Influence of the Binomial Crossover in the DE Variants Based on the Robot Design with Optimum Mechanical Energy

Differential evolution (DE) is a powerful algorithm to find an optimal solution in real world problems. Nevertheless, the binomial crossover parameter is an important issue for the success of the algorithm. The proper selection of the binomial crossover parameter depends on the problem at hand. In this work, the effect of the binomial crossover in the DE/Rand/1/bin, DE/Best/1/Bin and DE/Current to rand/1/Bin is empirically studied and analyzed in the optimum design of the kinematic and the dynamic parameters of links for a parallel robot. The optimum design minimizes mechanical energy and consequently reduces the energy provided by the actuator. Based on the experimental results, the range of crossover parameter values that properly explores the search space is obtained. The importance of finding a proper crossover parameter is highlighted. In addition, the optimal design shows a decrease in the parallel robot mechanical energy compared with non-optimal design.