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Optimization with extremal dynamics.

S Boettcher1, A G Percus

  • 1Physics Department, Emory University, Atlanta, Georgia 30322, USA. sboettc@emory.edu

Physical Review Letters
|June 1, 2001
PubMed
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We introduce extremal optimization, a novel heuristic inspired by physics, to solve complex problems. This method efficiently finds high-quality solutions by updating undesirable variables, aiding in understanding phase transitions and spin glass energies.

Area of Science:

  • Computational Physics
  • Statistical Mechanics
  • Computer Science

Background:

  • Discrete optimization problems are computationally challenging.
  • Existing heuristics may struggle with complex solution landscapes.
  • Self-organized criticality offers insights into emergent complexity.

Purpose of the Study:

  • Introduce a new general-purpose heuristic: extremal optimization.
  • Apply extremal optimization to discrete optimization problems.
  • Investigate its effectiveness in exploring solution spaces.

Main Methods:

  • Extremal optimization updates undesirable variables in a solution.
  • Random reassignment of variables induces large fluctuations.
  • Exploration of local optima through these fluctuations.

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Main Results:

  • Successfully applied extremal optimization to the 3-coloring problem.
  • Elucidated the phase transition in the 3-coloring problem.
  • Confirmed previous findings on spin glass ground-state energies in dimensions 3 and 4.

Conclusions:

  • Extremal optimization is a promising heuristic for hard discrete optimization.
  • The method efficiently explores complex solution spaces.
  • Provides a novel approach for problems in physics and computer science.