Comparison study on the nonlinear parameter optimization of nonlinear grey Bernoulli model (NGBM(1,1)) between intelligent optimizers

Abstract

PurposeThe purpose of this paper is to find out which algorithm, among Genetic Algorithm (GA), Particle Swarm Optimizer (PSO), the novel Grey Wolf Optimizer (GWO) and the novel Ant Lion Optimizer (ALO), is the best to obtain the optimal value of the nonlinear parameter γ of nonlinear grey Bernoulli model (NGBM(1,1)) under different situations.Design/methodology/approachThe optimization of γ has been attributed to a nonlinear programming problem at first. The convergence, convergence rate, time consuming and stability of GA, PSO, GWO and ALO are compared in the numerical experiments, and in each subcase the criteria are set to be the same. Over 10,000 iterations have been run on the same environment in order to guarantee the reliability of the results.FindingsAll the selected algorithms can converge to the same optimal value with sufficient iterations. But the best algorithm should be chose under different situations.Practical implicationsThe optimal value of γ seems to exist uniquely due to the empirical results. And there does not exist a best algorithm for all the cases. The researchers and commercial software developers should choose a proper algorithm due to different cases.Originality/valueThe performance of GA, PSO, GWO and ALO to compute the optimal γ of NGBM(1,1) has been compared for the first time. And it is the original work which uses the GWO and ALO to optimize the NGBM(1,1).