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Poster Abstract

DOI: 10.4230/LIPIcs.GD.2024.51

Evolutionary Algorithms for One-Sided Bipartite Crossing Minimisation (Poster Abstract)

Authors: Jakob Baumann, Ignaz Rutter, and Dirk Sudholt

Published in: LIPIcs, Volume 320, 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)

Abstract

Evolutionary algorithms (EAs) are universal solvers inspired by principles of natural evolution. In many applications, EAs produce astonishingly good solutions. To complement recent theoretical advances in the analysis of EAs on graph drawing [Baumann et al., 2024], we contribute a fundamental empirical study. We consider the so-called 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 (exchange), swapping adjacent elements (swap) and jumping an element to a new position (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.

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Jakob Baumann, Ignaz Rutter, and Dirk Sudholt. Evolutionary Algorithms for One-Sided Bipartite Crossing Minimisation (Poster Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 51:1-51:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{baumann_et_al:LIPIcs.GD.2024.51,
  author =	{Baumann, Jakob and Rutter, Ignaz and Sudholt, Dirk},
  title =	{{Evolutionary Algorithms for One-Sided Bipartite Crossing Minimisation}},
  booktitle =	{32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
  pages =	{51:1--51:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-343-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{320},
  editor =	{Felsner, Stefan and Klein, Karsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.51},
  URN =		{urn:nbn:de:0030-drops-213353},
  doi =		{10.4230/LIPIcs.GD.2024.51},
  annote =	{Keywords: Mutation Operator, Layered Graphs, Crossing Minimisation}
}

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DOI: 10.4230/DagSemProc.08051.6

Runtime Analysis of Binary PSO

Authors: Dirk Sudholt and Carsten Witt

Published in: Dagstuhl Seminar Proceedings, Volume 8051, Theory of Evolutionary Algorithms (2008)

Abstract

We investigate the runtime of the Binary Particle Swarm Optimization (PSO) algorithm introduced by Kennedy and Eberhart (1997). The Binary PSO maintains a global best solution and a swarm of particles. Each particle consists of a current position, an own best position and a velocity vector used in a probabilistic process to update the particle's position. We present lower bounds for a broad class of implementations with swarms of polynomial size. To prove upper bounds, we transfer a fitness-level argument well-established for evolutionary algorithms (EAs) to PSO. This method is then applied to estimate the expected runtime on the class of unimodal functions. A simple variant of the Binary PSO is considered in more detail. The1-PSO only maintains one particle, hence own best and global best solutions coincide. Despite its simplicity, the 1-PSO is surprisingly efficient. A detailed analysis for the function Onemax shows that the 1-PSO is competitive to EAs.

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Dirk Sudholt and Carsten Witt. Runtime Analysis of Binary PSO. In Theory of Evolutionary Algorithms. Dagstuhl Seminar Proceedings, Volume 8051, pp. 1-22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{sudholt_et_al:DagSemProc.08051.6,
  author =	{Sudholt, Dirk and Witt, Carsten},
  title =	{{Runtime Analysis of Binary PSO}},
  booktitle =	{Theory of Evolutionary Algorithms},
  pages =	{1--22},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8051},
  editor =	{Dirk V. Arnold and Anne Auger and Jonathan E. Rowe and Carsten Witt},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08051.6},
  URN =		{urn:nbn:de:0030-drops-14800},
  doi =		{10.4230/DagSemProc.08051.6},
  annote =	{Keywords: Particle swarm optimization, runtime analysis}
}

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Documents authored by Sudholt, Dirk

Evolutionary Algorithms for One-Sided Bipartite Crossing Minimisation (Poster Abstract)

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Runtime Analysis of Binary PSO

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