On the Convergence of Biogeography-Based Optimization for Binary Problems

Table 2

Convergence rate comparison for the three-bit multimodal problem 𝑓₂.

Mutation rate	Theoretical analysis				Average generation number using simulation
	Parameter 𝜌		Convergence time 𝑡
	BBO	GA	BBO	GA	BBO	GA
0.1	0.61	0.59	27.95	25.16	26.09	24.87
0.01	0.11	0.17	6.26	7.95	6.17	7.72
0.001	0.04	0.05	4.29	4.76	4.18	4.63

The table shows the convergence time 𝑡 in seconds, the corresponding 𝜌 based on (11) and (28), and the generation number of first finding an all-optimal population using BBO and GA, averaged over 25 Monte Carlo simulations.