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The issue of designing and tuning an effective and efficient multivariable PID controller for a multivariable control system to obtain high-quality performance is of great theoretical importance and practical significance. As a novel evolutionary algorithm inspired from statistical physics and co-evolution, extremal optimization (EO) has successfully applied to a variety of optimization problems while the applications of EO into the design of multivariable PID and PI controllers are relatively rare. This paper presents a novel real-coded population-based EO (RPEO) method for the design of multivariable PID and PI controllers. The basic idea behind RPEO is based on population-based iterated optimization process consisting of the following key operations including generation of a real-coded random initial population by encoding the parameters of a multivariable PID or PI controller into a set of real values, evaluation of the …