<p>The arithmetic optimization algorithm (AOA) is a newly developed meta-heuristic algorithm that draws inspiration from the combination of arithmetic operations. Since many scholars have widely used traditional one-dimensional chaotic mapping at home and abroad in function optimization, the AOA based on cosine transform two-dimensional composite chaotic mapping is proposed. Firstly, seven two-dimensional chaotic mappings are proposed to be embedded into the MOA and MOP in AOA. Secondly, one-dimensional chaotic systems based on the cosine transform are put forward. Then the proposed chaotic system based on the cosine transform is combined with the two-dimensional chaotic mapping to form the cosine transformed two-dimensional composite chaotic mapping. Finally, six more cosine transformed two-dimensional composite chaotic mappings are embedded into the MOA and MOP of the AOA to balance the algorithm's global and local searching ability and improve the algorithm's performance. The superiority of the improved algorithm is verified by employing 12 benchmark test functions in CEC2022. Then it is compared with the Coati Optimization Algorithm (COA), Prairie Dog Optimization (PDO), Butterfly Optimization Algorithm (BOA), Reptile Search Algorithm (RSA), Bat Algorithm (BAT), and Rat Swarm Optimization (RSO) to verify its convergence. Finally, four engineering design problems (tension/compression spring problem, pressure vessel problem, cantilever beam design problem, and slotted bulkhead design problem) were optimized to validate the efficiency of the improved algorithm. The simulation experiments demonstrate that the improved AOA exhibits superior performance in addressing both function and engineering optimization problems. It showcases remarkable optimization capabilities and improves convergence accuracy.</p>