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作者： Ramirez Calderon, Jose Ernesto Texas A&M University

学位级别：Ph.D., Doctor of Philosophy

This dissertation focuses on binary linear programming problems (BLP) affected by uncertainties preventing the implementation of the solutions exactly as prescribed. This type of uncertainty is termed implementation uncertainty and occurs due to model *** dissertation presents a model of binary variables under implementation uncertainty and develops a methodology to solve BLPs under this type of uncertainty consisting in a robust formulation (RBIU). The RBIU identifies solutions that satisfy given levels of optimality and feasibility for any realizations of the uncertainty. A solution methodology of the RBIU consists of an equivalent linear programming *** solutions tend to be conservative in the sense that they sacrifice optimality to achieve the given level of feasibility. This dissertation presents two methodologies to control the conservatism of the RBIU solutions. The first method consists in controlling the feasibility relaxation level and selecting the solutions bounding the value of the objective function. The second method is an extension of a well-known method in the field of robust optimization and consists in the development of a cardinality-constrained robust BLP under implementation uncertainty (CBIU) that controls the conservatism by bounding the maximum number of variables under uncertainty with different implemented and prescribed values. The proposed concepts of robustness are applied to the knapsack problem, assignment problem and shortest path problem (SPP) under implementation uncertainty to identify their solutions immune to uncertainty and to show how particular problem structures permit to identify different important theoretical and practical properties. This work examines the properties of the robust counterparts including configurations of the control parameters, complexity and the development of solutions *** dissertation includes experimental studies to show how the proposed concepts of robustnes

关键词： Robust optimization binary linear programming Implementation uncertainty Knapsack problem Assignment problem Shortest path problem Optimization under uncertainty

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Solving the binary linear programming Model in Polynomial Time

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American Journal of Operations Research 2016年第1期6卷 1-7页

作者： Elias Munapo School of Accounting Economics and Decision Sciences North West University Mafeking South Africa

The paper presents a technique for solving the binary linear programming model in polynomial time. The general binary linear programming problem is transformed into a convex quadratic programming problem. The convex quadratic programming problem is then solved by interior point algorithms. This settles one of the open problems of whether P = NP or not. The worst case complexity of interior point algorithms for the convex quadratic problem is polynomial. It can also be shown that every liner integer problem can be converted into binary linear problem.

关键词： NP-Complete binary linear programming Convex Function Convex Quadratic programming Problem Interior Point Algorithm and Polynomial Time

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Optimal scheduling of shared autonomous electric vehicles with multi-agent reinforcement learning: A MAPPO-based approach

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NEUROCOMPUTING 2025年 622卷

作者： Tian, Jingjing Jia, Hongfei Wang, Guanfeng Huang, Qiuyang Wu, Ruiyi Gao, Heyao Liu, Chao Jilin Univ Coll Transportat Changchun 130022 Peoples R China

The advent of shared autonomous electric vehicles (SAEVs) is expected to decarbonize the transport sector and enable large-scale mobility on demand. Considering the highly dynamic nature of operation environments, it is appealing to investigate the optimal schedule decisions, comprising order-matching, relocation, and charge/ discharge with the V2G technology. Recent literature has investigated these schedule decisions with deep reinforcement learning (DRL) independently, neglecting the collaborative interactions among multiple autonomous vehicles. To this end, the fully dynamic schedule task is integrally described as a partially observable Markov decision process (POMDP) under the constraints of time-dependent demand, spatial-temporal varying electricity price, available vehicles and chargers. Then, we design a robust and extensible framework that combines multi-agent proximal policy optimization (MAPPO) and a binary linear programming (BLP) model to solve the optimization problem, in which SAEVs are regarded as agents to make decisions according to their local observations. Additionally, observation normalization and action masking are utilized to improve training efficiency. Numerical experiments are conducted with New York City yellow taxi data to simulate the real-time SAEV operating environment. These results demonstrate that the proposed MAPPO approach is expected to enhance the operators' revenue while improving the customer service rate compared to benchmark algorithms.

