Solving nonlinear bilevel programming models of the equilibrium network design problem: A comparative review

Suh, Sunduck; Kim, Tschangho John

doi:10.1007/bf02098180

Cited by 75 publications

(21 citation statements)

References 18 publications

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“…Abdulaal and LeBlanc (1979) introduced the CNDP with user equilibrium and presented a direct search algorithm. Suh and Kim (1992) presented a descent algorithm for non-linear bilevel problems. Due to the complexity of the problem, many metaheuristics were proposed in the literature.…”

Section: Discrete Network Design Problemmentioning

confidence: 99%

Methodological Advances and New Formulations for Bilevel Network Design Problems

Fontaine

2018

Operations Research Proceedings

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Section: Discrete Network Design Problemmentioning

confidence: 99%

Methodological Advances and New Formulations for Bilevel Network Design Problems

Fontaine

2018

Operations Research Proceedings

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“…The bilevel programming problem (BLPP) has a wide variety of applications, and bilevel programming techniques have been applied with remarkable success in different domains such as decentralized resource planning [30], transport system planning [31], civil engineering [32], road network management [33], power market [34], economics, and management [35,36]. The existing methods for solving BP can be categorized as traditional method and heuristic (stochastic) method.…”

Section: Background and Related Workmentioning

confidence: 99%

Two novel price-based algorithms for spectrum sharing in cognitive radio networks

Weng

Lee

Chen

2013

J Wireless Com Network

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Cognitive radio network is expected to use flexible radio frequency spectrum sharing techniques for achieving more efficient frequency spectrum usage. In this article, we consider the spectrum sharing problem that one primary user (PU) can share its frequency spectrum by renting this spectrum to multiple secondary users (SUs). The pricing scheme is a key issue for spectrum sharing in cognitive radio network. We first propose a nonlinear one-leader-multiple-follower (NLMF) sharing spectrum scheme as a multi-object optimization problem; the prices are offered by PU to SUs at the same time. This problem can be solved using particle swarm optimization (PSO); SUs gradually and iteratively adjust their strategies respectively based on the observations on their opponents' previous strategies until Nash equilibrium is completed. We then present a general nonlinear bilevel one-leader-multiple-follower (NBMF) optimization problem to further consider the revenue of the PU and a new optimal strategic pricing optimization technique which applies bilevel programming and swarm intelligence. A leader-follower game is formulated to obtain the Stackelberg-Nash equilibrium for spectrum sharing that considers not only revenue of a PU but also the SUs utility. We develop a swarm particle algorithm to iteratively solve the problem defined in the NBMF decision model for searching the strategic pricing optimization. The behaviors of two pricing models have been evaluated, and the performance results show that the proposed algorithms perform well to solve the spectrum sharing in a cognitive radio network.

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“…Returning, then, to the issues concerning the interpretation of the sensitivity analysis, the point we would make secondly is that at no stage shall we apply the interpretation of the sensitivity analysis as a gradient (or sub-gradient) of at = 0, as one may do, for example, in some applications to bi-level optimisation (Suh & Kim, 1992;Davis, 1994;Josefson & Patriksson, 2003;Patriksson, 2004). In particular, our algorithm in section 4.6 makes no explicit use of the sensitivity analysis as a gradient.…”

Section: Interpretations Of Sensitivity Analysismentioning

confidence: 99%

Applications of sensitivity analysis for probit stochastic network equilibrium

Clark

Watling

2006

European Journal of Operational Research

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-Network equilibrium models are widely used by traffic practitioners to aid them in making decisions concerning the operation and management of traffic networks. The common practice is to test a prescribed range of hypothetical changes or policy measures through adjustments to the input data, namely the trip demands, the arc performance (travel time) functions, and policy variables such as tolls or signal timings. Relatively little use is, however, made of the full implicit relationship between model inputs and outputs inherent in these models. By exploiting the representation of such models as an equivalent optimisation problem, classical results on the sensitivity analysis of non-linear programs may be applied, to produce linear relationships between input data perturbations and model outputs. We specifically focus on recent results relating to the probit Stochastic User Equilibrium (PSUE) model, which has the advantage of greater behavioural realism and flexibility relative to the conventional Wardrop user equilibrium and logit SUE models. The paper goes on to explore four applications of these sensitivity expressions in gaining insight into the operation of road traffic networks. These applications are namely: identification of sensitive, 'critical' parameters; computation of approximate, re-equilibrated solutions following a change (postoptimisation); robustness analysis of model forecasts to input data errors, in the form of confidence interval estimation; and the solution of problems of the bi-level, optimal network design variety. Finally, numerical experiments applying these methods are reported.

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Solving nonlinear bilevel programming models of the equilibrium network design problem: A comparative review

Cited by 75 publications

References 18 publications

Methodological Advances and New Formulations for Bilevel Network Design Problems

Methodological Advances and New Formulations for Bilevel Network Design Problems

Two novel price-based algorithms for spectrum sharing in cognitive radio networks

Applications of sensitivity analysis for probit stochastic network equilibrium

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