Transit sets of -point crossover operators

Topological Representation of the Transit Sets of k-Point Crossover Operators

k-point crossover operators and their recombination sets are studied from different perspectives. We show that transit functions of k-point crossover generate, for all k > 1, the same convexity as the interval function of the underlying graph. This settles in the negative an open problem by Mulder about whether the geodesic convexity of a connected graph G is uniquely determined by its interval...

POWERSET OPERATORS OF EXTENSIONAL FUZZY SETS

Powerset structures of extensional fuzzy sets in sets with similarity relations are investigated. It is proved that extensional fuzzy sets have powerset structures which are powerset theories in the category of sets with similarity relations, and some of these powerset theories are defined also by algebraic theories (monads). Between Zadeh's fuzzy powerset theory and the classical powerset theo...

One-Point Geometric Crossover

Uniform crossover for binary strings has a natural geometric interpretation that allows us to generalize it rigorously to any search space endowed with a notion of distance and any representation [6]. In this paper, we present an analogous characterization for one-point crossover and explicitly derive formally specific one-point crossovers for a number of well-known representations.

Rate of convergence of crossover operators

We study the convergence of mating operators on {0, 1}n. In particular, we answer questions of Rabani, Rabinovich and Sinclair (cf. [5]) by giving tight estimates on the divergence between the finiteand infinite-population processes, thus solving positively the problem of the simulability of such quadratic dynamical systems. c © (Year) John Wiley & Sons, Inc.

Fuzzy sets form A meta-system-theoretic point of view