15,259 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
Multi-criteria Evolution of Neural Network Topologies: Balancing Experience and Performance in Autonomous Systems
Majority of Artificial Neural Network (ANN) implementations in autonomous
systems use a fixed/user-prescribed network topology, leading to sub-optimal
performance and low portability. The existing neuro-evolution of augmenting
topology or NEAT paradigm offers a powerful alternative by allowing the network
topology and the connection weights to be simultaneously optimized through an
evolutionary process. However, most NEAT implementations allow the
consideration of only a single objective. There also persists the question of
how to tractably introduce topological diversification that mitigates
overfitting to training scenarios. To address these gaps, this paper develops a
multi-objective neuro-evolution algorithm. While adopting the basic elements of
NEAT, important modifications are made to the selection, speciation, and
mutation processes. With the backdrop of small-robot path-planning
applications, an experience-gain criterion is derived to encapsulate the amount
of diverse local environment encountered by the system. This criterion
facilitates the evolution of genes that support exploration, thereby seeking to
generalize from a smaller set of mission scenarios than possible with
performance maximization alone. The effectiveness of the single-objective
(optimizing performance) and the multi-objective (optimizing performance and
experience-gain) neuro-evolution approaches are evaluated on two different
small-robot cases, with ANNs obtained by the multi-objective optimization
observed to provide superior performance in unseen scenarios
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