A differential evolution algorithm combined with Lévy Flight for dimensional synthesis of four-bar linkage

Abstract

The paper considers dimensional synthesis of a path generator four-bar linkage by applying the modified Differential Evolution (DE) algorithm. During the search of the space, the DE algorithm may skip the right solution and lead to premature convergence. If the step is reduced, the search space is reduced as well, so that convergence becomes slower. Search efficiency may be achieved by including Lévy Flight in the DE algorithm. Namely, when the DE algorithm identifies the space of best solution, then a Levý Flight step is used for local search in that region, which significantly increases the exploitation capability and allows obtaining a very efficient solution of the optimization problem. The algorithm was tested with three examples of dimensional synthesis of a path generator four-bar linkage. The proposed algorithm can be very efficiently applied to solving very complex optimization problems.