The Kepler Optimisation Algorithm (KOA) is a recently proposed algorithm that is inspired by Kepler’s laws to predict the positions and velocities of planets at a given time. However, although promising, KOA can encounter challenges such as convergence to sub-optimal solutions or slow convergence speed. This paper proposes an improvement to KOA by integrating chaotic maps to solve complex engineering problems. The improved algorithm, named Chaotic Kepler Optimization Algorithm (CKOA), is characterized by a better ability to avoid local minima and to reach globally optimal solutions thanks to a dynamic diversification strategy based on chaotic maps. To confirm the effectiveness of the suggested approach, in-depth statistical analyses were carried out using the CEC2020 and CEC2022 benchmarks. These analyses included mean and standard deviation of fitness, convergence curves, Wilcoxon tests, as well as population diversity assessments. The experimental results, which compare CKOA not only to the original KOA but also to eight other recent optimizers, show that the proposed algorithm performs better in terms of convergence speed and solution quality. In addition, CKOA has been successfully tested on three complex engineering problems, confirming its robustness and practical effectiveness. These results make CKOA a powerful optimisation tool in a variety of complex real-world contexts. After final acceptance, the source code will be uploaded to the Github account: nawal.elghouate@usmba.ac.ma.