Evolutionary Diversity Optimization and the Minimum Spanning Tree Problem

TL;DR

This paper explores diversity optimization for the Minimum Spanning Tree problem using evolutionary algorithms, providing theoretical insights and demonstrating effective diversification of high-quality solutions.

Contribution

It offers the first theoretical analysis of diversity optimization in MST and shows that simple evolutionary algorithms can efficiently produce diverse, high-quality spanning trees.

Findings

Polynomial-time computation of diverse solutions

Fitness landscape insights for MST diversity optimization

Effective diversification with simple evolutionary algorithms

Abstract

In the area of evolutionary computation the calculation of diverse sets of high-quality solutions to a given optimization problem has gained momentum in recent years under the term evolutionary diversity optimization. Theoretical insights into the working principles of baseline evolutionary algorithms for diversity optimization are still rare. In this paper we study the well-known Minimum Spanning Tree problem (MST) in the context of diversity optimization where population diversity is measured by the sum of pairwise edge overlaps. Theoretical results provide insights into the fitness landscape of the MST diversity optimization problem pointing out that even for a population of $\mu=2$ fitness plateaus (of constant length) can be reached, but nevertheless diverse sets can be calculated in polynomial time. We supplement our theoretical results with a series of experiments for the unconstrained and constraint case where all solutions need to fulfill a minimal quality threshold. Our results show that a simple $(\mu+1)$-EA can effectively compute a diversified population of spanning trees of high quality.