Fitness-Probability Cloud and a Measure of Problem Hardness for Evolutionary Algorithms

Evolvability is an important feature directly related to problem hardness for Evolutionary Algorithms (EAs). A general relationship that holds for Evolvability and problem hardness is the higher the degree of evolvability, the easier the problem is for EAs. This paper presents, for the first time, the concept of Fitness-Probability Cloud (fpc) to characterise evolvability from the point of view of escape probability and fitness correlation. Furthermore, a numerical measure called Accumulated Escape Probability (aep) based on fpc is proposed to quantify this feature, and therefore problem difficulty. To illustrate the effectiveness of our approach, we apply it to four test problems: OneMax, Trap, OneMix and Subset Sum. We then contrast the predictions made by the aep to the actual performance measured using the number of fitness evaluations. The results suggest that the new measure can reliably indicate problem hardness for EAs.

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