Extremal optimization: heuristics via coevolutionary avalanches

The extremal dynamics of the Bak-Sneppen model can be converted into an optimization algorithm called extremal optimization. Attractive features of the model include the following: it is straightforward to relate the sum of all fitnesses to the cost function of the system; in the self-organized critical state to which the system inevitably evolves, almost all species have a much better than random fitness; most species preserve a good fitness for long times unless they are connected to poorly adapted species, providing the system with a long memory; the system retains a potential for large, hill-climbing fluctuations at any stage; and the model accomplishes these features without any control parameters.