Dominant and recessive genes in evolutionary systems applied to spatial reasoning

Abstract

Learning genetic representation has been shown to be a useful tool in evolutionary computation. It can reduce the time required to find solutions and it allows the search process to be biased towards more desirable solutions. Learning genetic representation involves the bottom-up creation of evolved genes from either original (basic) genes or from other evolved genes and the introduction of those into the population. The evolved genes effectively protect combinations of genes that have been found useful from being disturbed by the genetic operations (cross-over, mutation).

However, this protection can rapidly lead to situations where evolved genes interlock in such a way that few or no genetic operations are possible on some genotypes. To prevent the interlocking previous implementations only allow the creation of evolved genes from genes that are direct neighbours on the genotype and therefore form continuous blocks.

In this paper it is shown that the notion of dominant and recessive genes can be used to remove this limitation. Using more than one gene at a single location makes it possible to construct genetic operations that can separate interlocking evolved genes. This allows the use of non-continuous evolved genes with only minimal violations of the protection of evolved genes from those operations. As an example, this paper shows how evolved genes with dominant and recessive genes can be used to learn features from a set of Mondrian paintings. The representation can then be used to create new designs that contain features of the examples. The Mondrian paintings can be coded as a tree, where every node represents a rectangle division, with values for direction, position, linewidth and colour. The modified evolutionary operations allow the system to create non-continuous evolved genes, for example associate two divisions with thin lines, without specifying other values. Analysis of the behaviour of the system shows that about one in ten genes is a dominant/recessive gene pair. This shows that while dominant and recessive genes are important to allow the use of noncontinuous evolved genes, they do not occur often enough to seriously violate the protection of evolved genes from genetic operations.