关键词： Shared autonomous electric vehicles Optimal scheduling Multi-agent proximal policy optimization binary linear programming

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Deriving a minimum distance-based collective preorder: a binary mathematical programming approach

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OR SPECTRUM 2012年第1期34卷 23-42页

作者： Jabeur, Khaled Martel, Jean-Marc Guitouni, Adel ISCCB Zarzouna 7021 Bizerte Tunisia Univ Laval Fac Sci Adm Ste Foy PQ G1K 7P4 Canada Def R&D Canada Valcartier Val Belair PQ G3J 1X5 Canada

Deriving the "closest" (minimal distance) collective judgment to all individual opinions is a complex aggregation problem that has been widely studied in group decision-making literature. However, most of the existing literature does not consider individual opinions expressed as partial preorders (i.e., a preference system which includes the incomparability relation). In this paper, we propose a method based on binary linear programming to derive a minimum distance-based collective preorder from individual preferences relational systems (p.r.s.). This method is threefold. First, each member determines a preorder (partial or total) over the set of alternatives. Second, an aggregation algorithm is proposed to derive at least one collective and not necessary transitive p.r.s. at minimum distance from all individual preorders. Third, a binary linear programming optimization will transform each non-transitive collective p.r.s. into a collective preorder (i.e. a transitive p.r.s.). The proposed method has three main advantages: (1) it deals with incomparability (partial preorders), (2) the relative importance of the members is explicitly considered and (3) the collective p.r.s. obtained after the aggregation step might be "exploited" according to different decision-making problematics (i.e. ranking, choice and sorting).

关键词： Group decision-making binary relations Preferences aggregation Distance measure binary linear programming Members' relative importance

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An optimal PMU placement method for power system observability under various contingencies

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INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS 2015年第4期25卷 589-606页

作者： Abiri, Ebrahim Rashidi, Farzan Niknam, Taher Shiraz Univ Technol Dept Elect & Elect Engn Shiraz Iran

In this paper, an efficient and comprehensive formulation for the optimal placement of phasor measurement units (PMUs) is proposed to minimize the number of PMU installation subject to full network observability. Moreover, the formulation is extended for assuring complete observability under single PMU loss or single line outage cases. Since the proposed optimization formulation is regarded to be a multiple-solution one, both the installation cost and measurement redundancy are employed to differentiate the solutions with the same number of PMUs to be installed. In all of the investigations, the effect of zero-injection buses in the power system is considered. The effectiveness of the proposed method is verified via some IEEE standard systems and compared with some newly reported methods. Results show that the proposed method is simple to implement and more accurate compared to other existing methods. Moreover, by considering the presented method, the minimum number of required PMUs is decreased in some cases. Copyright (c) 2014 John Wiley & Sons, Ltd.

关键词： phasor measurement units optimal placement state estimation binary linear programming power system observability

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Developing Smart Grids Based on GPRS and ZigBee Technologies Using Queueing Modeling-Based Optimization Algorithm

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ETRI JOURNAL 2016年第1期38卷 41-51页

作者： de Castro Souza, Gustavo Batista Teles Vieira, Flavio Henrique Lima, Claudio Ribeiro de Deus Junior, Getulio Antero de Castro, Marcelo Stehling de Araujo, Sergio Granato Vasques, Thiago Lara Univ Fed Goias Sch Elect Engn Mech & Comp Engn Goias Go Brazil AGX Energia Dept Telecommun Goias Go Brazil

Smart metering systems have become widespread around the world. RF mesh communication systems have contributed to the creation of smarter and more reliable power systems. This paper presents an algorithm for positioning GPRS concentrators to attain delay constraints for a ZigBee-based mesh network. The proposed algorithm determines the number and placement of concentrators using integer linear programming and a queueing model for the given mesh network. The solutions given by the proposed algorithm are validated by verifying the communication network performance through simulations.

关键词： Smart Grid queue theory binary linear programming mesh networks ZigBee

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Precise Worst-Case Blocking Time of Tasks Under Priority Inheritance Protocol

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IEEE TRANSACTIONS ON COMPUTERS 2021年第11期70卷 1901-1913页

作者： Faldella, Eugenio Loreti, Daniela Univ Bologna Dept Comp Sci & Engn I-40126 Bologna Italy

The problem of precisely computing the worst-case blocking time that tasks may experience is one of the fundamental issues of schedulability analysis of real-time applications. While exact methods have been proposed for more sophisticated protocols, the problem is indeed complex in case of the Priority Inheritance Protocol, even restricting the attention to uniprocessor systems, non-nested resource accesses, and non-self-suspending tasks. Besides a very simple method leading in general to loose upper bounds, only one algorithm of exponential complexity has been so far reported in literature to tighten such bounds. In this article, we describe a novel approach which, leveraging an operational research technique for modeling the problem, computes the same tight bounds in polynomial time. We then discuss the scenarios in which, assuming no conditional statements in the tasks' code, the computed bounds derive from an actually impossible blocking chain, and we refine the initial model to more precisely compute the worst-case blocking times for any task set in any possible operating condition.

