Investigation of the Performance of Different Mapping Orders for GE on the Max Problem

Abstract

We present an analysis of how the genotype-phenotype map in Grammatical Evolution (GE) can effect performance on the Max Problem. Earlier studies have demonstrated a performance decrease for Position Independent Grammatical Evolution (πGE ) in this problem domain. In πGE the genotype-phenotype map is changed so that the evolutionary algorithm controls not only what the next expansion will be but also the choice of what position in the derivation tree is expanded next. In this study we extend previous work and investigate whether the ability to change the order of expansion is responsible for the performance decrease or if the problem is simply that a certain order of expansion in the genotype-phenotype map is responsible. We conclude that the reduction of performance in the Max problem domain by πGE is rooted in the way the genotype-phenotype map and the genetic operators used with this mapping interact.

Understanding Grammatical Evolution: Grammar Design

“…An example is the typical grammar used with GE for the Max problem [8]. Inconsistent results were obtained with different GE mapping orders [5], and further analysis [4] produced no clear explanations for this issue; it was subsequently shown [27] that the grammar used in those experiments suffered from functionally linked productions.…”

Natural Computing Algorithms

“…A number of variations including breadth-first, random and evolved orders have been examined [182,183,184,206]. The standard GE mapper adopts a depth-first expansion of the available nonterminals.…”

Genotype-phenotype mapping in dynamic environments with grammatical evolution

“…In [6] investigation into this observed decrease in performance of πGE on the Max problem led to the introduction of some new variants of both the GE and πGE mappings. Some new variations of mappers where required.…”

“…Can further inspiration be taken from biology which first inspired the GPM in GP to improve the EA. Recently these topics have started to be tackled [8,15,6,7,1,14], but many more avenues of exploration remain as the interpretation of mapping used by GE is simplistic and lacking in some of the desired advanced features of the GPM that exist in nature [3].…”