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Fuzzy Relation bilevel Optimization Model in the Wireless Communication Station System

IEEE ACCESS 2020年 8卷 60811-60823页

作者： Qiu, Jianjun Xue, Huanbin Li, Guanrong Yang, Xiaopeng Lingnan Normal Univ Sch Math & Stat Zhanjiang 524048 Peoples R China Hanshan Normal Univ Sch Math & Stat Chaozhou 521041 Peoples R China

In order to minimize the intensity of electromagnetic radiation, as well as the operation cost of the base stations in a wireless communication station system, we construct a bilevel programming problem with max-product fuzzy relation inequalities constraint. We first investigate the first level programming problem based on the concept of minimal solution matrix. The complete optimal solution set of the first level problem, as a union of a finite number of closed intervals, is a non-convex infinite set in some cases. Hence the second level programming is a nonlinear optimization problem with non-convex feasible domain. For solving the second level programming, we convert it into a discrete optimization problem, in which the constraint is the set of all minimum max-norm matrix solutions. Furthermore, the discrete optimization problem is equivalently converted into a 0-1 integer programming problem, which could be solved by the famous branch-and-bound technique. Numerical examples are given to illustrate the feasibility and efficiency of our proposed algorithm. In addition, the bilevel programming problem is further generalized and discussed considering a wider range of managerial requirements.

关键词： Fuzzy relation inequality bilevel programming problem max-product composition nonlinear optimization minimum max-norm matrix solution

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Toward a Theory of Systems Engineering Processes: A Principal-Agent Model of a One-Shot, Shallow Process

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IEEE SYSTEMS JOURNAL 2020年第3期14卷 3277-3288页

作者： Safarkhani, Salar Bilionis, Ilias Panchal, Jitesh H. Purdue Univ Sch Mech Engn W Lafayette IN 47907 USA

Systems engineering processes (SEPs) coordinate the effort of different individuals to generate a product satisfying certain requirements. As the involved engineers are self-interested agents, the goals at different levels of the systems engineering hierarchy may deviate from the system-level goals, which may cause budget and schedule overruns. Therefore, there is a need of a systems engineering theory that accounts for the human behavior in systems design. As experience in the physical sciences shows, a lot of knowledge can be generated by studying simple hypothetical scenarios, which nevertheless retain some aspects of the original problem. To this end, the objective of this article is to study the simplest conceivable SEP, a principalagent model of a one-shot, shallow SEP. We assume that the systems engineer (SE) maximizes the expected utility of the system, while the subsystem engineers (sSE) seek to maximize their expected utilities. Furthermore, the SE is unable to monitor the effort of the sSE and may not have complete information about their types. However, the SE can incentivize the sSE by proposing specific contracts. To obtain an optimal incentive, we pose and solve numerically a bilevel optimization problem. Through extensive simulations, we study the optimal incentives arising from different system-level value functions under various combinations of effort costs, problem-solving skills, and task complexities. Our numerical examples show that, the passed-down requirements to the agents increase as the task complexity and uncertainty grow and they decrease with increasing the agents' costs.

关键词： Task analysis Complexity theory Numerical models problem-solving Schedules bilevel programming problem complex systems contract theory expected utility game theory mechanism design optimal incentives principal-agent model systems engineering theory systems science

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Optimality Conditions for Optimistic bilevel programming problem Using Convexifactors

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2012年第3期152卷 632-651页

作者： Kohli, Bhawna Univ Delhi Dept Math Delhi 110007 India

In this article, we introduce two versions of nonsmooth extension of Abadie constraint qualification in terms of convexifactors and Clarke subdifferential and employ the weaker one to develop new necessary Karush-Kuhn-Tucker type optimality conditions for optimistic bilevel programming problem with convex lower-level problem, using an upper estimate of Clarke subdifferential of value function in variational analysis and the concept of convexifactor.

