Search Trajectory Networks of Population-based Algorithms in Continuous Spaces

Abstract

We introduce search trajectory networks (STNs) as a tool to analyse and visualise the behaviour of population-based algorithms in continuous spaces. Inspired by local optima networks (LONs) that model the global structure of search spaces, STNs model the search tra-jectories of algorithms. Unlike LONs, the nodes of the network are not restricted to local optima but instead represent a given state of the search process. Edges represent search progression between consecutive states. This extends the power and applicability of network-based models to understand heuristic search algorithms. We extract and analyse STNs for two well-known population-based algorithms: particle swarm optimi-sation and differential evolution when applied to benchmark continuous optimisation problems. We also offer a comparative visual analysis of the search dynamics in terms of merged search trajectory networks.