Extremal optimization  Extremal optimization (EO) is an optimization heuristic inspired by the Bak–Sneppen model of self-organized criticality from the field of statistical physics. This heuristic was designed initially to address combinatorial optimization problems such as the travelling salesman problem and spin glasses, although the technique has been demonstrated to function in optimization domains. Self-organized criticality (SOC) is a statistical physics concept to describe a class of dynamical systems that have a critical point as an attractor. Specifically, these are non-equilibrium systems that evolve through avalanches of change and dissipations that reach up to the highest scales of the system. SOC is said to govern the dynamics behind some natural systems that have these burst-like phenomena including landscape formation, earthquakes, evolution, and the granular dynamics of rice and sand piles. Of special interest here is the Bak–Sneppen model of SOC, which is able to describe evolution via punctuated equilibrium (extinction events) – thus modelling evolution as a self-organised critical process. Another piece in the puzzle is work on computational complexity, specifically that critical points have been shown to exist in NP-complete problems, where near-optimum solutions are widely dispersed and separated by barriers in the search space causing local search algorithms to get stuck or severely hampered. It was the evolutionary self-organised criticality model by Bak and Sneppen and the observation of critical points in combinatorial optimisation problems that lead to the development of Extremal Optimization by Stefan Boettcher and Allon Percus. EO was designed as a local search algorithm for combinatorial optimization problems. Unlike genetic algorithms, which work with a population of candidate solutions, EO evolves a single solution and makes local modifications to the worst components. This requires that a suitable representation be selected which permits individual solution components to be assigned a quality measure ("fitness"). This differs from holistic approaches such as ant colony optimization and evolutionary computation that assign equal-fitness to all components of a solution based upon their collective evaluation against an objective function. The algorithm is initialized with an initial solution, which can be constructed randomly, or derived from another search process. The technique is a fine-grained search, and superficially resembles a hill climbing (local search) technique. A more detailed examination reveals some interesting principles, which may have applicability and even some similarity to broader population-based approaches (evolutionary computation and artificial immune system). The governing principle behind this algorithm is that of improvement through selectively removing low-quality components and replacing them with a randomly selected component.