Destructiveness of Lexicographic Parsimony Pressure and Alleviation by a Concatenation Crossover in Genetic Programming

TL;DR

This paper analyzes how lexicographic parsimony pressure causes destructiveness in genetic programming and demonstrates that concatenation crossover can alleviate this issue, leading to more efficient optimization of certain test functions.

Contribution

It introduces a simple concatenation crossover operator combined with local search, showing its effectiveness in mitigating bloat and improving optimization in GP.

Findings

Concatenation crossover improves optimization efficiency.

Lexicographic parsimony pressure can be destructive in GP.

The proposed method outperforms local search alone on test functions.

Abstract

For theoretical analyses there are two specifics distinguishing GP from many other areas of evolutionary computation. First, the variable size representations, in particular yielding a possible bloat (i.e. the growth of individuals with redundant parts). Second, the role and realization of crossover, which is particularly central in GP due to the tree-based representation. Whereas some theoretical work on GP has studied the effects of bloat, crossover had a surprisingly little share in this work. We analyze a simple crossover operator in combination with local search, where a preference for small solutions minimizes bloat (lexicographic parsimony pressure); the resulting algorithm is denoted Concatenation Crossover GP. For this purpose three variants of the well-studied MAJORITY test function with large plateaus are considered. We show that the Concatenation Crossover GP can efficiently optimize these test functions, while local search cannot be efficient for all three variants independent of employing bloat control.