Optimal design of truss structures with frequency constraints using improved differential evolution algorithm based on an adaptive mutation scheme

The paper presents an improved differential evolution (IDE) and its application for solving shape and size optimization problems of truss structures with frequency constraints. The improvements are made in mutation and selection phases but mainly focused on the mutation phase. In the mutation phase of the IDE, a new selection scheme is proposed by using multi-mutation operators that adaptively employ all four popular mutation operators, including “rand/1,” “rand/2,” “best/1,” and “best/2” for selecting target vectors in population. This new scheme helps maintain effectively the balance between the global exploration and local exploitation abilities for searching process of the DE. In the selection phase of the IDE, an elitist selection technique that helps save good individuals for the next generation is suggested to replace traditional selection technique of the original DE. The suggested technique can help increase the convergence rate of the IDE. The efficiency and robustness of the IDE are demonstrated through five benchmark problems. Numerical results show that in most of the cases considered, the optimum design obtained by the IDE and DE are nearly the same and they are better than those gained by some other well-known methods in the literature. However, the IDE is much better than the DE in terms of the computational cost.