关键词： bilevel programming problem Value function Convexifactor Constraint qualifications Optimality conditions

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Integrating link-based discrete credit charging scheme into discrete network design problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第1期272卷 176-187页

作者： Wang, Guangmin Gao, Ziyou Xu, Meng China Univ Geosci Sch Econ & Management Wuhan 430074 Hubei Peoples R China Beijing Jiaotong Univ Sch Traff & Transportat Beijing 100044 Peoples R China Beijing Jiaotong Univ State Key Lab Rail Traff Control & Safety Beijing 100044 Peoples R China

In this paper, we present an optimization model for integrating link-based discrete credit charging scheme into the discrete network design problem, to improve the transport performance from the perspectives of both transport network planning and travel demand management. The proposed model is a mixed-integer nonlinear bilevel programming problem, which includes an upper level problem for the transport authority and a lower level problem for the network users. The lower level sub-model is the traffic network user equilibrium (UE) formulation for a given network design strategy determined by the upper level problem. The network user at the lower level tries to minimize his/her own generalized travel cost (including both the travel time and the value of the credit charged for using the link) by choosing his/her route. While the transport authority at the upper level tries to find the optimal number of lanes and credit charging level with their locations to minimize the total system travel time (or maximize the transportation system performance). A genetic algorithm is used to solve the proposed mixed-integer nonlinear bilevel programming problem. Numerical experiments show the efficiency of the proposed model for traffic congestion mitigation, reveal that interaction effects across the tradable credit scheme and the discrete network design problem which amplify their individual effects. Moreover, the integrated model can achieve better performance than the sequential decision problems. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Transportation Discrete network design problem (DNDP) bilevel programming problem Tradable credit scheme (TCS)

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A genetic algorithm for solving linear integer bilevel programming problems 14

A genetic algorithm for solving linear integer bilevel progr...

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14th International Conference on Computational Intelligence and Security (CIS)

作者： Liu Yuhui Li Hecheng Chen Huafei Qinghai Normal Univ Sch Comp Sci & Technol Xining 810008 Qinghai Peoples R China Qinghai Normal Univ Sch Math & Stat Xining 810008 Qinghai Peoples R China Sichuan Univ Sci & Engn Sch Math & Stat Zigong 643000 Peoples R China

ISBN: (纸本)9781728101699

This manuscript discusses a class of linear integer bilevel programming problems, in which the objective functions and the constraints are linear. A genetic algorithm based on gradient information guidance is proposed for this kind of problems. First of all, for each fixed upper-level variable x, it is proved that the optimal solution y to the lower level integer programming problem can be obtained by solving associated relaxed problems, and then a simplified branch and bound approach is used to solve the follower-level programming problems. In addition, a crossover operator based on gradient information guidance is designed, and the descendant individual is produced in the negative gradient direction of the upper-level function. The simulation results illustrate that the proposed algorithm is efficient and robust.

关键词： bilevel programming problem genetic algorithm integer programming gradient information optimal solutions

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bilevel programming for generating discrete representations in multiobjective optimization

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MATHEMATICAL programming 2018年第2期169卷 585-604页

作者： Kirlik, Gokhan Sayin, Serpil Univ Maryland Med Syst Enterprise Data & Analyt Linthicum MD 21090 USA Koc Univ Coll Adm Sci & Econ TR-34450 Istanbul Turkey

The solution to a multiobjective optimization problem consists of the nondominated set that portrays all relevant trade-off information. The ultimate goal is to identify a Decision Maker's most preferred solution without generating the entire set of nondominated solutions. We propose a bilevel programming formulation that can be used to this end. The bilevel program is capable of delivering an efficient solution that maps into a given set, provided that one exits. If the Decision Maker's preferences are known a priori, they can be used to specify the given set. Alternatively, we propose a method to obtain a representation of the nondominated set when the Decision Maker's preferences are not available. This requires a thorough search of the outcome space. The search can be facilitated by a partitioning scheme similar to the ones used in global optimization. Since the bilevel programming formulation either finds a nondominated solution in a given partition element or determines that there is none, a representation with a specified coverage error level can be found in a finite number of iterations. While building a discrete representation, the algorithm also generates an approximation of the nondominated set within the specified error factor. We illustrate the algorithm on the multiobjective linear programming problem.

关键词： Multiobjective optimization Decision Maker Representation Nondominated set Coverage error bilevel programming problem

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Towards a fully integrated market for demand response, energy and reserves

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IET GENERATION TRANSMISSION & DISTRIBUTION 2016年第16期10卷 4130-4139页

作者： Saebi, Javad Duy Thanh Nguyen Javidi, Mohammad Hossein Univ Bojnord Dept Elect Engn Bojnord Iran Univ Tasmania Sch Engn & ICT Hobart Tas Australia Ferdowsi Univ Mashhad Dept Elect Engn Mashhad Iran

There is a trend for demand response (DR) market as a dedicated competitive environment for trading DR. In this market, aggregators participate as DR providers, while system operator, retailers and distributors are the DR buyers. Scheduling DR through the DR markets leads to a fair allocation of the benefits and payments across all participants. However, the integration of the DR markets into the existing power markets leads to technical and economic challenges. Those challenges associated with the integration of the DR markets into the energy/reserve markets are addressed in this study. To clear the DR markets jointly with the energy/reserve market, a bilevel approach is proposed in which the upper level belongs to energy/reserve market problem and the lower level includes DR market clearance. The proposed bilevel programming problem is then recast as a mixed-integer linear programming problem which can be solved using commercially available software. Finally, numerical results are provided to illustrate the performance of the proposed approach, demonstrating it brings about lower reserve price and higher social welfare compared with the existing markets.

