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A tri-level programming-based frequency regulation market equilibrium under cyber attacks

PROTECTION AND CONTROL OF MODERN POWER SYSTEMS 2023年第1期8卷 1-11页

作者： Wang, Ying Chen, Chunyu Zhang, Sen Liu, Yilong Huang, Chongxin Du, Yuxin Southeast Univ Nanjing Peoples R China China Univ Min & Technol Xuzhou Peoples R China State Grid Jiangsu Elect Power Co Ltd Res Inst Nanjing Peoples R China KTH Royal Inst Technol Stockholm Sweden Nanjing Univ Posts & Telecommun Nanjing Peoples R China Xuzhou Univ Technol Xuzhou Peoples R China

Owing to their flexibility and rapid response, grid-connected distributed energy resources (DERs) are wielding growing influence in frequency regulation markets (FRMs). Nevertheless, compared with conventional large-scale generators, small-scale DERs are usually weakly shielded by cyber security measures. This offers attackers the opportunity of disrupting the clearing and settlement of FRMs by manipulating the bid information of DERs. In this paper, the frequency regulation market equilibrium is studied considering the dynamic gaming between attackers and defenders, both of which need the knowledge of FRMs for their interventions. Specifically, a tri-level programming model characterizing the attacker-defender-operator (ADO) interdiction problem in FRMs is developed and then analyzed using a column and constraint generation algorithm, thereby achieving market equilibrium representing the defender's best response to the attacker. The defense strategy in the market equilibrium can attenuate the negative influence of cyber attacks upon the FRMs to the maximum extent. Finally, based on the operating rules of the California Independent System Operator, the FRM process considering the ADO interdiction is simulated and the numerical equilibrium results are presented.

关键词： Cyber attack Frequency regulation market Defender-attacker-operator interdiction tri-level programming

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Hybrid optimizers to solve a tri-level programming model for a tire closed-loop supply chain network design problem

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APPLIED SOFT COMPUTING 2018年 70卷 701-722页

作者： Fathollahi-Fard, Amir Mohammad Hajiaghaei-Keshteli, Mostafa Mirjalili, Seyedali Univ Sci & Technol Mazandaran Dept Ind Engn Behshahr Iran Griffith Univ Inst Integrated & Intelligent Syst Nathan Qld 4111 Australia

The Closed-loop Supply Chain (CLSC) is one way to collect and recycle scraped tires. CLSC consists of a set of suppliers, manufacturers, distributors and customers in a forward system. Collectors and recyclers are formed a reverse one as well. The decisions in such systems are adopted in a hierarchy. Regarding this issue, this study develops a tri-level programming model to design the location-allocation of the tire CLSC for the first time. The proposed model is formulated on the static Stackelberg game between manufacturers, distributors and collectors in the framework of CLSC. The performance of the current exact solutions for this problem suffers from degraded performance when solving large-scale problems. To alleviate this drawback, this study proposes a number of new hybrid optimizers by considering the benefits of recent metaheuristics. An extensive comparative study confirms the efficiency of developed model and the performance of the hybrid optimizers proposed when solving the large-scale problems. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Hybrid optimizers Metaheuristic algorithms tri-level programming Location-Allocation problem Tire closed-loop supply chain

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Designing a model for service facility protection with a time horizon based on tri-level programming

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ENGINEERING OPTIMIZATION 2020年第1期52卷 90-105页

作者： Parvasi, Seyed Parsa Tavakkoli-Moghaddam, Reza Bashirzadeh, Reza Taleizadeh, Ata Allah Baboli, Armand Univ Tehran Coll Engn Sch Ind Engn Tehran Iran KN Toosi Univ Technol Dept Ind Engn Tehran Iran CNRS UMR 5205 LIRIS Lab INSA Lyon Villeurbanne France

This study investigates the tri-level location problem of defence facilities with a time horizon. This research focuses on the r-interdiction median model over a finite time horizon. This research aims to protect the service facilities using the defence facilities against the most severe attack scenario of the attacker, so that the system is able to use its maximum power to serve the customers after being damaged. This problem is established on the basis of leader-follower games in the form of defender-attacker-defender. Moreover, attempts are made to make the model more realistic by considering a time horizon. To solve the problem, a combination of a genetic algorithm, simulated annealing and an exact method is used. Comparison of the solution method of the applied metaheuristic algorithm and the exact solution method in a number of small samples indicates the desirable performance of this algorithm in a reasonable time.

