623 research outputs found
A hybrid cross entropy algorithm for solving dynamic transit network design problem
This paper proposes a hybrid multiagent learning algorithm for solving the
dynamic simulation-based bilevel network design problem. The objective is to
determine the op-timal frequency of a multimodal transit network, which
minimizes total users' travel cost and operation cost of transit lines. The
problem is formulated as a bilevel programming problem with equilibrium
constraints describing non-cooperative Nash equilibrium in a dynamic
simulation-based transit assignment context. A hybrid algorithm combing the
cross entropy multiagent learning algorithm and Hooke-Jeeves algorithm is
proposed. Computational results are provided on the Sioux Falls network to
illustrate the perform-ance of the proposed algorithm
A Consensus-ADMM Approach for Strategic Generation Investment in Electricity Markets
This paper addresses a multi-stage generation investment problem for a
strategic (price-maker) power producer in electricity markets. This problem is
exposed to different sources of uncertainty, including short-term operational
(e.g., rivals' offering strategies) and long-term macro (e.g., demand growth)
uncertainties. This problem is formulated as a stochastic bilevel optimization
problem, which eventually recasts as a large-scale stochastic mixed-integer
linear programming (MILP) problem with limited computational tractability. To
cope with computational issues, we propose a consensus version of alternating
direction method of multipliers (ADMM), which decomposes the original problem
by both short- and long-term scenarios. Although the convergence of ADMM to the
global solution cannot be generally guaranteed for MILP problems, we introduce
two bounds on the optimal solution, allowing for the evaluation of the solution
quality over iterations. Our numerical findings show that there is a trade-off
between computational time and solution quality
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Using EPECs to model bilevel games in restructured electricity markets with locational prices
CWPE0619 (EPRG0602) Xinmin Hu and Daniel Ralph (Feb 2006) Using EPECs to model bilevel games in restructured electricity markets with locational prices We study a bilevel noncooperative game-theoretic model of electricity markets with locational marginal prices. Each player faces a bilevel optimization problem that we remodel as a mathematical program with equilibrium constraints, MPEC. This gives an EPEC, equilibrium problem with equilibrium constraints. We establish sufficient conditions for existence of pure strategy Nash equilibria for this class of bilevel games and give some applications. We show by examples the effect of network transmission limits, i.e. congestion, on existence of equilibria. Then we study, for more general EPECs, the weaker pure strategy concepts of local Nash and Nash stationary equilibria. We model the latter via complementarity problems, CPs. Finally, we present numerical examples of methods that attempt to find local Nash or Nash stationary equilibria of randomly generated electricity market games. The CP solver PATH is found to be rather effective in this context
Does bilevel optimization result in more competitive racing behavior?
Two-vehicle racing is natural example of a competitive dynamic game. As with
most dynamic games, there are many ways in which the underlying information
pattern can be structured, resulting in different equilibrium concepts. For
racing in particular, the information pattern assumed plays a large impact in
the type of behaviors that can emerge from the two interacting players. For
example, blocking behavior is something that cannot emerge from static Nash
play, but could presumably emerge from leader-follower play. In this work, we
develop a novel model for competitive two-player vehicle racing, complete with
simplified aerodynamic drag and drafting effects, as well as position-dependent
collision-avoidance responsibility. We use this model to explore the impact
that different information patterns have on the resulting competitiveness of
the players. A solution approach for solving bilevel optimization problems is
developed, which allows us to run a large-scale empirical study comparing how
bilevel strategy generation (both as leader and as follower) compares with Nash
equilibrium strategy generation as well as a single-player, constant velocity
prediction baseline. Each of these choices are evaluated against different
combinations of opponent strategy selection method. The somewhat surprising
results of this study are discussed throughout
Integer Bilevel Linear Programming Problems: New Results and Applications
Integer Bilevel Linear Programming Problems: New Results and Application
Integer Bilevel Linear Programming Problems: New Results and Applications
Integer Bilevel Linear Programming Problems: New Results and Application
A reducibility method for the weak linear bilevel programming problems and a case study in principal-agent
© 2018 A weak linear bilevel programming (WLBP) problem often models problems involving hierarchy structure in expert and intelligent systems under the pessimistic point. In the paper, we deal with such a problem. Using the duality theory of linear programming, the WLBP problem is first equivalently transformed into a jointly constrained bilinear programming problem. Then, we show that the resolution of the jointly constrained bilinear programming problem is equivalent to the resolution of a disjoint bilinear programming problem under appropriate assumptions. This may give a possibility to solve the WLBP problem via a single-level disjoint bilinear programming problem. Furthermore, some examples illustrate the solution process and feasibility of the proposed method. Finally, the WLBP problem models a principal-agent problem under the pessimistic point that is also compared with a principal-agent problem under the optimistic point
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