Evolutionary Algorithms for One-Sided Bipartite Crossing Minimisation

TL;DR

This paper empirically evaluates evolutionary algorithms for the one-sided bipartite crossing minimisation problem, demonstrating that jump mutation operators outperform deterministic algorithms and that optimized EAs can significantly reduce runtime.

Contribution

It provides the first comprehensive empirical analysis of EAs for OBCM, comparing mutation operators and optimizing algorithm efficiency.

Findings

Jump mutation operators outperform deterministic algorithms in solution quality.

Optimized EAs achieve same quality up to 100 times faster.

EAs effectively solve complex graph drawing optimisation problems.

Abstract

Evolutionary algorithms (EAs) are universal solvers inspired by principles of natural evolution. In many applications, EAs produce astonishingly good solutions. As they are able to deal with complex optimisation problems, they show great promise for hard problems encountered in the field of graph drawing.To complement recent theoretical advances in the analysis of EAs on graph drawing, we contribute a fundamental empirical study. We consider the so-called \textsc{One-Sided Bipartite Crossing Minimisation (OBCM)}: given two layers of a bipartite graph and a fixed horizontal order of vertices on the first layer, the task is to order the vertices on the second layer to minimise the number of edge crossings. We empirically analyse the performance of simple EAs for OBCM and compare different mutation operators on the underlying permutation ordering problem: exchanging two elements (\textit{exchange}), swapping adjacent elements (\textit{swap}) and jumping an element to a new position (\textit{jump}). EAs using jumps easily outperform all deterministic algorithms in terms of solution quality after a reasonable number of generations. We also design variations of the best-performing EAs to reduce the execution time for each generation. The improved EAs can obtain the same solution quality as before and run up to 100 times faster.