A multilevel algorithm for partitioning graphs
Supercomputing '95 Proceedings of the 1995 ACM/IEEE conference on Supercomputing
2+p-SAT: relation of typical-case complexity to the nature of the phase transition
Random Structures & Algorithms - Special issue on statistical physics methods in discrete probability, combinatorics, and theoretical computer science
Artificial Intelligence
Extremal optimization: heuristics via coevolutionary avalanches
Computing in Science and Engineering
Frozen development in graph coloring
Theoretical Computer Science - Phase transitions in combinatorial problems
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Meta-Heuristics: Theory and Applications
Meta-Heuristics: Theory and Applications
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Memetic Algorithms and the Fitness Landscape of the Graph Bi-Partitioning Problem
PPSN V Proceedings of the 5th International Conference on Parallel Problem Solving from Nature
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
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A new general-purpose heuristic for finding high-quality solutions for many hard optimization problems is explored. The method is inspired by recent progress in understanding far-from-equilibrium phenomena in terms of self-organized criticality, a concept introduced to describe emergent complexity in physical systems. This method, called extremal optimization, successively replaces the value of extremely undesirable variables in a sub-optimal solution with new, random ones. Large, avalanche-like fluctuations in the cost function self-organize from this dynamics, effectively scaling barriers to explore local optima in distant neighborhoods of the configuration space while eliminating the need to tune parameters. Drawing upon models used to simulate the dynamics of granular media, evolution, or geology, extremal optimization complements approximation methods inspired by equilibrium statistical physics, such as simulated annealing. It may be but one example of applying new insights into non-equilibrium phenomena systematically to hard optimization problems. This method is widely applicable, quickly adapted to real-world problems, and so far has proved competitive with - and even superior to - more elaborate general-purpose heuristics on testbeds of constrained optimization problems with up to 105 variables, such as bipartitioning, coloring, and satisfiability. This heuristic is particularly successful near phase transitions in combinatorial optimization, which are deemed to be the origin of the hardest instances in terms of computational complexity. Analysis of a model problem predicts the only free parameter of the method in accordance with all experimental results.