关键词： Task analysis Protocols Real-time systems Upper bound Computational modeling Complexity theory linear programming Hard real-time multitasking applications exclusive access resources basic priority inheritance protocol binary linear programming

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Optimal sensor placement with signal propagation effects and inhomogeneous coverage preferences

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INTERNATIONAL JOURNAL OF SENSOR NETWORKS 2011年第2期9卷 107-120页

作者： Vecherin, Sergey N. Wilson, D. Keith Pettit, Chris L. USA Cold Reg Res & Engn Lab Hanover NH 03755 USA USN Acad Dept Aerosp Engn Annapolis MD 21402 USA

The optimal sensor placement problem consists of determining the number, types, and locations of sensors satisfying inhomogeneous coverage requirements while minimising a specified cost function. The cost function can reflect various factors such as the actual cost of the sensors, their total number, and energy consumption. A strict and general formulation of the problem is described here for sensors characterised by probability of detection at some specified probability of false alarm. The formulation includes non-uniform coverage preferences and realistic, non-line-of-sight detection accounting on signal propagation effects. The optimisation is expressed as a solution to a binary linear programming problem. While exact solution of this problem is typically prohibitive, a fast greedy algorithm is presented that yields a near-optimal solution. It can also be successfully applied to improve coverage of an existing sensor network. This approach compares very favourably to an alternative heuristic strategy based on placing sensors one-by-one in the previously worst-covered location.

关键词： binary linear programming optimal sensor configuration sensor placement sensor networks sensor location optimisation distributed sensor networks

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Optimal phasor measurement units placement to maintain network observability using a novel binary particle swarm optimization and fuzzy system

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2015年第1期28卷 477-483页

作者： Abiri, Ebrahim Rashidi, Farzan Shiraz Univ Technol Elect & Elect Engn Dept Shiraz Iran

This paper presents a hybrid modified binary particle swarm optimization and fuzzy system for obtaining the optimal number of PMUs which makes the power system completely observable. Observability assessment is done by means of topological observability rules. Moreover a new rule is employed which can decrease the number of required PMUs for full network observability. In all of the investigations, the effect of zero-injection buses in the power system is considered. Developed PMU placement method is illustrated using IEEE standard systems to demonstrate the effectiveness of the proposed algorithm. The results show that the whole system can be observable with installing PMUs on less than 20% of system buses.

关键词： Phasor measurement units (PMUs) state estimation binary linear programming binary particle swarm optimization fuzzy systems power system observability

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On the energy cost of robustness for green virtual network function placement in 5G virtualized infrastructures

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COMPUTER NETWORKS 2017年 125卷 64-75页

作者： Marotta, Antonio D'Andreagiovanni, Fabio Kassler, Andreas Zola, Enrica Karlstad Univ Univ Gatan 2 S-65188 Karlstad Sweden Sorbonne Univ Univ Technol Compiegne CNRS Heudiasyc UMR 7253 CS 60319 F-60203 Compiegne France Univ Politecn Cataluna C Jordi Girona 1-3 ES-08034 Barcelona Spain

Next generation 5G networks will rely on virtualized Data Centers (vDC) to host virtualized network functions on commodity servers. Such Network Function Virtualization (NFV) will lead to significant savings in terms of infrastructure cost and reduced management complexity. However, green strategies for networking and computing inside data centers, such as server consolidation or energy aware routing, should not negatively impact the quality and service level agreements expected from network operators. In this paper, we study how robust strategies that place virtual network functions (VNF) inside vDC impact the energy savings and the protection level against resource demand uncertainty. We propose novel optimization models that allow the minimization of the energy of the computing and network infrastructure which is hosting a set of service chains that implement the VNFs. The model explicitly provides for robustness to unknown or imprecisely formulated resource demand variations, powers down unused routers, switch ports and servers, and calculates the energy optimal VNF placement and network embedding also considering latency constraints on the service chains. We propose both exact and heuristic methods. Our experiments were carried out using the virtualized Evolved Packet Core (vEPC), which allows us to quantitatively assess the trade-off between energy cost, robustness and the protection level of the solutions against demand uncertainty. Our heuristic is able to converge to a good solution in a very short time, in comparison to the exact solver, which is not able to output better results in a longer run as demonstrated by our numerical evaluation. We also study the degree of robustness of a solution for a given protection level and the cost of additional energy needed because of the usage of more computing and network elements. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Virtualization binary linear programming Robust optimization Network function virtualization (NW) EPC 5G

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