Understanding Grammatical Evolution: Grammar Design

Abstract

A frequently overlooked consideration when using Grammatical Evolution (GE) is grammar design. This is because there is an infinite number of grammars that can specify the same syntax. There are, however, certain aspects of grammar design that greatly affect the speed of convergence and quality of solutions generated with GE. In this chapter, general guidelines for grammar design are presented. These are domain-independent, and can be used when applying GE to any problem. An extensive analysis of their effect and results across a large set of experiments are reported.

Specializing Context-Free Grammars With a (1 + 1)-EA

“…The study was inconclusive, as no statistically significant differences were found between using the original grammar and using the corresponding simplified grammar. More consistent results regarding the relation between grammar structure and search effectiveness have been found recently by Nicolau and Agapitos [12] in the context of GE with linear genome representation. The cited work mostly focused on symbolic regression problems and considered several grammar design aspects, including grammar balancing, type of notation, and symbol biases.…”

“…The key idea is that if a better candidate solution has a higher probability of being generated, then the entire evolutionary search can reach the optimum faster. In fact, it has already been shown experimentally that the quality of the initial population [15] and the biases in the grammar [12] can greatly influence the effectiveness and efficiency of the search. However, we remark that degenerate cases exist: for example, with trap functions [47], increasing the average fitness of the generated candidate solutions might be counterproductive because we might favor the convergence toward local optima, rather than the global optimum.…”

“…It is interesting to point out that the shortcut mutation where the selected subset forms a tree of height limited to 1 corresponds to duplicating existing rules in the grammar. This technique is practically relevant and has been used in GE to change the bias of a grammar [12], often based on some knowledge about the problem being tackled (i.e., about G and f ).…”

“…The relationship between CFGs and fitness landscapes might be exploited to carefully shape the fitness landscape and make the specific problem at hand easier to solve [12]. For example, a CFG could be restructured to repeat the production rules for symbols that should occur more often in candidate solutions of good quality [13,14].…”

Multiobjective Genetic Programming Can Improve the Explanatory Capabilities of Mechanism-Based Models of Social Systems

“…e level of abstraction is also important: lower levels of abstraction usually have more elements and possible combinations. As for the grammar design, good practices can be found in the work of Nicolau and Agapitos [40].…”