A crossover for complex building blocks overlapping

Abstract

We propose a crossover method to combine complexly overlapping building blocks (BBs). Although there have been several techniques to identify linkage sets of loci o form a BB [4,6,7,10, 11], the way to to realize effective crossover from the linkage information from such techniques has not been studied enough. Especially for problems with overlapping BBs, a crossover method proposed by Yu et al. [13] is the first and only known research, however it cannot perform well for problems with complexly overlapping BBs due to insufficient variety of crossover sites. In this paper, we propose a crossover method which examines values of given parental strings minutely and defines which variables are exchanged to produce new and different strings without increasing BB disruptions as much as possible. The method is combined with a scalable linkage identification technique to construct an efficient algorithm for problems with overlapping BBs. We design test functions with controllable complexity of overlap and test the method with the functions.

Empirical investigations on parallel competent genetic algorithms

“…We employ test functions composed of the sum of overlapping 5-bit trap functions used in [27]. Unlike the original 5-bit trap function defined in (2), the components of each trap function are chosen stochastically.…”

“…Before considering the above mentioned parallel competent GAs, we show and parallelize another competent GA employing a linkage identification method called Dependency Detection for Distribution Derived from fitness Differences (D 5 ) [28] and a crossover method for complexly overlapping BBs called Context Dependent Crossover (CDC) [27].…”

“…For overlapping BBs such as 1 * * 11 * * * · and * * 100 * * * · · · , D 5 -GA employs Context Dependent Crossover (CDC) [27] to combine them appropriately. CDC is the extension of the crossover method proposed by Yu et.…”

“…The D 5 (Dependency detection for distribution derived from fitness differences) [28] identifies the linkage in a hybrid manner, by combining linkage identification techniques of PMs and EDAs. To exploit the linkage, D 5 -GA employs a crossover method called CDC (Context dependent crossover) [27] which can combine overlapping building blocks.…”

The essence of real-valued characteristic function for pairwise relation in linkage learning for EDAs

“…The idea is using a minimal cut algorithm to disrupt minimal number of overlapping BBs. Tsuji et al [16] then modified Yu's crossover method so that it could increase BB mixing rate without disrupting more BBs by considering identical allele values. The above crossover methods do not have static cross sites (some BBs will be disrupted).…”