A Model for Analysing the Collective Dynamic Behaviour and Characterising the Exploitation of Population-Based Algorithms

Several previous studies have focused on modelling and analysing the collective dynamic behaviour of population-based algorithms. However, an empirical approach for identifying and characterising such a behaviour is surprisingly lacking. In this paper, we present a new model to capture this collective behaviour, and to extract and quantify features associated with it. The proposed model studies the topological distribution of an algorithm's activity from both a genotypic and a phenotypic perspective, and represents population dynamics using multiple levels of abstraction. The model can have different instantiations. Here it has been implemented using a modified version of self-organising maps. These are used to represent and track the population motion in the fitness landscape as the algorithm operates on solving a problem. Based on this model, we developed a set of features that characterise the population's collective dynamic behaviour. By analysing them and revealing their dependency on fitness distributions, we were then able to define an indicator of the exploitation behaviour of an algorithm. This is an entropy-based measure that assesses the dependency on fitness distributions of different features of population dynamics. To test the proposed measures, evolutionary algorithms with different crossover operators, selection pressure levels and population handling techniques have been examined, which lead populations to exhibit a wide range of exploitation-exploration behaviours.