Search results for "Travelling salesman problem"
showing 2 items of 32 documents
A Primer on Memetic Algorithms
2012
Memetic Algorithms (MAs) are population-based metaheuristics composed of an evolutionary framework and a set of local search algorithms which are activated within the generation cycle of the external framework, see [376]. The earliest MA implementation has been given in [621] in the context of the Travelling Salesman Problem (TSP) while an early systematic definition has been presented in [615]. The concept of meme is borrowed from philosophy and is intended as the unit of cultural transmission. In other words, complex ideas can be decomposed into memes which propagate andmutate within a population.Culture, in this way, constantly undergoes evolution and tends towards progressive improvemen…
Intrinsic Lipschitz Graphs and Vertical β-Numbers in the Heisenberg Group
2016
The purpose of this paper is to introduce and study some basic concepts of quantitative rectifiability in the first Heisenberg group $\mathbb{H}$. In particular, we aim to demonstrate that new phenomena arise compared to the Euclidean theory, founded by G. David and S. Semmes in the 90's. The theory in $\mathbb{H}$ has an apparent connection to certain nonlinear PDEs, which do not play a role with similar questions in $\mathbb{R}^{3}$. Our main object of study are the intrinsic Lipschitz graphs in $\mathbb{H}$, introduced by B. Franchi, R. Serapioni and F. Serra Cassano in 2006. We claim that these $3$-dimensional sets in $\mathbb{H}$, if any, deserve to be called quantitatively $3$-rectifi…