关键词： tri-level programming interdiction models metaheuristic algorithms time horizon maximal covering

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Shared energy storage configuration in distribution networks: A multi-agent tri-level programming approach

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APPLIED ENERGY 2024年 372卷

作者： Xie, Yulong Li, Lee Hou, Tianyu Luo, Kang Xu, Zhenyu Dai, Mingcheng Zhang, Lixiong Huazhong Univ Sci & Technol Sch Elect & Elect Engn Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol Wuhan Natl High Magnet Field Ctr Wuhan 430074 Peoples R China

Shared energy storage has the potential to decrease the expenditure and operational costs of conventional energy storage devices. However, studies on shared energy storage configurations have primarily focused on the peer -to -peer competitive game relation among agents, neglecting the impact of network topology, power loss, and other practical factors on energy storage configuration. Additionally, they do not differentiate between various roles of agents, such as shared energy storage operators, electricity consumers, and distribution network operators. To address the challenges presented by the complex interest structures, diverse usage patterns, and potentially sensitive location associated with shared energy storage, we present a multi -agent model for shared energy storage services that takes into account the perspectives of different actors in distribution networks. We develop a tri-level programming model for the optimal allotment of shared energy storage and employ a combination of analytical and heuristic methods to solve it. A case study demonstrates that our model can attain effective allocation of shared energy storage, take into account the interests of multiple parties, and converge well. We examine the impacts of different energy storage service patterns on distribution network operation modes and compare the benefits of shared and non -shared energy storage patterns. By analyzing data on the cost of operating distribution networks, voltage stability, and distributed power consumption, we investigate the potential advantages of the multi -agent distributed shared energy storage service pattern in distribution networks. Our research provides valuable insights into implementing shared energy storage on a large scale in distribution networks.

关键词： Shared energy storage Distributed energy storage tri-level programming Multi-agent decision Power flow optimization Kkt conditions Heuristic algorithm

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A solution to bi/tri-level programming problems using particle swarm optimization

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INFORMATION SCIENCES 2016年第0期370卷 519-537页

作者： Jialin, Han Guangquan, Zhang Yaoguang, Hu Jie, Lu Univ Technol Sydney Decis Syst & E Serv Intelligence Lab Ctr Quantum Computat & Intelligent Syst Fac Engn & Informat Technol Sydney NSW 2007 Australia Beijing Inst Technol Sch Mech Engn Ind & Syst Engn Lab Beijing Peoples R China

Multilevel (including bi-level and tri-level) programming aims to solve decentralized decision-making problems that feature interactive decision entities distributed throughout a hierarchical organization. Since the multilevel programming problem is strongly NP-hard and traditional exact algorithmic approaches lack efficiency, heuristics-based particle swarm optimization (PSO) algorithms have been used to generate an alternative for solving such problems. However, the existing PSO algorithms are limited to solving linear or small-scale bi-level programming problems. This paper first develops a novel bi-level PSO algorithm to solve general bi-level programs involving nonlinear and large-scale problems. It then proposes a tri-level PSO algorithm for handling tri-level programming problems that are more challenging than bi-level programs and have not been well solved by existing algorithms. For the sake of exploring the algorithms' performance, the proposed bi/tri-level PSO algorithms are applied to solve 62 benchmark problems and 810 large-scale problems which are randomly constructed. The computational results and comparison with other algorithms clearly illustrate the effectiveness of the proposed PSO algorithms in solving bi-level and tri-level programming problems. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Bi-level programming tri-level programming Multilevel decision-making Particle swarm optimization Computational intelligence

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A tri-level programming Framework for Modelling Attacks and Defences in Cyber-Physical Systems 33rd

A Tri-level Programming Framework for Modelling Attacks and ...

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33rd Australasian Joint Conference on Artificial Intelligence (AI)

作者： Yamany, Waleed Moustafa, Nour Turnbull, Benjamin Univ New South Wales Sch Engn & Informat Technol ADFA Canberra ACT 2600 Australia

ISBN: (纸本)9783030649838;9783030649845

Smart power grids suffer from coordinated attacks that exploit both their physical and cyber layers. It is an inevitable requirement to study power systems under such complex hacking scenarios to discover the system vulnerabilities and protect against those vulnerabilities and their attack vectors with appropriate defensive actions. This paper proposes an efficient tri-level programming framework that dynamically determines attacking scenarios, along with the best defensive actions in cyber-physical systems. A tri-level optimisation framework is proposed to fit the optimal decisions of defence strategies, malicious vectors and their operators for optimising the unmet demand while launching hacking behaviours. Defending resource allocation is designed using an evolutionary algorithm to examine coordinated attacks that exploit power systems. The proposed framework includes a Genetic Algorithm (GA) to solve each of the model levels in power systems. This proposed framework can flexibly model malicious vectors and their defences. IEEE 14-bus benchmark is employed to evaluate the proposed framework.

