Optimal design of truss structures with frequency constraints: a comparative study of DE, IDE, LSHADE, and CMAES algorithms

The present study examines the performance of three powerful methods including the original differential evolution (DE), the improved differential evolution (IDE), and the winner of the CEC-2014 competition, LSHADE, in addition to the covariance matrix adaptation evolution strategy (CMAES) for size optimization of truss structures under natural frequency constraints. Despite the abundant researches on novel meta-heuristic algorithms in the literature, the application of CMAES, one of the most powerful and reliable optimization algorithms, on the optimal solution of the truss structures has received scant attention. For consistent comparison between these algorithms, four stopping criteria are defined and for each of these criteria, all algorithms are executed 30 times. Statistical analysis of the results for each algorithm is performed, and the mean, standard deviation, minimum, and maximum for 30 executions of the algorithms are calculated. For the small population size, results show that the CMAES algorithm not only has the best performance and the least standard deviation values among other given algorithms in all cases but also finds the best ever optimal solutions for the design of the benchmark truss structures which have not been reported in other studies. However, by increasing the number of decision variables and the population size, the CMAES algorithm needs more function evaluations to converge to the global optimal solution with higher accuracy.