Improved Monarch Butterfly Optimization Algorithm Based on Opposition-Based Learning and Random Local Perturbation

Algorithm 2

Step 1. Set the population quantity , the maximum generation , the dimensions , the max walk step size ,

the adjusting rate , the migration period and the migration rate . Let the current cycle counter = 1.

//Initialization operation

Step 2. Generate the opposition-based population according to OBL. Select the individuals with better fitness to enter

the next generation from the original and opposition-based populations.

Step 3. Calculate their fitness values according to the location of each monarch butterfly. //Fitness evaluation

Step 4.  While    do

Sort the population according to monarch butterfly fitness using Quicksort algorithm in [31].

Divide the monarch butterfly population into two subpopulations, i.e., Subpopulation1 and Subpopulation2.

for   = 1 to   do

Update Subpopulation1 using Algorithm 1.

end for

for   = 1 to   do

Update Subpopulation2 by Eq. (2).

end for

Merge two new subpopulations into a new population.

Recalculate the fitness values of each monarch butterfly according to the updated position.

Let .

Step 5. end while

Step 6. Output the optimal values.