Parameter estimation of nonlinear chaotic system by improved TLBO strategy

Estimation of parameters of chaotic systems is a subject of substantial and well-developed research issue in nonlinear science. From the viewpoint of optimization, parameter estimation can be formulated as a multi-modal constrained optimization problem with multiple decision variables. This investigation makes a systematic examination of the feasibility of applying a newly proposed population-based optimization method labeled here as teaching–learning-based optimization (TLBO) to identify the unknown parameters for a class of chaotic system. The preliminary test demonstrates that despite its global fast coarse search capability, teaching–learning-based optimization often risks getting prematurely stuck in local optima. To enhance its fine (local) searching performance of TLBO, Nelder–Mead simplex algorithm-based local improvement is incorporated into TLBO so as to continually search for the global optima through the reflection, expansion, contraction, and shrink operators. Working with the well-established Lorenz system, we assess the effectiveness and efficiency of the proposed improved TLBO strategy. The empirical results indicate the success of the proposed hybrid approach in which the global exploration and the local exploitation are well balanced, providing the best solutions for all instances used over other state-of-the-art metaheuristics for chaotic identification in literature, including particle swarm optimization, genetic algorithm, and quantum-inspired evolutionary algorithm.