In this work, three-dimensional nonlinear food chain system is numerically treated using the computational heuristic framework of artificial neural networks (ANNs) together with the proficiencies of global and local search approaches based on genetic algorithm (GA) and interior-point algorithm scheme (IPAS), i.e. ANN-GA-IPAS. The three-dimensional food chain system consists of prey populations, specialist predator and top-predator. The formulation of an objective function using the differential system of three-species food chain and its initial conditions is presented and the optimization is performed by using the hybrid computing efficiency of GA-IPAS. The achieved numerical solutions through ANN-GA-IPAS to solve the nonlinear three-species food chain system are compared with the Adams method to validate the exactness of the designed ANN-GA-IPAS. The comparison of the results is presented to authenticate the correctness of the designed ANN-GA-IPAS for solving the nonlinear three-species food chain system. Moreover, statistical representations for 40 independent trials and 30 variables validate the efficacy, constancy and reliability of ANN-GA-IPAS.