Algorithm 1 Pseudo code of the EMSMA

Begin:

//Initialization

Initialize z, N, T, L;

Initialize the the positions of agent X

//Main loop

While (t < T) do

Calculate the fitness of X and obtain $X_{best}$

Construct $X_{leader}$ by Equation (10)

Calculate the W by Equation (8)

Update $C_i$, $X_{mean}$ by Equations (12) and (13)

For i = 1: N do

Update p,a by Equations (4) and (7)

If rand < z then

Update positions by Equation (9) //Leader covariance learning strategy

else

Update positions by Equations (4) and (5)

End if

End For

Update $X_{best}$ by Equations (17) and (18) //Improved non-monopoly search mechanism

For i = 1: N do

Update positions by Equation (19) //Random differential restart mechanism

End for

t = t + 1

End While

Return: the best fitness and $X_{best}$$X_{best}$