Arithmetic optimization algorithm with cosine composite chaotic mapping in polar coordinate system for economic load dispatching problems in power systems

Economic load dispatch (ELD) aims to minimize the total cost of generating electricity while satisfying load demand and different operational constraints. The Arithmetic Optimization Algorithm (AOA) with cosine composite chaotic mapping in polar coordinate system is put forward to solve the ELD problems in the power system with the valve point effect, prohibited operation area, transmission loss and other factors. Firstly, seven polar coordinate system chaotic mappings are proposed to be embedded into the MOP and MOA parameters in the AOA. Secondly, a chaotic system based on the cosine transform is put forward. Then, the proposed cosine transform based chaotic system is combined with polar coordinate system chaotic mapping to form polar coordinate system cosine transform composite chaotic mapping. Eventually, these six polar coordinate system cosine transform composite chaotic mapping is then embedded into the MOA and MOP of the AOA to balance the algorithm's global and local search capabilities, improve the performance of the algorithm and avoid falling into the local optima. 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 Osprey Optimization Algorithm (OOA) to verify its convergence. The ELD problem for a total demand of 2500 MW is solved by using the AOA with cosine composite chaotic mapping in polar coordinate system. The experimental results show that the improved AOA outperforms other optimization algorithms on the 12 benchmark functions in CEC2022 and the ELD problems.