Optimization algorithms play a crucial role in a wide range of fields, from designing complex systems to solving mathematical and engineering problems. However, these algorithms frequently face major challenges, such as convergence to local optima, which limits their ability to find global, optimal solutions. To overcome these challenges, it has become imperative to explore more efficient approaches by incorporating chaotic maps within these original algorithms. Incorporating chaotic variables into the search process offers notable advantages, including the ability to avoid local minima, diversify the search, and accelerate convergence toward optimal solutions. In this study, we propose an improved Archimedean optimization algorithm called Chaotic_AO (CAO), based on the use of ten distinct chaotic maps to replace pseudorandom sequences in the three essential components of the classical Archimedean optimization algorithm: initialization, density and volume update, and position update. This improvement aims to achieve a more appropriate balance between the exploitation and exploration phases, offering a greater likelihood of discovering global solutions. CAO performance was extensively validated through the exploration of three distinct groups of problems. The first group, made up of twenty-three benchmark functions, served as an initial reference. Group 2 comprises three crucial engineering problems: the design of a welded beam, the modeling of a spring subjected to tension/compression stresses, and the planning of pressurized tanks. Finally, the third group of problems is dedicated to evaluating the efficiency of the CAO algorithm in the field of signal reconstruction, as well as 2D and 3D medical images. The results obtained from these in-depth tests revealed the efficiency and reliability of the CAO algorithm in terms of convergence speeds, and outstanding solution quality in most of the cases studied.

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.