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Constrained Markov decision processes with uncertain costs

OPERATIONS RESEARCH LETTERS 2022年第2期50卷 218-223页

作者： Varagapriya, V. Singh, Vikas Vikram Lisser, Abdel Indian Inst Technol Delhi Dept Math New Delhi 110016 India Univ Paris Saclay CNRS Cent Supelec Lab Signaux & Syst F-91190 Gif Sur Yvette France

We consider a finite state-action discounted constrained Markov decision process with uncertain running costs and known transition probabilities. We propose equivalent linear programming, second-order cone programming and semidefinite programming problems for the robust constrained Markov decision processes when the uncertain running cost vectors belong to polytopic, ellipsoidal, and semidefinite cone uncertainty sets, respectively. As an application, we study a variant of a machine replacement problem and perform numerical experiments on randomly generated instances of various sizes. (C) 2022 Elsevier B.V. All rights reserved.

关键词： Constrained Markov decision processes Uncertainty sets linear programming problem Second-order cone programming problem Semidefinite programming problem Machine replacement problem

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MAX-MIN SOLUTIONS FOR FUZZY MULTIOBJECTIVE MATRIX GAMES

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FUZZY SETS AND SYSTEMS 1994年第1期67卷 53-69页

作者： SAKAWA, M NISHIZAKI, I SETSUNAN UNIV FAC BUSINESS ADM & INFORMATNEYAGAWAOSAKA 572JAPAN

In this paper we consider two-person zero-sum games with fuzzy multiple payoff matrices. We assume that each player has a fuzzy goal for each of the payoffs. A degree of attainment of the fuzzy goal is defined and the max-min strategy with respect to the degree of attainment of the fuzzy goal is examined. If all of the membership functions both for the fuzzy payoffs and for the fuzzy goals are linear, the formulated mathematical programming problem which yields the max-min strategy can be reduced to the linear programming problem by making use of Sakawa's method, the variable transformations, and the relaxation procedure.

关键词： 2-PERSON ZERO-SUM GAMES FUZZY PAYOFF MATRIX FUZZY GOAL MULTIPLE PAYOFF MATRICES MAX-MIN SOLUTION RELAXATION PROCEDURE linear programming problem

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Functional observers design for positive systems with delays and unknown inputs

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IET CONTROL THEORY AND APPLICATIONS 2020年第12期14卷 1656-1661页

作者： Arogbonlo, Adetokunbo Van Thanh Huynh Oo, AmanullahMaung Than Trinh, Hieu Deakin Univ Sch Engn Geelong Vic 3217 Australia

This study addresses the problem of synthesising functional observers for positive time-delay systems subjected to unknown inputs. A functional observer architecture for the problem is presented. The existence conditions of the observer and a linear programming problem characterising the existence conditions of such a functional observer are also established. An algorithm for designing the observer is presented. Finally, examples are given to showcase the effectiveness of the observer.

关键词： linear programming delay systems observers delays linear systems functional observers design positive systems delays positive time-delay systems functional observer architecture existence conditions linear programming problem

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Exponential stabilisation of positive singular linear discrete-time delay systems with bounded control

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IET CONTROL THEORY AND APPLICATIONS 2019年第7期13卷 905-911页

作者： Vu Ngoc Phat Nguyen Huu Sau VAST Inst Math 18 Hoang Quoc Viet Rd Hanoi Vietnam Hanoi Univ Ind Fac Sci 298 Caudien Hanoi Vietnam

Inspired by the results obtained in Liu et al. (2008, 2009), this study extends the constrained control problem to singular linear positive discrete-time systems with delay. By using the singular value decomposition approach, delay-dependent sufficient conditions for the regularity, causality, positivity and exponential stabilisation with a given decay rate of the system are established in terms of linear programming problem. A numerical example to demonstrate the effectiveness of the proposed method is given.

