Optimization with Extremal Dynamics

Phys. Rev. Lett. 86, 5211 – Published 4 June 2001
Stefan Boettcher and Allon G. Percus


We explore a new general-purpose heuristic for finding high-quality solutions to hard discrete optimization problems. The method, called extremal optimization, is inspired by self-organized criticality, a concept introduced to describe emergent complexity in physical systems. Extremal optimization successively updates extremely undesirable variables of a single suboptimal solution, assigning them new, random values. Large fluctuations ensue, efficiently exploring many local optima. We use extremal optimization to elucidate the phase transition in the 3-coloring problem, and we provide independent confirmation of previously reported extrapolations for the ground-state energy of ±J spin glasses in d=3 and 4.

DOI: http://dx.doi.org/10.1103/PhysRevLett.86.5211

  • Received 23 October 2000
  • Published in the issue dated 4 June 2001

© 2001 The American Physical Society

Authors & Affiliations

Stefan Boettcher1,* and Allon G. Percus2,†

  • 1Physics Department, Emory University, Atlanta, Georgia 30322
  • 2Computer & Computational Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

  • *Electronic address: sboettc@emory.edu
  • Electronic address: percus@lanl.gov

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