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TopGene Expression Programming
Gene expression programming was created by Portuguese scientist Ferreira. It is a development of GA (genetic algorithm) and GP (genetic programming design). GEP combines the advantages of both, including the simple and fixed-length coding characteristics of GA, and the indefinite length and indefinite characteristics of the tree structure in GP. Therefore, gene expression programming is much faster than GA or GP.
Gene expression programming processes chromosomes, which consist of genes connected by linking functions. A gene consists of a head and a tail, and the head contains function sets and terminals, while the tail contains only terminals. Thereinto:
(1) where
t represents the length of the gene tail,
h represents the length of the gene head, and
n denotes the maximum number of parameters in the function set.
K-Expressions
Chromosomes are made up of one or more fixed-length, linear, equal-length genes, so genes are also linear and fixed-length. Chromosomes can determine the size and shape of the expression tree. For example, in this simple algebraic equation:
(2)The expression tree of this equation is shown in Figure 1, where q represents the square root. Traversing the expression tree in Figure 1 from top to bottom and left to right yields the corresponding K-expression, as shown in equation (3). The genotype in gene expression programming is:
(3)Figure 1.
The Expression Tree for Equation (2)