On the Avoidance of Fruitless Wraps in Grammatical Evolution

Abstract

Abstract. Grammatical Evolution (GE) is an evolutionary system that employs variable length linear chromosomes to represent computer programs. GE uses the individuals to produce derivation trees that adhere to a Backus Naur Form grammar, which are then mapped onto a program. One unusual characteristic of the system is the manner in which chromosomes can be "wrapped", that is, if an individual has used up all of its genes before a program is completely mapped, the chromosome is reread. While this doesn't guarantee that an individual will map, prior work suggested that wrapping is beneficial for the system, both in terms of increased success rates and a reduced number of invalid individuals. However, there has been no research into the number of times an individual should be wrapped before the system gives up, and an arbitrary upper limit is usually chosen. This paper discusses the different types of grammars that could be used with this system, and indicates the circumstances under which individuals will fail. It then presents a heuristic to minimize the number of wraps that have to be made before the system can determine that an individual will fail. It is shown that this can drastically reduce the amount of wrapping on a pathologically difficult problem, as well as on two classes of grammar often used by the system.

A Competitive Building Block Hypothesis

“…Further, for certain sequences towards the end of the chromosomes, we see relatively high peaks, indicating that many individuals have those sequences, albeit not in the correct position. This seems to support the findings of [17] which postulated the existence of a "stop sequence" in GE. That is, a sequence of genes that can successfully terminate most of the chromosomes in the population.…”

“…The genetic material is reused if the mapping is incomplete at the end of a single pass through the individual. The phenomenon is termed as wrapping and discussed comprehensively in [17].…”

Termination in Grammatical Evolution: grammar design, wrapping, and tails

“…Therefore, a sequence of integers from the genotype will either lead to the termination state, or forever lead back to the <e> state. One can therefore conclude that, with single non-terminal grammars, wrapping never works (this has been shown previously [14]). The reduction of the grammar to a single non-terminal symbol has caused wrapping not to work.…”

“…After a solution was found, each run was stopped, and each codon from each individual was identified as a Producer or Consumer (using the definition originally suggested by Ryan et. al [14]), depending on whether the formula codon % 8 was lower than 4 (meaning the codon will choose a recursive rule from the grammar) or not (opposite case), respectively.…”

Managing Repetition in Grammar-Based Genetic Programming

“…This is particularly the case with mutation on GE's linear representation. Figure 2 shows the grammar used for the K6 experiments; it was designed to minimise biases [15], minimise the number of non-terminal symbols (to reduce the crossover rippleeffect in linear GE [16]), and to be balanced in the sense of choice of producing vs. consuming rules [22,8]. Grammars for all three problems were designed in this way, using the same operators and functions, but with obvious differences in the number of predictors (x1..x5 for V4, x1..x57 for Dow), and with corresponding adapted number of arithmetic operator choices, to re-balance biases.…”