Extremal Optimization: Methods derived from Co-Evolution

TL;DR

Extremal Optimization is a versatile, parameter-efficient method inspired by co-evolutionary models, effectively solving complex optimization problems by iteratively removing the worst components of a candidate solution.

Contribution

The paper introduces Extremal Optimization, a novel optimization technique inspired by co-evolution, which outperforms some existing methods with minimal parameter tuning.

Findings

Competitive performance on graph partitioning

Effective on the traveling salesman problem

Requires only one adjustable parameter

Abstract

We describe a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organized critical models of co-evolution such as the Bak-Sneppen model. The method, called Extremal Optimization, successively eliminates extremely undesirable components of sub-optimal solutions, rather than ``breeding'' better components. In contrast to Genetic Algorithms which operate on an entire ``gene-pool'' of possible solutions, Extremal Optimization improves on a single candidate solution by treating each of its components as species co-evolving according to Darwinian principles. Unlike Simulated Annealing, its non-equilibrium approach effects an algorithm requiring few parameters to tune. With only one adjustable parameter, its performance proves competitive with, and often superior to, more elaborate stochastic optimization procedures. We demonstrate it here on two classic hard optimization problems: graph partitioning and the traveling salesman problem.