Efficient Initialization Methods for Population-Based Metaheuristic Algorithms: A Comparative Study

The size, nature, and diversity of the initial population of population-based metaheuristic algorithms and the number of times the algorithm iterates play a significant role in the performance of the algorithms. In this paper, we presented a comprehensive comparison of the effect of population size, the maximum number of iterations, and eleven (11) different initialization methods on the convergence and accuracy of ten (10) population-based metaheuristic optimizers: Bat algorithm (BA), Grey Wolf optimizer (GWO), Butterfly optimization algorithm (BOA), Whale optimization algorithm (WOA), Moth Flame optimization (MFO), Harris Hawks optimization (HHO), Moth search (MS), Elephant Herding optimization (EHO), linear population size reduction success-history based adaptive DE (LSHADE), and covariance matrix learning with Euclidean neighborhood ensemble sinusoidal LSHADE (LSHADE-cnEpSin). The possible effect of these initialization schemes was tested on ten (10) different classical and ten (10) CEC2020 test functions with different properties and modalities. The simulation results and exhaustive statistical analysis show that for classical functions considered, BA, EHO, WOA, MFO, HHO, and MS are sensitive to the initialization schemes, whereas GWO, BOA, LSHADE, and LSHADE_cnEpSin are not. For CEC2020 test functions, BA and GWO are sensitive to the initialization schemes, whereas BOA, WOA, MFO, HHO, EHO, MS, LSHADE, and LSHADE_cnEpSin are not. The modified BA showed sensitivity for both classical and CEC2020 functions, which confirms that the diversity and nature of the initial population play a role in the algorithm's performance. The sensitivity of the algorithms is also problem-dependent, meaning some functions were insensitive to the initialization schemes. For example, for those algorithms that showed sensitivity to the initialization schemes, only between 70 and 83% of the functions considered are sensitive to those schemes whereas, 37–45% of the functions showed sensitivity for those overall insensitive algorithms to the initialization schemes. The population size and number of iterations also play a role in the performance of the algorithms. We found out that BA performed better with larger population sizes. GWO, WOA, BOA, MS, and LSHADE_cnEpSin performed better when the number of iterations is larger. MFO, LSHADE, EHO, and HHO perform optimally when the population size and the number of iterations are relatively even. This conclusion is heavily dependant on the problem dimension; however, we believe that good population diversity and the number of iterations will most likely lead to optimal solutions.