Search results for "Bilevel optimization"
showing 5 items of 5 documents
Two-Player Noncooperative Games over a Freight Transportation Network''
2004
A game between two players acting on the same road transportation network is considered in this paper. The first player aims at minimizing the transportation costs, whereas the second player aims at maximizing her profit (or, in general, her utility) that is proportional to the flow passing through the arcs under her control. We introduce bilevel linear programming formulations for this problem. We derive conditions of existence and properties of the equilibrium points and propose an algorithm finding a local optimal solution. Finally, we present an application of the model to a real system involving trucks travelling through Europe from a Middle Eastern country.
Implicit differentiation for fast hyperparameter selection in non-smooth convex learning
2022
International audience; Finding the optimal hyperparameters of a model can be cast as a bilevel optimization problem, typically solved using zero-order techniques. In this work we study first-order methods when the inner optimization problem is convex but non-smooth. We show that the forward-mode differentiation of proximal gradient descent and proximal coordinate descent yield sequences of Jacobians converging toward the exact Jacobian. Using implicit differentiation, we show it is possible to leverage the non-smoothness of the inner problem to speed up the computation. Finally, we provide a bound on the error made on the hypergradient when the inner optimization problem is solved approxim…
Simultaneous and multi-criteria optimization of TS requirements and maintenance at NPPs
2002
Abstract One of the main concerns of the nuclear industry is to improve the availability of safety-related systems at nuclear power plants (NPPs) to achieve high safety levels. The development of efficient testing and maintenance has been traditionally one of the different ways to guarantee high levels of systems availability, which are implemented at NPP through technical specification and maintenance requirements (TS&M). On the other hand, there is a widely recognized interest in using the probabilistic risk analysis (PRA) for risk-informed applications aimed to emphasize both effective risk control and effective resource expenditures at NPPs. TS&M-related parameters in a plant are associ…
Modelling Airlines Competition on Fares and Frequencies of Service by Bi-level Optimization
2011
Abstract The research aims to understand how airlines make operative decisions on fares and frequencies of service in a competitive envi-ronment. A game approach has been developed to model the airlines’ choices in a duopolistic market. In particular, the short haul market for intercity linkages has been investigated. In this segment the air mode is in competition with other ground modes (i.e. road and high speed rail). A bi-level optimization program has been realized. The variables of model are: fares and frequencies of airlines.
Connections Between Single-Level and Bilevel Multiobjective Optimization
2011
The relationship between bilevel optimization and multiobjective optimization has been studied by several authors and there have been repeated attempts to establish a link between the two. We unify the results from the literature and generalize them for bilevel multiobjective optimization. We formulate sufficient conditions for an arbitrary binary relation to guarantee equality between the efficient set produced by the relation and the set of optimal solutions to a bilevel problem. In addition, we present specially structured bilevel multiobjective optimization problems motivated by real-life applications and an accompanying binary relation permitting their reduction to single-level multiob…