Algorithm 1: Pseudocode of the BGOA-TVG algorithm.

Initialize $C_{max}$, $C_{min}$, and Max_Iterations

Initialize a population of solutions $X_i$ (i = 1, 2, …, n)

Evaluate each solution in the population

Set T as the best solution

While (t < Max_Iterations)

Update c using Equation (9)

For each search agent

Normalize the distances between grasshoppers in [1, 4]

Update the step vector ΔX of the current solution using Equation (10)

For i = 1: dim

Use Equation (8) to obtain the current position

Use Equations (10)–(13) to obtain the binary position

Use Equations (14)–(17) to obtain the final position

Calculate $\alpha ,\beta ,sigma$ based on Equations (13), (15), and (16)

End           Reevaluate the fitness of each individual in the population           If there is a better solution, replace T with it           Update T

End

End

Return T