A novel splicing/decomposable binary encoding and its operators for genetic and evolutionary algorithms

In this paper, we introduce a new genetic representation - a splicing/decomposable (S/D) binary encoding, which was proposed based on some theoretical guidance and existing recommendations for designing efficient genetic representations. The S/D binary representation can be spliced and decomposed to describe potential solutions of the problem with different precisions by different number of uniform-salient building blocks (BBs). According to the characteristics of the S/D binary representation, genetic and evolutionary algorithms (GEAs) can be applied from the high scaled to the low scaled BBs sequentially to avoid a noise from the competing BBs and improve GEAs' performance. Our theoretical and empirical investigations reveal that the S/D binary representation is more proper than other existing binary encodings for GEAs searching. Moreover, we define a new genotypic distance on the S/D binary space, which is equivalent to the Euclidean distance on the real-valued space during GEAs convergence. Based on the new genotypic distance, GEAs can reliably and predictably solve problems of bounded complexity and the methods depended on the Euclidean distance for solving different kinds of optimization problems can be directly used on the S/D binary space.