关键词： power markets demand side management power generation scheduling integer programming linear programming fully integrated market demand response DR scheduling power markets energy reserve market DR market clearance bilevel programming problem mixed-integer linear programming social welfare

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Mid-term vulnerability analysis of power systems under intentional attacks

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IET GENERATION TRANSMISSION & DISTRIBUTION 2016年第15期10卷 3745-3755页

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

This study addresses the vulnerability analysis of power systems over a time horizon. The authors introduce a model which could be used by system operators to assess where and when, over a specific time horizon, their power systems are most vulnerable to intentional attacks. This new time-phased vulnerability analysis is modelled as a bilevel programming problem in which in the upper level, an attacker determines the best attack plan, including the best locations and the best times over the time horizon, for launching attacks. In the lower level, the system operator minimises the system operation and load shedding costs. Using duality theory, the bilevel optimisation problem is converted into a mathematical programming with equilibrium constraints which is subsequently converted to a single-level mixed integer linear programming problem by means of linearisation techniques. This model is tested on modified Garver 6-bus test system, modified IEEE 24-bus reliability test system, and IEEE 300-bus test system. The results appreciate the capability of the proposed model and show that it is indispensable to consider the time in analysing the vulnerability of power systems.

关键词： integer programming linear programming minimisation power system economics load shedding IEEE standards power system mid-term vulnerability analysis intentional attacks time horizon time-phased vulnerability analysis bilevel programming problem load shedding cost minimisation operation cost minimisation duality theory bilevel optimisation problem mathematical programming single-level mixed integer linear programming problem linearisation technique modified Garver 6-bus test system modified IEEE 24-bus reliability test system IEEE 300-bus test system

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Closed-loop Formulation for Nonlinear Dynamic Real-time Optimization

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IFAC-PapersOnLine 2016年第7期49卷 406-411页

作者： Jamaludin, Mohammad Zamry Swartz, Christopher L.E. Department of Chemical Engineering McMaster University 1280 Main St. West HamiltonONL8S 4L7 Canada

Dynamic real-time optimization (DRTO) is a higher level online strategy that exploits plant economic potential by making appropriate adjustments to the lower level controller set-point trajectories. In this work, we propose a closed-loop formulation for a nonlinear DRTO calculation in the form of a bilevel programming problem. A nonlinear differential algebraic equation (DAE) system that describes the process dynamic behavior is utilized with an embedded constrained predictive control (MPC) optimization subproblem to generate the approximate closed-loop response dynamics at the primary economic optimization layer. The bilevel DRTO problem is reformulated as a single-level mathematical program with complementarity constraints (MPCC) by replacing the MPC optimization subproblem by its Karush-Kuhn-Tucker (KKT) optimality conditions. We investigate the economics and control performance of the proposed strategy based on a polymer grade transition case study in the presence of plant-model mismatch and a disturbance, and a comparison is made with the application of a linear DRTO prediction model. © 2016

关键词： Constrained optimization Differential equations Economics Model predictive control Nonlinear equations Predictive control systems Back off mechanisms bilevel programming problem Complementarity constraint Economic optimization Karush Kuhn Tucker (KKT) Mathematical program with complementarity constraints Nonlinear differential algebraic equations Real time optimization

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Indefinite quadratic integer bilevel programming problem with bounded variables

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OPSEARCH 2009年第4期46卷 428-448页

作者： Narang, Ritu Arora, S. R. Univ Delhi Dept Math Delhi India Univ Delhi Hans Raj Coll Dept Math Delhi India

In this paper, an algorithm is developed to solve an indefinite quadratic integer bilevel programming problem with bounded variables. The problem is solved by solving the relaxed problem. A mixed integer cut for findi... 详细信息

关键词： Indefinite quadratic programming problem bilevel programming problem Integer bilevel programming problem with bounded variables Integer programming

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