Motif Difficulty (MD): A Predictive Measure of Problem Difficulty for Evolutionary Algorithms Using Network Motifs

Abstract

One of the major challenges in the field of evolutionary algorithms (EAs) is to characterise which kinds of problems are easy and which are not. Researchers have been attracted to predict the behaviour of EAs in different domains. We introduce fitness landscape networks (FLNs) that are formed using operators satisfying specific conditions and define a new predictive measure that we call motif difficulty (MD) for comparison-based EAs. Because it is impractical to exhaustively search the whole network, we propose a sampling technique for calculating an approximate MD measure. Extensive experiments on binary search spaces are conducted to show both the advantages and limitations of MD. Multidimensional knapsack problems (MKPs) are also used to validate the performance of approximate MD on FLNs with different topologies. The effect of two representations, namely binary and permutation, on the difficulty of MKPs is analysed.