A bit-masking oriented data structure for evolutionary operators implementation in genetic algorithms

Abstract

In the present paper a special bit-masking oriented data structure for an improved implementation of crossover and mutation operators in genetic algorithms is shown. The developed data structure performs evolutionary operators in two separate steps: crossover and mutation mask ®ll and a special boolean based function application. Both phases are optimized to reach a more ef®cient, fast and¯exible genetic reproduction than standard implementations. The method has been powered adding a multi-layered, bit-masking oriented data structure and a boolean operation based control mixer, allowing special blended crossover operators obtained by superposition of the standard ones. Several examples of crossover schemes produced by these extended controls are presented. In addition, a special purpose crossover scheme, capable to process at the same time two distinct groups of design variables with separate crossover schemes is shown, in order to improve ef®ciency and convergence speed of some discrete/continuous optimization problems. Finally, to highlight further capabilities of the bit-masking approach, a special single-step version of an evolutionary direction operator is also illustrated. IntroductionThe data structures usually employed in binary code based Genetic Algorithms (bGAs) can be essentially subdivided into two typical groups: explicit or implicit binary formulation [1]. First type is obtained using a simple boolean matrix structure (or an equivalent data type) for the population genetic code and a decoding function to properly represent chromosomal, design variable oriented information, packed into an equivalent discrete domain of representation [2] (in this work is de®ned chromosome a genetic structure related to the current design variable, typically a sub-string in explicit binary formulation and an integer decimal value in the implicit one, while genes are binary digits which constitute it, without further distinction between position [locus] and contents [allele]). The main advantage of explicit binary representation is à`n atural'' transposition of the abstract genoma model used for genetic simulations as to the binary data type, with a consequent simpli®cation of genetic operators implementation. The crossover and mutation operators can be easily de®ned by programming a set of operations which, according to a selected scheme (i.e. cut-crossover, mutation), directly works on the boolean array structure, allowing a simple parent-to-child string bit transfer. However, this approach requires additional steps to extract and decode design variables related sub-strings, causing a considerable computer time consuming activity. On the other hand, an implicit binary codi®cation based data structure is simply formed by an integer matrix. This explicit data object is related to a chromosomal level abstraction data, therefore no decoding operations are required to obtain integer design variables values, but a speci®c function, allowing bit weighted integer modi®ca-tions, must be de®ned and applied to emulate genetic i...

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“…In this special version of GA classical procedural genetic operators are replaced by a unique synthetic generator able to emulate all the traditional crossover and mutation schemes, plus many others suggested by specific requests, simply varying the arguments of a special boolean function [13]. In this context the features offered by BMOGA are mainly used to define a multi-level crossover operating in parallel with different methods on partitions of the chromosomal strings.…”

Maintaining regularity and generalization in data using the minimum description length principle and genetic algorithm: Case of grammatical inference

“…In this paper, we have implemented an algorithm GAWMDL for the CFG induction. The proposed GAWMDL is different from the other approaches as it uses the BMODS to perform the reproduction operations [10]. The breeding process is also very different than the former approaches as the proposed GAWMDL incorporates the BBP uses the Boolean based operators (substep-3 in Figure 3), which not only generates the new offspring's, but also alleviates the risk of premature convergence [30] by introducing the diversity in the population.…”

“…Step-3 shows the main functions of the proposed GAWMDL. It utilizes the BMODS [10] to improve the capability of the crossover and mutation operations, replaces various algorithms and codifies specialized rules of mating, supports a formal separation between searching for a proper bit composition and an effective achievement of the offspring's. The previous research signifies that the binary code based GA can be grouped into an explicit and implicit binary formulation [11].…”

“…On the other hand, in bit masking scheme, there is no need to use an explicit data structure, since only high level operations, working on an integer values are mapped into a discrete representation domain are executed. Iuspa [10] has presented a detailed description about the construction of the BMODS. Two integer arrays known as CM and MM are used to perform the crossover and mutation operations.…”

“…The implementation of the BMODS for any real life problem is a two-step process: first apply crossover and mutation maskfill operation and then apply mask application on the selected parent strings. Three crossovers (cut crossover, bit-by-bit and local cut) and a mutation (mutation mask-fill: similar to an inverted mutation has been applied based on a specific mutation rate) operations are applied as suggested in [10].…”