Discrete Particle Swarm Optimization for TSP: Theoretical Results and Experimental Evaluations

  • Matthias Hoffmann
  • Moritz Mühlenthaler
  • Sabine Helwig
  • Rolf Wanka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6943)


Particle swarm optimization (PSO) is a nature-inspired technique originally designed for solving continuous optimization problems. There already exist several approaches that use PSO also as basis for solving discrete optimization problems, in particular the Traveling Salesperson Problem (TSP). In this paper, (i) we present the first theoretical analysis of a discrete PSO algorithm for TSP which also provides insight into the convergence behavior of the swarm. In particular, we prove that the popular choice of using “sequences of transpositions” as the difference between tours tends to decrease the convergence rate. (ii) In the light of this observation, we present a new notion of difference between tours based on “edge exchanges” and a new method to combine differences by computing their “centroid.” This leads to a more PSO-like behavior of the algorithm and avoids the observed slow down effect. (iii) Then, we investigate implementations of our methods and compare them with previous implementations showing the competitiveness of our new approaches.


Particle Swarm Optimization Particle Swarm Optimization Algorithm Travel Salesman Problem Global Attractor Convergence Behavior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Matthias Hoffmann
    • 1
  • Moritz Mühlenthaler
    • 1
  • Sabine Helwig
    • 1
  • Rolf Wanka
    • 1
  1. 1.Department of Computer ScienceUniversity of Erlangen-NurembergGermany

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