcrowding can be considerably reduced by allowing a dynamic selection among a limited set of simple policies for queue management.

众所周知,过度拥挤是影响急诊室(ED)行为的一个主要问题,因为它会导致病人不满,并对工作人员的工作质量产生负面影响。由于急诊室过度拥挤缺乏准确的定义,而且服务请求具有外生性和随机性,因此处理急诊室过度拥挤问题非常复杂。在本文中,我们介绍了一种决策支持系统(DSS),该系统基于深度神经网络的集成,用于处理不确定性来源和模拟工具,以评估特定管理政策对急诊室行为的影响。该决策支持系统可在线运行,动态建议最适合在 ED 中实施的政策。我们在位于意大利北部的一个特定大型急诊室对 DSS 的性能进行了评估。数值结果表明,通过在有限的简单队列管理策略中进行动态选择,可以大大缓解拥挤状况。
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引用次数: 0
Increasing supply chain resiliency through equilibrium pricing and stipulating transportation quota regulation 通过平衡定价和规定运输配额监管提高供应链的弹性
IF 6.9 2区 管理学 Q1 MANAGEMENT Pub Date : 2024-04-17 DOI: 10.1016/j.omega.2024.103097
Mostafa Pazoki , Hamed Samarghandi , Mehdi Behroozi

Supply chain disruption can occur for a variety of reasons, including natural disasters or market dynamics for which resilient strategies should be designed. If the disruption is profound and has dire consequences for the economy, it calls for the regulator’s intervention to minimize the impact for the betterment of the society. This paper investigates the minimum quota regulation on transport amounts of a shipping company with limited capacity that transports a group of products with heterogeneous transportation and production costs and prices. An interesting example can be found in the North American rail transportation market, where rail capacity is used for a variety of products and commodities, such as oil and grains. Similarly, in Europe, the supply chain for grain produced in Ukraine is disrupted by the Ukraine war and the blockade of the maritime transport routes. This siege puts pressure on the rail transport capacity of Ukraine and its neighboring countries to the west, which needs to be shared to ship a variety of products, including grains, military, and humanitarian supplies. Such situations require the proper execution of government intervention for effective management of limited transport capacity to avoid rippling effects throughout the economy. We propose mathematical models and solutions for market players and the government in a Canadian case study. Subsequently, the conditions that justify government intervention are identified, and an algorithm is presented to obtain the optimum minimum quotas.

供应链中断的原因多种多样,包括自然灾害或市场动态,应针对这些原因制定弹性战略。如果中断严重并对经济造成严重后果,则需要监管机构进行干预,以尽量减少影响,改善社会。本文研究了一家运力有限的航运公司对运输量的最低配额监管,该公司运输的是一组具有不同运输和生产成本及价格的产品。北美铁路运输市场就是一个有趣的例子,铁路运力用于运输石油和谷物等多种产品和商品。同样,在欧洲,乌克兰战争和对海上运输路线的封锁扰乱了乌克兰生产的谷物供应链。这种封锁对乌克兰及其西面邻国的铁路运输能力造成了压力,而这些能力需要共享,以运输包括谷物、军事和人道主义物资在内的各种产品。在这种情况下,政府必须采取适当的干预措施,对有限的运输能力进行有效管理,以避免对整个经济产生连锁反应。我们以加拿大为例,为市场参与者和政府提出了数学模型和解决方案。随后,我们确定了政府干预的合理条件,并提出了一种获得最佳最低配额的算法。
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引用次数: 0
When outpatient appointment meets online consultation: A joint scheduling optimization framework 当门诊预约遇上在线咨询:联合排班优化框架
IF 6.9 2区 管理学 Q1 MANAGEMENT Pub Date : 2024-04-16 DOI: 10.1016/j.omega.2024.103101
Hainan Guo , Yue Xie , Bowen Jiang , Jiafu Tang

