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Runtime Analysis of Discrete Particle Swarm Optimization Applied to Shortest Paths Computation

  • Alexander RaßEmail author
  • Jonas Schreiner
  • Rolf Wanka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11452)

Abstract

We mathematically analyze a discrete particle swarm optimization (PSO) algorithm solving the single-source shortest path (SSSP) problem. Key features are an improved and extended study on Markov chains expanding the adaptability of this technique and its application on the well-known SSSP problem. The results are upper and lower bounds on the expected optimization time. For upper bounds, we combine return times within a Markov model with the well known fitness level method which is appropriate even for the non-elitist PSO algorithm. For lower bounds we prove that the recently introduced property of indistinguishability applies in this setting and we also combine it with a further Markov chain analysis. We prove a cubic upper and a quadratic lower bound and an exponential upper and lower bound on the expected runtime, respectively, depending on a PSO parameter.

Keywords

Discrete particle swarm optimization Runtime analysis Single-source shortest paths Markov chains 

Notes

Acknowledgement

The authors would like to thank Bernd Bassimir for useful discussions.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of Erlangen-NurembergErlangenGermany

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