1,379 research outputs found
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
A parametric integer programming algorithm for bilevel mixed integer programs
We consider discrete bilevel optimization problems where the follower solves
an integer program with a fixed number of variables. Using recent results in
parametric integer programming, we present polynomial time algorithms for pure
and mixed integer bilevel problems. For the mixed integer case where the
leader's variables are continuous, our algorithm also detects whether the
infimum cost fails to be attained, a difficulty that has been identified but
not directly addressed in the literature. In this case it yields a ``better
than fully polynomial time'' approximation scheme with running time polynomial
in the logarithm of the relative precision. For the pure integer case where the
leader's variables are integer, and hence optimal solutions are guaranteed to
exist, we present two algorithms which run in polynomial time when the total
number of variables is fixed.Comment: 11 page
Fuzzy Bi-level Decision-Making Techniques: A Survey
© 2016 the authors. Bi-level decision-making techniques aim to deal with decentralized management problems that feature interactive decision entities distributed throughout a bi-level hierarchy. A challenge in handling bi-level decision problems is that various uncertainties naturally appear in decision-making process. Significant efforts have been devoted that fuzzy set techniques can be used to effectively deal with uncertain issues in bi-level decision-making, known as fuzzy bi-level decision-making techniques, and researchers have successfully gained experience in this area. It is thus vital that an instructive review of current trends in this area should be conducted, not only of the theoretical research but also the practical developments. This paper systematically reviews up-to-date fuzzy bi-level decisionmaking techniques, including models, approaches, algorithms and systems. It also clusters related technique developments into four main categories: basic fuzzy bi-level decision-making, fuzzy bi-level decision-making with multiple optima, fuzzy random bi-level decision-making, and the applications of bi-level decision-making techniques in different domains. By providing state-of-the-art knowledge, this survey paper will directly support researchers and practitioners in their understanding of developments in theoretical research results and applications in relation to fuzzy bi-level decision-making techniques
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