While the provision of Online Consultation Services (OCS) has brought convenience to patients, the original offline outpatient workflow may struggle to maintain efficiency. Hospital managers’ concerns lie on how to reconcile the operations of offline service with the provision of OCS and what are the latent impacts of OCS on the operational performances of healthcare system. The outpatient appointment scheduling is a crucial part of the workflow decision that affects both quality of offline services and the fragmented idle time that doctors can reply to their Follow-up patients (FUP) during working hours. To smooth the fluctuations in workload of OCS, we introduce a novel decision variable—the recommended maximum number of FUP that a doctor should serve during overtime hours (FUP-MN)—and propose an inter-day service shifting strategy that any requests for OCS exceeding the FUP-MN will be deferred to be served in the fragmented idle time of the next session. We formulate a stochastic programming model to search for the optimal combination of the appointment schedule and FUP-MN. Propositions are conducted to demonstrate the model is valid not only in coordinating the dual demand for online and offline services, but also in restricting the potential overflow of OCS requests. We provide a general solution approach and also develop a heuristic algorithm to quickly obtain optimal workflows at different OCS demand levels. The numerical experimental results indicate that an appropriate introduction of OCS can give the healthcare system a strong ability to resist the adverse effects of uncertainty.

在线咨询服务(OCS)为患者带来了便利,但原有的线下门诊工作流程可能难以维持效率。医院管理者关心的是,如何协调线下服务与在线咨询服务的运作,以及在线咨询服务对医疗系统运作绩效的潜在影响。门诊预约安排是工作流程决策的关键部分,既影响线下服务的质量,也影响医生在工作时间内回复复诊病人(FUP)的碎片化空闲时间。为了平滑门诊预约工作量的波动,我们引入了一个新的决策变量--医生在加班时间内应服务的复诊病人的建议最大数量(FUP-MN)--并提出了一种跨日服务转移策略,即任何超过 FUP-MN 的门诊预约请求都将推迟到下一个时段的碎片空闲时间内处理。我们建立了一个随机编程模型,以寻找预约时间表和 FUP-MN 的最佳组合。我们提出了一些命题,以证明该模型不仅在协调在线和离线服务的双重需求方面有效,而且在限制 OCS 请求的潜在溢出方面也有效。我们提供了一种通用的求解方法,还开发了一种启发式算法,以快速获得不同 OCS 需求水平下的最优工作流。数值实验结果表明,适当引入 OCS 可以使医疗系统具有很强的抵御不确定性不利影响的能力。
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引用次数: 0
CWBCM method to determine the importance of classification performance evaluation criteria in machine learning: Case studies of COVID-19, Diabetes, and Thyroid Disease 用 CWBCM 方法确定机器学习中分类性能评估标准的重要性:COVID-19、糖尿病和甲状腺疾病案例研究
IF 6.9 2区 管理学 Q1 MANAGEMENT Pub Date : 2024-04-09 DOI: 10.1016/j.omega.2024.103096
Maede Parishani, Morteza Rasti-Barzoki

Problems with multiple conflicting criteria are usually modeled by the methods proposed in the field of Multi-Criteria Decision Making (MCDM). In MCDM, one of the most important topics is the weighting of criteria. On the other hand, classification is employed in numerous real-world issues, like disease diagnosis. Diverse algorithms have been developed for this purpose. It is important to evaluate the classification performance in every problem by evaluating algorithms. The evaluation of algorithms includes several conflicting criteria; Therefore, it can be represented as an MCDM problem. We aim to develop a new weighting method that can be used for the classification problem with more than two classes, involve the risk of threatening human life, and consider minor features for different diseases in weighting. At present, none of the existing weighting methods fulfill these requirements. This research presents a new method called “Criteria Weighting Based on Confusion Matrix (CWBCM)” and our innovation is that, for the first time, all these gaps are filled with this method. This method calculates the exact importance of criteria using the confusion matrix in machine learning. The proposed method has been implemented on six different datasets of three diseases: COVID-19, thyroid, and diabetes, and compared with two common methods, Shannon and AHP. Two methods, TOPSIS and EDAS, were also used to rank the classifiers. Finally, the results show that our method is superior to the other two weighting methods in all critical factors and has unique features that other methods do not have.

