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.
This paper presents an investigation of genetic programming fitness landscapes. We propose a new indicator of problem hardness for tree-based genetic 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 generated 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.
Abstract-Usually the offspring-parent fitness correlation is used to visualize and analyze some caracteristics 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 emphasise 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 to visualize bottleneck and neutrality of landscapes. To confirm the relevance of the FC representation we show where the bottlenecks are in the wellknow NK fitness landscape and also how to use neutrality information from the FC to combine some neutral operator with local search heuristic.
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