37,953 research outputs found
ND-Tree-based update: a Fast Algorithm for the Dynamic Non-Dominance Problem
In this paper we propose a new method called ND-Tree-based update (or shortly
ND-Tree) for the dynamic non-dominance problem, i.e. the problem of online
update of a Pareto archive composed of mutually non-dominated points. It uses a
new ND-Tree data structure in which each node represents a subset of points
contained in a hyperrectangle defined by its local approximate ideal and nadir
points. By building subsets containing points located close in the objective
space and using basic properties of the local ideal and nadir points we can
efficiently avoid searching many branches in the tree. ND-Tree may be used in
multiobjective evolutionary algorithms and other multiobjective metaheuristics
to update an archive of potentially non-dominated points. We prove that the
proposed algorithm has sub-linear time complexity under mild assumptions. We
experimentally compare ND-Tree to the simple list, Quad-tree, and M-Front
methods using artificial and realistic benchmarks with up to 10 objectives and
show that with this new method substantial reduction of the number of point
comparisons and computational time can be obtained. Furthermore, we apply the
method to the non-dominated sorting problem showing that it is highly
competitive to some recently proposed algorithms dedicated to this problem.Comment: 15 pages, 21 figures, 3 table
A Formal Methods Approach to Pattern Synthesis in Reaction Diffusion Systems
We propose a technique to detect and generate patterns in a network of
locally interacting dynamical systems. Central to our approach is a novel
spatial superposition logic, whose semantics is defined over the quad-tree of a
partitioned image. We show that formulas in this logic can be efficiently
learned from positive and negative examples of several types of patterns. We
also demonstrate that pattern detection, which is implemented as a model
checking algorithm, performs very well for test data sets different from the
learning sets. We define a quantitative semantics for the logic and integrate
the model checking algorithm with particle swarm optimization in a
computational framework for synthesis of parameters leading to desired patterns
in reaction-diffusion systems
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