关键词： singular value decomposition asymptotic stability discrete time systems linear programming linear systems delay systems exponential stabilisation positive singular linear discrete-time delay systems bounded control constrained control problem singular linear positive discrete-time systems delay-dependent sufficient conditions linear programming problem singular value decomposition

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A new method to determine the Fermatean fuzzy optimal solution of transportation problems

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2023年第1期44卷 309-328页

作者： Akram, Muhammad Shah, Syed Muhammad Umer Allahviranloo, Tofigh Univ Punjab Dept Math New Campus Lahore Pakistan Bahcesehir Univ Fac Engn & Nat Sci Istanbul Turkiye

Transportation problems (TP) have multiple applications in supply chain management to reduce costs. Efficient methods have been developed to address TP when all factors, including supply, demand, and unit transportation costs, are precisely known. However, due to uncertainty in practical applications, it is necessary to study TP in an uncertain environment. In this paper, we define the Trapezoidal Fermatean Fuzzy Number (TrFFN) and its arithmetic operations. Then we introduce a new approach to solve TP, where transportation cost, supply, and demand are treated as TrFFN, and we call it Fermatean Fuzzy TP (FFTP). We illustrate the feasibility and superiority of this method with two application examples, and compare the performance of this method with existing methods. Furthermore, the advantages of the proposed method over existing methods are described to address TP in uncertain environments.

关键词： Trapezoidal Fermatean fuzzy sets linear programming problem transportation problem supply and demand

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One class proximal support vector machines

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PATTERN RECOGNITION 2016年 52卷 96-112页

作者： Dufrenois, F. Noyer, J. C. Univ Littoral Cote dOpale Lab Informat Signal & Image Cote Opale BP71950 Rue Ferdinand Buisson F-62228 Calais France

Recently in Dufrenois [1], a new Fisher type contrast measure has been proposed to extract a target population in a dataset contaminated by outliers. Although mathematically sound, this work presents some further shortcomings in both the formalism and the field of use. First, we propose to re-express this problem from the formalism of proximal support vector machines as introduced in Mangasarian and Wild [2]. This change is far from harmless since it introduces a suited writing for solving the problem. Another limiting factor of the method is that its performance relies on the assumption that the density between the target and outliers are different. This consideration can easily prove to be over-optimistic for real world datasets making the method unreliable, at least directly. The computation of the decision boundary is a time consuming part of the algorithm since it is based on solving a generalized eigenvalue problem (GEP). This method is therefore limited to medium sized data sets. In this paper, we propose appropriate strategies to unlock all these shortcomings and fully benefit from the interest of the approach. Firstly, we show under some conditions that generating appropriate artificial outliers allows to stay within the constraints of the method and thus enlarges the conditions of use. Secondly, we show that the GEP can be advantageously replaced by a conjugate gradient solution (CG) significantly decreasing the computational cost. Lastly, the proposed algorithm is compared with recent novelty detectors on synthetic and real datasets. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Outlier detection Proximal support vector machines linear programming problem Contrast measure

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Cut-through switching, pipelining, and scheduling for network evacuation

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IEEE-ACM TRANSACTIONS ON NETWORKING 1999年第1期7卷 88-97页

作者： Tassiulas, L Univ Maryland Dept Elect Engn College Pk MD 20742 USA Univ Maryland Syst Res Inst College Pk MD 20742 USA

A general model of a virtual circuit network consisting of a number of servers and a number of traffic classes is considered, A traffic class is identified by the sequence of servers that should be visited and the corresponding service rates before a message (customer) of the class leaves the network. The following cases are distinguished: 1) the messages need nonpreemptive service: 2) the service of a message can be preempted at any time;3) pipelining of the service in a sequence of servers is allowed;and 4) pipelining is not allowed. All of these cases arise in different transmission slr itching techniques and scheduling schemes. A fluid model that emerges when both preemption and pipelining are allowed is considered, Scheduling schemes in the quid model are compared with corresponding ones in the network with nonpreemptive service and no pipelining, The problem of evacuating the network from an initial backlog without further arrival is identified in the fluid model. Rased on that, a policy with nearly optimal evacuation time is identified for the store-and-forward case. Finally, scheduling with deadlines is considered and it is shown that in the fluid model, the evacuation problem is equivalent to a linear programming problem. The evacuation times under different work-conserving policies are considered in specific examples.

