2 research outputs found
A practical approach to solve coupled systems of nonlinear partial differential equations
In this paper we present the tanh method to obtain exact solutions to coupled
MkDV system. This method may be applied to a variety of coupled systems of
nonlinear ordinary and partial differential equations
Clustering with Penalty for Joint Occurrence of Objects: Computational Aspects
The method of Hol\'y, Sokol and \v{C}ern\'y (Applied Soft Computing, 2017,
Vol. 60, p. 752-762) clusters objects based on their incidence in a large
number of given sets. The idea is to minimize the occurrence of multiple
objects from the same cluster in the same set. In the current paper, we study
computational aspects of the method. First, we prove that the problem of
finding the optimal clustering is NP-hard. Second, to numerically find a
suitable clustering, we propose to use the genetic algorithm augmented by a
renumbering procedure, a fast task-specific local search heuristic and an
initial solution based on a simplified model. Third, in a simulation study, we
demonstrate that our improvements of the standard genetic algorithm
significantly enhance its computational performance