多标准决策(MCDM)领域提出的方法通常用于模拟具有多重冲突标准的问题。在 MCDM 中,最重要的课题之一就是标准的权重。另一方面,分类被广泛应用于现实世界中的各种问题,如疾病诊断。为此,人们开发了多种算法。通过评估算法来评价每个问题的分类性能非常重要。对算法的评估包括多个相互冲突的标准;因此,可以将其视为一个多因素强迫管理问题。我们的目标是开发一种新的加权方法,可用于两类以上、涉及威胁人类生命风险的分类问题,并在加权时考虑不同疾病的次要特征。目前,现有的加权方法都无法满足这些要求。本研究提出了一种名为 "基于混淆矩阵的标准加权法(CWBCM)"的新方法,我们的创新之处在于首次用这种方法填补了所有这些空白。这种方法利用机器学习中的混淆矩阵精确计算标准的重要性。我们在三种疾病的六个不同数据集上实施了所提出的方法:COVID-19、甲状腺和糖尿病,并与香农和 AHP 两种常用方法进行了比较。此外,还使用了 TOPSIS 和 EDAS 两种方法对分类器进行排序。最后,结果表明,我们的方法在所有关键因素上都优于其他两种加权方法,并且具有其他方法所不具备的独特功能。
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引用次数: 0
Intelligent design of sensor networks for data-driven sensor maintenance at railways 用于铁路数据驱动传感器维护的传感器网络智能设计
IF 6.9 2区 管理学 Q1 MANAGEMENT Pub Date : 2024-04-09 DOI: 10.1016/j.omega.2024.103094
Alena Otto , Christian Tilk

With rapid advances in digitization, many critical processes in transportation, industries, and our daily life rely on sensor measurements. With time, however, the measurements may get gradually biased and their precision deteriorates, leading to an enhanced risk of major disruptions caused by false sensor measurements. All single sensor measurements are uncertain and deviate from the true value. To detect malfunctioning sensors early on, a set of recent measurements of each sensor has to be constantly cross-checked against the measurements of a given number of other sensors, i.e., sensors should form a diagnosable network.

In this article, we examine the intelligent positioning of safety-relevant sensors at railways such that the installed sensors can constantly cross-check each other and the number of the required sensors is minimized. The arising sensor positioning problem (SPP) belongs to the family of the coordinated set covering problems with two binary matrices: the choice of columns in one matrix implies the selection of specific columns and rows in the other matrix. We formulate an integer program, provide some formal analysis of the SPP and design a customized large neighborhood search metaheuristic RuM, which finds close-to-optimality solutions fast. In our computational experiments, we show that if we ignore the diagnosability requirement, the installed sensors cannot sufficiently cross-check each other in most cases. However, it costs only a few (or even no) additional sensors to ensure the diagnosability of the sensor network.

随着数字化的快速发展,交通、工业和日常生活中的许多关键过程都依赖于传感器测量。然而,随着时间的推移,测量结果可能会逐渐出现偏差,精度也会下降,从而导致因错误的传感器测量结果而造成重大干扰的风险增加。所有单一传感器的测量值都是不确定的,都会偏离真实值。为了及早发现故障传感器,每个传感器最近的一组测量值必须与一定数量的其他传感器的测量值不断进行交叉校验,即传感器应形成一个可诊断的网络。由此产生的传感器定位问题(SPP)属于有两个二元矩阵的协调集覆盖问题:一个矩阵中列的选择意味着另一个矩阵中特定列和行的选择。我们提出了一个整数程序,对 SPP 进行了一些形式分析,并设计了一种定制的大邻域搜索元启发式 RuM,它能快速找到接近最优的解。在计算实验中,我们发现如果忽略可诊断性要求,安装的传感器在大多数情况下无法充分地相互交叉检查。然而,只需增加几个(甚至不增加)传感器,就能确保传感器网络的可诊断性。
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