Extremal Optimization Algorithm on Evolving Networks

A new extremal optimization algorithm is proposed based on evolving networks. The algorithm makes use of extremal processes in natural, and eliminates the elements with the least fitness like in an evolving network. Each variable acts as a species with a defined fitness according to the optimization problem and N candidate solutions form the species population. The corresponding object of a solution is defined as its fitness. The quality of solutions is improved by mutations of unfit variables. In the species population, addition and removal of solutions is permitted according to their contribution to the objective, which means the solution with the best objective function value gives birth to a new candidate solution and the solution with the worst objective value disappears. The new solution will inherit the relations of its "mother" with others. Because of the availability of local information of variables and the power law probability of the selection of variables to mutate, the algorithm has both good local and global searching properties. The simple structure makes the algorithm direct available in combinatorial optimizations