Controlling Individuals Growth in Semantic Genetic Programming through Elitist Replacement.

Mauro Castelli,Aleš Popovič,Leonardo Vanneschi

doi:10.1155/2016/8326760

Abstract

In 2012, Moraglio and coauthors introduced new genetic operators for Genetic Programming, called geometric semantic genetic operators. They have the very interesting advantage of inducing a unimodal error surface for any supervised learning problem. At the same time, they have the important drawback of generating very large data models that are usually very hard to understand and interpret. The objective of this work is to alleviate this drawback, still maintaining the advantage. More in particular, we propose an elitist version of geometric semantic operators, in which offspring are accepted in the new population only if they have better fitness than their parents. We present experimental evidence, on five complex real-life test problems, that this simple idea allows us to obtain results of a comparable quality (in terms of fitness), but with much smaller data models, compared to the standard geometric semantic operators. In the final part of the paper, we also explain the reason why we consider this a significant improvement, showing that the proposed elitist operators generate manageable models, while the models generated by the standard operators are so large in size that they can be considered unmanageable.

Highlights

In the original definition of Genetic Programming (GP) [1, 2], the operators used to explore the search space, crossover, and mutation produce offspring by manipulating the syntax of the parents
We propose an elitist version of geometric semantic operators, in which offspring are accepted in the new population only if they have better fitness than their parents
Principle of Elitist Geometric Semantic Operators. To partially counteract this problem we propose the following replacement method: (i) Considering two parents P1 and P2, the offspring Ocross obtained from the semantic crossover between P1 and P2 is accepted in the new population if and only if its fitness is better than the fitness of both P1 and P2

Summary

Introduction

In the original definition of Genetic Programming (GP) [1, 2], the operators used to explore the search space, crossover, and mutation produce offspring by manipulating the syntax of the parents. Even using implementation that allows executing the system in a very efficient way (like the one presented in [12]), the problem persists, in the sense that it is in general practically impossible to fully reconstruct the final model generated by GP and whenever it is possible, the resulting expression is so big that it cannot be understood by a human being. For this reason, in this study we define a very simple but effective method that allows GP to produce more compact solutions, without affecting the quality of the final solutions.

Geometric Semantic Operators

Elitist Geometric Semantic Operators

Experimental Study

Findings

Conclusions