ATM cash management is a set of transactions to optimize the amount of money that should be kept on ATM devices. ATM Cash Management Optimization studies are the studies carried out to keep the most appropriate amount of cash on the ATM by the types and models of ATMs in the banking system, following each time zone. In this study, ATM cash management will be handled as an optimization problem, and the decision variable values that will minimize the treasury and operation costs will be calculated. The main purpose of the study is to estimate the most appropriate amount of money that should be in ATM devices daily and to recommend the amount of cash that should be in the ATM to the system owners. In this study, the most ideal result was tried to be found by using metaheuristic multi objective optimization algorithms used in the literature. First of all, the decision variables and features of ATM data were determined by a detailed study. The optimization algorithm was decided to produce results with a new approach for the determined data areas. The arithmetic Optimization Algorithm (AOA) algorithm, one of the newly proposed metaheuristic algorithms, was chosen as the optimization algorithm. The fuzzy logic algorithm was used to find the weighting coefficients of the values used as input parameters for the AOA algorithm. By using the fuzzy logic algorithm, the effect values of the features on the result were weighted, and together with the obtained weighting information, it was proposed as research that the most appropriate cash amount value should be used in the AOA algorithm. In this way, it is aimed to present a successful solution by exhibiting a hybrid approach. The results obtained were compared with the values in the system and the success rates were tried to be revealed.