Ruggedness, funnels and gradients in fitness landscapes and the effect on PSO performance

Fitness landscape analysis has focussed on many different aspects of optimisation problems such as ruggedness, neutrality, epistasis and evolvability. Although many techniques have been proposed, there are very few that have been shown to be practically useful as predictors of algorithm performance. This paper investigates three metrics related to the structure of fitness landscapes of continuous problems: a ruggedness measure based on entropy, a dispersion index measure for detecting the presence of funnels and a new proposed technique for estimating gradients. Results on a range of benchmark problems show that all proposed measures show some correlation to performance of a traditional particle swarm optimisation (PSO) algorithm on the same benchmark problems. The three metrics could therefore have value as part-predictors of PSO performance on unknown problems if used in conjunction with measures approximating other features that have been linked to problem difficulty for PSOs.