A new improved Newton metaheuristic algorithm for solving mathematical and structural optimization problems

As the objective function in complex structural optimization problems is implicit, in the present improved Newton method using the higher-order approximation, a new and simple formulation is proposed to calculate the first and second-order derivatives of the objective function. Furthermore, by combining the presented improved Newton method with an innovative metaheuristic algorithm an efficient approach, called improved Newton metaheuristic algorithm (INMA), is presented to balance between exploration and exploitation during optimization process. The performance of the proposed INMA algorithm is investigated on the CEC2019 and CEC2020 benchmark functions, three benchmark truss problems with stress constraints as well as four truss problems with multiple frequency constraints. The results demonstrate that the efficiency of the proposed INMA algorithm for both mathematical and structural optimization problems is better than other algorithms. Anyway, it can be seen from the results that INMA algorithm is an efficient method to solve problems in different optimization domains.