Chaotic African Vultures Optimisation Algorithm for parameter identification in nonlinear dynamic models and solving Diophantine equations

This study introduces chaos theory into the standard African Vultures Algorithm (AFRICAN) to accelerate global convergence speed through the maintained balance between the exploration and exploitation phases. The AFRICAN algorithm’s chaotic variants are first applied to thirty-two unconstrained multidimensional benchmark functions. Then, the most successful chaotic algorithm is employed to solve four different real-world engineering problems. A set of Diophantine equations with other functional characteristics is solved to investigate the efficiency of the chaotic AFRICAN method on integer programming problems. Finally, five dynamic optimisation cases have been solved based on parameter identification of nonlinear models. It is seen that the Ikeda chaotic map-assisted AFRICAN algorithm yields the most accurate predictions for a variety of test instances for most cases and proves its efficiency in solving continuous and integer programming problems.