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Optimization of robust area traffic control with equilibrium flow under demand uncertainty

COMPUTERS & OPERATIONS RESEARCH 2014年第1期41卷 399-411页

作者： Chiou, Suh-Wen Natl Dong Hwa Univ Dept Informat Management Shoufeng 97401 Hualien Taiwan

For area traffic control road network under realization of uncertain travel demand, a robust signal setting is investigated in this paper. Due to certain hierarchy in a decision-making order, a min-max bilevel program is proposed. A new solution method is presented to determine a Nash-Stackelberg solution where a proposed signal setting is found for area traffic control under demand uncertainty. In order to investigate the robustness of the proposed signal settings, numerical computations are performed for various initial data sets in a medium-sized example road network. Good computational results indicated that the proposed signal settings can successfully reduce a worst-case travel cost substantially while incurring a relatively slight loss of optimality with respect to the optimal deterministic solutions for nominal travel demands. Particularly, our computation results showed that the proposed signal settings become even attractive as demand growth increases under a worst-case realization taken by uncertain travel demands. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Robust area traffic control bilevel programming problem Equilibrium network flow A min-max program

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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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Multiobjective optimization problem with variational inequality constraints

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MATHEMATICAL programming 2003年第1期96卷 139-160页

作者： Ye, JJ Zhu, QJ Univ Victoria Dept Math & Stat Victoria BC V8W 3P4 Canada Western Michigan Univ Dept Math & Stat Kalamazoo MI 49008 USA

We study a general multiobjective optimization problem with variational inequality, equality, inequality and abstract constraints. Fritz John type necessary optimality conditions involving Mordukhovich coderivatives are derived. They lead to Kuhn-Tucker type necessary optimality conditions under additional constraint qualifications including the calmness condition, the error bound constraint qualification, the no nonzero abnormal multiplier constraint qualification, the generalized Mangasarian-Fromovitz constraint qualification, the strong regularity constraint qualification and the linear constraint qualification. We then apply these results to the multiobjective optimization problem with complementarity constraints and the multiobjective bilevel programming problem.

关键词： multiobjective optimization variational inequality complementarity constraint constraint qualification bilevel programming problem preference utility function subdifferential calculus variational principle

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New uniform parametric error bounds

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1998年第1期98卷 197-219页

作者： Ye, JJ Univ Victoria Dept Math & Stat Victoria BC Canada

A uniform parametric error bound is a uniform error estimate for feasible solutions of a family of parametric mathematical programming problems. It has been proven useful in exact penalty formulation for bilevel programming problems. In this paper, we derive new sufficient conditions for the existence of uniform parametric error bounds.

关键词： uniform parametric error bounds uniform weak sharp minima bilevel programming problem exact penalty functions

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Which efficient solution in multi objective programming problem should be taken?

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CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH 2021年第3期29卷 967-987页

作者： Matejas, Josip Peric, Tunjo Mlinaric, Danijel Fac Econ & Business Zagreb Trg JF Kennedy 6 Zagreb 10000 Croatia

In practical problems, which can be stated in the form of multi objective programming problem, we have usually a large set of efficient solutions. So, which solution from this set should be taken, appears as a natural question here. In the paper we propose some sustainable principles and simple numerical method for such choice. The method respects aspirations and priorities of decision makers and enables iterations for possible improvement of the solution. In this way decision makers can clearly understand why a particular solution is obtained and when and how it can be improved. The features of the method are explained by a practical example. An applications to bilevel programming problems are also presented, where the both side mapping, between the set of efficient solutions and the set of all possible priorities, is shown. It is illustrated in detail through several linear and nonlinear examples.

关键词： Multi objective programming problem Efficient solution Priority Aspiration bilevel programming problem

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A bilevel programming approach to double optimal stopping

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APPLIED MATHEMATICS AND COMPUTATION 2014年 238卷 393-396页

作者： Makasu, Cloud Univ Western Cape Dept Maths & Appl Maths ZA-7535 Bellville South Africa

This paper treats a class of double optimal stopping problems arising in the pricing of integral options. Under certain conditions, we give an explicit form of the double stopping time for such type of optimal stopping problems. The present results are essentially derived by solving a certain nonlinear bilevel programming problem explicitly. (C) 2014 Elsevier Inc. All rights reserved.

关键词： bilevel programming problem Double optimal stopping problem Integral options

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Models and a relaxation algorithm for continuous network design problem with a tradable credit scheme and equity constraints

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COMPUTERS & OPERATIONS RESEARCH 2014年第1期41卷 252-261页

作者： Wang, Guangmin Gao, Ziyou Xu, Meng Sun, Huijun Beijing Jiaotong Univ Inst Syst Sci Beijing 100044 Peoples R China China Univ Geosci Sch Econ & Management Wuhan 430074 Peoples R China Beijing Jiaotong Univ MOE Key Lab Urban Transportat Complex Syst Theory Beijing 100044 Peoples R China

The sustainable problems of transportation have become noticeable in the majority of cities worldwide. Many researchers are devoted themselves into traffic congestion. Generally, traffic congestion could be alleviated via increasing road capacity (supply) or reducing traffic (demand). In this paper, we model CNDP which has a tradable credit scheme and equity constraints in order to research on the way of releasing congestion by combining increasing supply and reducing demand. Firstly, the bilevel programming problem is proposed to model the CNDP with a tradable credit scheme. The upper level (the government) chooses optimal capacity enhancement for some existing links to minimize the total system costs under a budget constraint. The lower level chooses the optimal route based on considering the generalized travel cost in which both travel time and credit charging for using the link are involved. And then, considering the inequity problem in terms of equilibrium O-D travel cost and link travel time, the model is proposed by incorporating equity constraints into CNDP with a tradable credit scheme. After presenting a relaxation algorithm, the experiments on Sioux Falls network are illustrated. Finally, conclusion and some future research directions are presented. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Continuous network design problem (CNDP) bilevel programming problem Relaxation algorithm Tradable credit scheme Equity

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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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Branch-and-bound algorithm for a competitive facility location problem

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COMPUTERS & OPERATIONS RESEARCH 2013年第8期40卷 2062-2070页

作者： Beresnev, Vladimir Sabolev Inst Math Novosibirsk 630090 Russia

We study a mathematical model generalizing the well-known facility location problem. In this model we consider two competing sides successively placing their facilities and aiming to "capture" consumers, in order to make maximal profit. We state the problem as a bilevel integer programming problem, regarding optimal noncooperative solutions as optimal solutions. We propose a branch-and-bound algorithm for finding the optimal noncooperative solution. While constructing the algorithm, we represent our problem as the problem of maximizing a pseudo-Boolean function. An important ingredient of the algorithm is a method for calculating an upper bound for the values of the pseudo-Boolean function on subsets of solutions. We present the results of a simulation demonstrating the computational capabilities of the proposed algorithm. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： bilevel programming problem Pseudo-Boolean function Upper bound Branch-and-bound algorithm Local search

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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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