750 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
Finding Optimal Strategies in a Multi-Period Multi-Leader-Follower Stackelberg Game Using an Evolutionary Algorithm
Stackelberg games are a classic example of bilevel optimization problems,
which are often encountered in game theory and economics. These are complex
problems with a hierarchical structure, where one optimization task is nested
within the other. Despite a number of studies on handling bilevel optimization
problems, these problems still remain a challenging territory, and existing
methodologies are able to handle only simple problems with few variables under
assumptions of continuity and differentiability. In this paper, we consider a
special case of a multi-period multi-leader-follower Stackelberg competition
model with non-linear cost and demand functions and discrete production
variables. The model has potential applications, for instance in aircraft
manufacturing industry, which is an oligopoly where a few giant firms enjoy a
tremendous commitment power over the other smaller players. We solve cases with
different number of leaders and followers, and show how the entrance or exit of
a player affects the profits of the other players. In the presence of various
model complexities, we use a computationally intensive nested evolutionary
strategy to find an optimal solution for the model. The strategy is evaluated
on a test-suite of bilevel problems, and it has been shown that the method is
successful in handling difficult bilevel problems.Comment: To be published in Computers and Operations Researc
Efficient Learning of Decision-Making Models: A Penalty Block Coordinate Descent Algorithm for Data-Driven Inverse Optimization
Decision-making problems are commonly formulated as optimization problems,
which are then solved to make optimal decisions. In this work, we consider the
inverse problem where we use prior decision data to uncover the underlying
decision-making process in the form of a mathematical optimization model. This
statistical learning problem is referred to as data-driven inverse
optimization. We focus on problems where the underlying decision-making process
is modeled as a convex optimization problem whose parameters are unknown. We
formulate the inverse optimization problem as a bilevel program and propose an
efficient block coordinate descent-based algorithm to solve large problem
instances. Numerical experiments on synthetic datasets demonstrate the
computational advantage of our method compared to standard commercial solvers.
Moreover, the real-world utility of the proposed approach is highlighted
through two realistic case studies in which we consider estimating risk
preferences and learning local constraint parameters of agents in a multiplayer
Nash bargaining game
AdaBiM: An adaptive proximal gradient method for structured convex bilevel optimization
Bilevel optimization is a comprehensive framework that bridges single- and
multi-objective optimization. It encompasses many general formulations,
including, but not limited to, standard nonlinear programs. This work
demonstrates how elementary proximal gradient iterations can be used to solve a
wide class of convex bilevel optimization problems without involving
subroutines. Compared to and improving upon existing methods, ours (1) can
handle a wider class of problems, including nonsmooth terms in the upper and
lower level problems, (2) does not require strong convexity or global Lipschitz
gradient continuity assumptions, and (3) provides a systematic adaptive
stepsize selection strategy, allowing for the use of large stepsizes while
being insensitive to the choice of parameters
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