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Operator equalisation was recently proposed as a new bloat control technique for genetic programming. By controlling the distribution of program lengths inside the population, it can bias the search towards smaller or larger programs. In this paper we propose a new implementation of operator equalisation and compare it to a previous version, using a hard real-world regression problem where bloat and overfitting are major issues. The results show that both implementations of operator equalisation are completely bloat-free, producing smaller individuals than standard genetic programming, without compromising the generalization ability. We also show that the new implementation of operator equalisation is more efficient and exhibits a more predictable and reliable behavior than the previous version. We advance some arguable ideas regarding the relationship between bloat and overfitting, and support them with our results. Copyright 2009 ACM.

A new model of Genetic Programming with variable size population is presented in this paper and applied to the reconstruction of target functions in dynamic environments (i.e. problems where target functions change with time). The suitability of this model is tested on a set of benchmarks based on some well known symbolic regression problems. Experimental results confirm that our variable size population model finds solutions of the same quality as the ones found by standard Genetic Programming, but with a smaller amount of computational effort.

Fitness-Proportional Negative Slope Coefficient is a fitness landscapes measure that has recently been introduced as a potential indicator of problem hardness for optimisation. It is inspired to an older measure, the Negative Slope Coefficient, and it has been theoretically modelled. Preliminary experiments have suggested that it may be a good predictor of problem hardness. However, this measure has not undergone any convincing and comprehensive empirical testing. Our objective is to fill this gap. So, we perform empirical tests using a large set of invertible functions of unitation. We find that while this measure may correctly predict the degree of evolvability of a landscape, this does not necessarily correlate with the difficulty of problems. Some landscapes may show, for example, limited evolvability and yet be easy to solve because either solutions are already present in the initial population or the computational resources provided exceed evolvability obstacles. Or it may be impossible to solve them irrespective of their evolvability simply because they are far too vast for the computational resources provided. These situations are hardly captured by the Fitness-Proportional Negative Slope Coefficient.