Enhanced equilibrium optimization method with fractional order chaotic and application engineering

Abstract

In this study, enhanced equilibrium optimization (E2O) algorithm was proposed by developing stochastic processes in equilibrium optimization (EO) method with fractional order chaotic (FOC) system models. FOC model was firstly used in an optimization algorithm in this study. System responses of the fractional order chaotic models were used instead of random coefficients in the basic EO method. The performance of many fractional order chaotic system models was tested on benchmark functions. It was experimentally determined fractional order chaotic models of Genesio Tesi, Chua Memristor and cellular neural network which were convenient for the EO method. Model coefficients and initial conditions of corresponding fractional order chaotic models were obtained for benchmark functions to find suitable models for E2O algorithm. In order to present engineering application performance of the proposed E2O method, controller parameters were optimized for liquid level control that was decoupled two-input and two-output (TITO) tank system. Fractional and integer order PI and PID controllers’ parameters were tuned according to the reference input signals for TITO tank system. Multi-objective function was defined with mean square error (MSE) definition as system’s overall objective function. Proposed multi-objective function was minimized during to optimization process. E2O algorithm results were compared with each other and existing literature studies results. In this way, it was shown comparatively that usage of fractional order chaotic models in the proposed E2O algorithm affected optimization algorithm performance and produced better results.