关键词： Switching Networks Telecommunication Traffic linear programming Pipeline Processing Packet Switching Network Topology Network Evacuation Scheduling Pipelining Cut Through Switching General Model Virtual Circuit Network Servers Traffic Classes Service Rates Nonpreemptive Service Preemptive Service Transmission Switching Techniques Fluid Model Optimal Evacuation Time Store And Forward Service Deadlines linear programming problem Packet Switched Network Network Topology Pipeline Processing Network Servers Processor Scheduling Telecommunication Traffic Traffic Control Asynchronous Transfer Mode Circuits linear programming Communication Networks Routing

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A new method for solving fuzzy linear fractional programming problems

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2016年第3期31卷 1831-1843页

作者： Veeramani, C. Sumathi, M. PSG Coll Technol Dept Appl Math & Computat Sci Coimbatore 641004 Tamil Nadu India PSG Coll Technol Dept Math Coimbatore Tamil Nadu India

Fuzzy linear Fractional programming problem has been used as an important planning tool for the different disciplines such as engineering, business, finance, economics, etc. In this paper, a new algorithm is developed to solve the Fuzzy linear Fractional programming problem (FLFPP) where the cost of the objective function, the resources and the technological coefficients are triangular fuzzy numbers. For this, the FLFPP is transformed into an equivalent deterministic Multi Objective linear Fractional programming problem (MOLFPP) and solved them each objective function. From the obtained solutions, we define an imprecise and aspiration level for each objectives. Hence, the objectives are transformed as fuzzy goal. Then the goal programming approach is used to achieve the highest degree of each of the membership goals by minimizing their deviational variables. Finally, two real examples and one case study problem will be used to illustrate our algorithm and compare it with the existing method.

关键词： Triangular fuzzy number linear programming problem multi objective linear programming problem goal programming

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Asynchronous l1 positive filter design for switched positive systems with overlapped detection delay

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IET CONTROL THEORY AND APPLICATIONS 2017年第3期11卷 319-328页

作者： Ren, Yu Er, Meng Joo Sun, Guanghui Harbin Inst Technol Res Inst Intelligent Control & Syst Harbin 150080 Peoples R China Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Wuhan Univ Sci & Technol Sch Machinery & Automat Wuhan 430081 Peoples R China

In this study, the asynchronous l positive filtering problem for a class of switched positive system with detection delay is investigated. The switched sequence satisfies modal-dwell-time (MDT) condition and the detection delay is both time-varying and allowed to be overlapped with each other. A new linear copositive Lyapunov function, which is time-dependent, mode-dependent and MDT-dependent, is constructed and the stability of the underlying filtering error system is established. Based on the established stability result, conditions guaranteeing the l stability of the corresponding filtering error system are further derived. The allowable total running time of the unmatched sub-filters is presented to be upper bounded by a linear combination of those running on matched sub-filters. An asynchronous positive filter with l disturbance suppression performance for the underlying switched positive system with overlapped detection delay is designed by solving a linear programming problem. The effectiveness of the proposed filter is illustrated by a numerical example.

关键词： delays switching systems (control) Lyapunov methods linear systems linear programming asynchronous (1) positive filter design switched positive systems overlapped detection delay switched sequence modal-dwell-time condition DT linear copositive Lyapunov function filtering error system unmatched subfilters linear combination linear programming problem

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Tri-level transmission expansion planning under intentional attacks: virtual attacker approach - part I: formulation

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IET GENERATION TRANSMISSION & DISTRIBUTION 2019年第3期13卷 390-398页

作者： Nemati, Hadi Latify, Mohammad Amin Yousefi, Gholam Reza Isfahan Univ Technol Dept Elect & Comp Engn Esfahan *** Iran

The first part of this two-part paper proposes tri-level transmission expansion planning (TTEP) under physical intentional attacks. In the first level, the network planner looks for an optimal transmission expansion plan to fortify the power network. In the second level, the attacker tries to maximise damages to the network. In the third level, the adverse effects of the attacks on the network operation are minimised by the network operator. Since the third level problem is a linear programming (LP) problem, the second and third levels are converted into a single-level model by using primal-dual transformation, and consequently, TTEP is converted into a bi-level programming problem. To achieve a single-level model, instead of assuming a unique attacker, a cooperative game of multiple virtual attackers (VAs) of which every VA is to maximise the damage by attacking one transmission line is introduced and modelled. The conditions that enforce Nash and Pareto equilibria of this game are derived as linear constraints which are lower level equivalent. By using this equivalence, the aforementioned bi-level TTEP model is converted into a single-level model that can be recast as a mixed integer LP problem. The numerical results are provided in the second part.

关键词： integer programming linear programming power transmission planning game theory physical attacks network operator network operation linear programming problem single-level model bi-level programming problem multiple virtual attackers virtual attacker approach tri-level transmission expansion planning model physical intentional attacks network planner problem optimal transmission expansion plan power network bi-level TTEP model Pareto equilibrium Nash equilibrium linear constraints

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