A novel real-coded population-based extremal optimization algorithm with polynomial mutation: A non-parametric statistical study on continuous optimization problems

As a recently developed optimization method inspired by far-from-equilibrium dynamics of self-organized criticality, extremal optimization (EO) has been successfully applied to a variety of combinatorial optimization problems while its applications in continuous optimization problems are relatively rare. Additionally, there are only few studies concerning the effects of mutation operation on EO algorithms although mutation operation plays a crucial role in controlling the optimization dynamics and consequently affecting the performance of EO-based algorithms. This paper proposes a novel real-coded population-based EO algorithm with polynomial mutation (RPEO-PLM) for continuous optimization problems. The basic idea behind RPEO-PLM is the population-based iterated optimization consisting of generation of a real-coded random initial population, evaluation of individual and population fitness, generation of a new population based on polynomial mutation, and updating the population by accepting the new population unconditionally. One of the most attractive advantages is its relative simplicity compared with other popular evolutionary algorithms due to its fewer adjustable parameters needing to be tuned and only selection and mutation operations. Furthermore, the experimental results on a large number of benchmark functions with the different dimensions by using non-parametric statistical tests including Friedman and Quade tests have shown that the proposed RPEO-PLM algorithm outperforms other popular population-based evolutionary algorithms, e.g., real-coded genetic algorithm (RCGA) with adaptive directed mutation (RCGA-ADM), RCGA with polynomial mutation (RCGA-PLM), intelligent evolutionary algorithm (IEA), a hybrid particle swarm optimization and EO algorithm (PSO–EO), the original population-based EO (PEO), and an improved RPEO algorithm with random mutation (IRPEO-RM) in terms of accuracy.