Influence of Topological Features on Spatially-Structured Evolutionary Algorithms Dynamics

TL;DR

This paper explores how different network topologies influence the behavior and effectiveness of spatially-structured evolutionary algorithms, particularly in multi-modal optimization, revealing that network features significantly affect diversity and convergence.

Contribution

It introduces a novel spatially-structured evolutionary algorithm framework and analyzes the impact of various network topologies, including weighted and time-varying graphs, on algorithm dynamics.

Findings

Networks with larger Average Path Length increase the number of optima found.

Weighted networks enable tuning of algorithm dynamics during execution.

Network topology significantly affects diversity and convergence in evolutionary algorithms.

Abstract

In the last decades, complex networks theory significantly influenced other disciplines on the modeling of both static and dynamic aspects of systems observed in nature. This work aims to investigate the effects of networks' topological features on the dynamics of an evolutionary algorithm, considering in particular the ability to find a large number of optima on multi-modal problems. We introduce a novel spatially-structured evolutionary algorithm and we apply it on two combinatorial problems: ONEMAX and the multi-modal NMAX. Considering three different network models we investigate the relationships between their features, algorithm's convergence and its ability to find multiple optima (for the multi-modal problem). In order to perform a deeper analysis we investigate the introduction of weighted graphs with time-varying weights. The results show that networks with a large Average Path Length lead to an higher number of optima and a consequent slow exploration dynamics (i.e. low First Hitting Time). Furthermore, the introduction of weighted networks shows the possibility to tune algorithm's dynamics during its execution with the parameter related with weights' change. This work gives a first answer about the effects of various graph topologies on the diversity of evolutionary algorithms and it describes a simple but powerful algorithmic framework which allows to investigate many aspects of ssEAs dynamics.