关键词： tri-level programming Evolutionary algorithm Power system Coordinated attacks

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Solving tri-level programming Problems Using a Particle Swarm Optimization Algorithm 10

Solving Tri-level Programming Problems Using a Particle Swar...

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10th IEEE Conference on Industrial Electronics and Applications

作者： Han, Jialin Zhang, Guangquan Hu, Yaoguang Lu, Jie Beijing Inst Technol Sch Mech Engn Beijing 100081 Peoples R China Univ Technol Sydney Fac Engn & Informat Technol Ctr Quantum Computat & Intelligent Syst Sydney NSW 2007 Australia

ISBN: (纸本)9781479983896

tri-level programming, a special case of multilevel programming, arises to deal with decentralized decision-making problems that feature interacting decision entities distributed throughout three hierarchical levels. As tri-level programming problems are strongly NP-hard and the existing solution approaches lack universality in solving such problems, the purpose of this study is to propose an intelligence-based heuristic algorithm to solve tri-level programming problems involving linear and nonlinear versions. In this paper, we first propose a general tri-level programming problem and discuss related theoretical properties. A particle swarm optimization (PSO) algorithm is then developed to solve the tri-level programming problem. Lastly, a numerical example is adopted to illustrate the effectiveness of the proposed PSO algorithm.

关键词： tri-level programming bi-level programming computational intelligence particle swarm optimization KuhnTucker conditions

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A tri-level programming Model Based on TsPSO for Cabin Layout Selection in Civil Airlines 2

A Tri-level Programming Model Based on TsPSO for Cabin Layou...

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2nd International Conference on System Reliability and Safety (ICSRS)

作者： Xu Yishu Ma Lin Beihang Univ Sch Reliabil & Syst Engn Beijing Peoples R China

ISBN: (纸本)9781538633229

In the airlines management, cabin layout selection is an important but weak link. Most of airlines determinate cabin layout by selection from several schemes provided by aircraft manufacturers rather than quantitative analysis and comprehensive assessment, which leads to deviation from their strategic objectives. This paper proposes to establish a decision-making mechanism based on strategic objectives to improve cabin layout selection process and build a quantitative analysis model according to it. For the model, we focus on layout pitch to build a nonlinear tri-level programming and develop an algorithm that embed chaos search factor Chebyshev map into tsPSO (extremum disturbed and simple particle swarm optimization) for better searching globe optimality. Lastly, a case study is presented to illustrate the effectiveness of the model.

关键词： cabin layout selection tri-level programming particle swarm optimization Chebyshev map

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tri-level mixed-binary linear programming: Solution approaches and application in defending critical infrastructure

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第3期298卷 1114-1131页

作者： Fakhry, Ramy Hassini, Elkafi Ezzeldin, Mohamed El-Dakhakhni, Wael McMaster Univ DeGroote Sch Business 1280 Main St West Hamilton ON L85 4M4 Canada McMaster Univ Inst Multihazard Syst Risk Studies INTERFACE 1280 Main St West Hamilton ON L8S 4L8 Canada

Decentralized decision-making is becoming more ubiquitous in different or ganizations that often follow a hierarchical structure. To model these problems, multi-level programming has been suggested as a suitable methodology for modeling the interaction between the different levels of decisions. However, multilevel programming, even for the case of bi-levels, is known to be strongly N P -hard. To address this computational challenge, we develop three different heuristic-based approaches for solving a specific class of tri-level programming problems, in which the leader has direct control over the follower's decisions to a certain extent, with a common objective function shared at all levels. As expected, each heuristic type offers a trade-off between solution quality and computational time. To illustrate our solution approach, we present an application for defending critical infrastructure to improve its resilience against intentional attacks. In this context we use a defender-attacker-defender model and apply it to electrical power grids. We also propose a modified implementation of a widely adopted enumeration algorithm in this area, with a warm-starting solution technique that significantly enhanced the computational performance of the enumeration algorithm. We test our solution approaches on three electrical transmission networks and present the results of our numerical computations as well as some insights.

关键词： Global optimization tri-level programming Critical infrastructure Electrical power grids Defender-attacher-defender model

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An iterative method for tri-level quadratic fractional programming problems using fuzzy goal programming approach

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Journal of Industrial Engineering International 2018年第2期14卷 255-264页

作者： Kassa, Semu Mitiku Tsegay, Teklay Hailay Department of Mathematics Addis Ababa University P.O. Box 1176 Addis Ababa Ethiopia Department of Mathematics and Statistical Sciences Botswana International University of Science and Technology (BIUST) P/Bag Mail 16 Palapye Botswana Department of Mathematics Wollo University P.O. Box 1145 Dessie Ethiopia

tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure. © 2017, The Author(s).

关键词： Deviational variables Fuzzy goal programming Membership functions Quadratic fractional programming tri-level programming

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