Algorithm 1 Improved pigeon-inspired optimization

Step 1: Set the flock parameters and initialize the flock, such as population number $N_p^{N_t}$, search dimension space $D$, compass operator $R$, map and compass operator’s maximum quantity of iterations $N_{t1}$, maximum amount of iterations for a landmark operator $N_{t2}$, maximum number of iterations $N_{t\max }$.

Step 2: Determine the current ideal position by assigning each pigeon a random speed and position, then figuring out each one’s fitness value.

Step 3: The population was crossed and mutated, and the pigeons’ positions were updated using the upgraded compass operator.

Step 4: Compute the relevant fitness value, and then use the fitness value comparison to update the current global optimal location.

Step 5: Verify if the compass operator’s maximum number of iterations has been reached. If yes, continue. Otherwise, go back to Step 3.

Step 6: The population’s center location is calculated, then the population is mutated and crossed, and the enhanced landmark operator is utilized to update the pigeons’ location.

Step 7: Calculate the corresponding fitness value, and then compare it to the current global ideal position.

Step 8: Replenishing the population. Step 9: Check whether the maximum quantity of iterations of the landmark operator is reached. If yes, the global optimal solution is displayed. Otherwise, go back to Step 6.