Manuel Clergue

A Study of Fitness Distance Correlation as a Difficulty Measure in Genetic Programming

We present an approach to genetic programming difficulty based on a statistical study of program fitness landscapes. The fitness distance correlation is used as an indicator of problem hardness and we empirically show that such a statistic is adequate in nearly all cases studied here. However, fitness distance correlation has some known problems and these are investigated by constructing an artificial landscape for which the correlation gives contradictory indications. Although our results confirm the usefulness of fitness distance correlation, we point out its shortcomings and give some hints for improvement in assessing problem hardness in genetic programming.

Fitness Clouds and Problem Hardness in Genetic Programming

This paper presents an investigation of genetic programming fitness landscapes. We propose a new indicator of problem hardness for tree-based ge- netic programming, called negative slope coefficient, based on the concept of fitness cloud. The negative slope coefficient is a predictive measure, i.e. it can be calculated without prior knowledge of the global optima. The fitness cloud is gener- ated via a sampling of individuals obtained with the Metropolis-Hastings method. The reliability of the negative slope coefficient is tested on a set of well known and representative genetic programming benchmarks, comprising the binomial-3 problem, the even parity problem and the artificial ant on the Santa Fe trail.

Fitness distance correlation in structural mutation genetic programming

A new kind of mutation for genetic programming based on the structural distance operators for trees is presented in this paper. We firstly describe a new genetic programming process based on these operators (we call it structural mutation genetic programming). Then we use structural distance to calculate the fitness distance correlation coefficient and we show that this coefficient is a reasonable measure to express problem difficulty for structural mutation genetic programming for the considered set of problems, i.e. unimodal trap functions, royal trees and MAX problem.

Where are bottlenecks in NK fitness landscapes

Usually the offspring-parent fitness correlations is used to visualize and analyze some characteristics of fitness landscapes such as evolvability. In this paper, we introduce a more general representation of this correlation, the fitness cloud (FC). We use the bottleneck metaphor to emphasis fitness levels in landscape that cause local search process to slow down. For a local search heuristic such as hill-climbing or simulated annealing, FC allows one to visualize the bottleneck and neutrality of landscapes. To confirm the relevance of the FC representation we show where the bottlenecks are in the well-known NK fitness landscape and also how to use neutrality information from the FC to combine some neutral operator with local search heuristic.

Maximum homologous crossover for linear genetic programming

We introduce a new recombination operator, the Maximum Homologous Crossover for Linear Genetic Programming. In contrast to standard crossover, it attempts to preserve similar structures from parents, by aligning them according to their homology, thanks to an algorithm used in Bio-Informatics. To highlight disruptive effects of crossover operators, we introduce the Royal Road landscapes and the Homology Driven Fitness problem, for Linear Genetic Programming. Two variants of the new crossover operator are described and tested on this landscapes. Results show a reduction in the bloat phenomenon and in the frequency of deleterious crossovers.

Scuba search: when selection meets innovation

We proposed a search heuristic using the scuba diving metaphor. This approach is based on the concept of evolvability and tends to exploit neutrality in fitness landscape. Despite the fact that natural evolution does not directly select for evolvability, the basic idea behind the scuba search heuristic is to explicitly push evolvability to increases. Globally the search process switches between two phases: conquest-of-the-waters and invasion-of-the-land. A comparative study of the algorithm and standard local search heuristics on the NKq-landscapes has shown advantage and limit of the scuba search. To enlighten qualitative differences between neutral search processes, the space is transformed into a connected graph to visualize the pathways that the search is likely to follow.

Anisotropic selection in cellular genetic algorithms

In this paper we introduce a new selection scheme in cellular genetic algorithms (cGAs). Anisotropic Selection (AS) promotes diversity and allows accurate control of the selective pressure. First we compare this new scheme with the classical rectangular grid shapes solution according to the selective pressure: we can obtain the same takeover time with the two techniques although the spreading of the best individual is different. We then give experimental results that show to what extent AS promotes the emergence of niches that support low coupling and high cohesion. Finally, using a cGA with anisotropic selection on a Quadratic Assignment Problem we show the existence of an anisotropic optimal value for which the best average performance is observed. Further work will focus on the selective pressure self-adjustment ability provided by this new selection scheme.

GA-hard functions built by combination of Trap functions

We propose to construct hard functions for genetic algorithms by combining two types of misleading functions. We consider on one hand the traditional Trap functions defined over the unitation, and on the other hand new Trap functions based on the alternation. We recall the performance of GA on these functions as well as the results on the predictive value of the coefficients of correlation between distance to the optimum and fitness. We show that the combination of such functions can generate misleading problems for a genetic algorithm. Moreover, some of these combinations constitute counterexamples for the predictive value of the coefficient of correlation.

On the influence of selection operators on performances in cellular Genetic Algorithms

In this paper, we study the influence of the selective pressure on the performance of cellular genetic algorithms. Cellular genetic algorithms are genetic algorithms where the population is embedded on a toroidal grid. This structure makes the propagation of the best so far individual slow down, and allows to keep in the population potentially good solutions. We present two selective pressure reducing strategies in order to slow down even more the best solution propagation. We experiment these strategies on a hard optimization problem, the quadratic assignment problem, and we show that there is a threshold value of the control parameter for both which gives the best performance. This optimal value does not find explanation on the selective pressure only, measured either by takeover time or diversity evolution. This study makes us conclude that we need other tools than the sole selective pressure measures to explain the performance of cellular genetic algorithms.

Difficulty of unimodal and multimodal landscapes in genetic programming

This paper presents an original study of fitness distance correlation as a measure of problem difficulty in genetic programming. A new definition of distance, called structural distance, is used and suitable mutation operators for the program space are defined. The difficulty is studied for a number of problems, including, for the first time in GP, multimodal ones, both for the new hand-tailored mutation operators and standard crossover. Results are in agreement with empirical observations, thus confirming that fitness distance correlation can be considered a reasonable index of difficulty for genetic programming, at least for the set of problems studied here.