Abstract A recently introduced general-purpose heuristic for finding high-quality solutions for many hard optimization problems is reviewed. 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 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 10 5 variables, such as bipartitioning, coloring, and satisfiability. Analysis of a suitable model predicts the only free parameter of the method in accordance with all experimental results.

Extremal Optimization, a recently introduced meta-heuristic for hard optimization problems, is analyzed on a simple model of jamming. The model is motivated first by the problem of finding lowest energy configurations for a disordered spin system on a fixed-valence graph. The numerical results for the spin system exhibits the same phenomenology found in all earlier studies of extremal optimization, and our analytical results for the model reproduce many of these features. PACS number(s): 02.60.Pn, 05.40.-a, 64.60.Cn, 75.10.Nr. I.

We explore a new general-purpose heuristic for finding high-quality solutions to hard optimization problems. The method, called extremal optimization, is inspired by "self-organized criticality", a concept introduced to describe emergent complexity in physical systems. In contrast to genetic algorithms, which operate on an entire "gene-pool" of possible solutions, extremal optimization successively replaces extremely undesirable elements of a single sub-optimal solution with new, random ones. Large fluctuations, or "avalanches", ensue that efficiently explore many local optima. Drawing upon models used to simulate far-from-equilibrium dynamics, extremal optimization complements heuristics inspired by equilibrium statistical physics, such as simulated annealing. With only one adjustable parameter, its performance has proved competitive with more elaborate methods, especially near phase transitions. Phase transitions are found in many combinatorial optimization problems, and have been co...

. We explore a new general-purpose heuristic for finding highquality solutions to hard optimization problems. The method, called extremal optimization, is inspired by "self-organized criticality," a concept introduced to describe emergent complexity in many physical systems. In contrast to Genetic Algorithms which operate on an entire "genepool " of possible solutions, extremal optimization successively replaces extremely undesirable elements of a sub-optimal solution with new, random ones. Large fluctuations, called "avalanches," ensue that efficiently explore many local optima. Drawing upon models used to simulate farfrom -equilibrium dynamics, extremal optimization complements approximation methods inspired by equilibrium statistical physics, such as simulated annealing. With only one adjustable parameter, its performance has proved competitive with more elaborate methods, especially near phase transitions. Those phase transitions are found in the parameter space of m...