Algorithm 1: The framework of the TLOCTO algorithm

1: Initialize the solution’s positions of population N randomly; 2: Set the maximum number of iterations (Tmax) and other parameters; 3: For t = 1 to Tmax do; 4: Calculate the average of the population; 5: Select the teacher; 6: Calculate the fitness function for the given solutions using Equation (1); 7: Find the best solution position and fitness value so far; 8: For i = 1 to N do; 9: Update the individual position using Equation (2); 10: Update the individual position using Equation (3); 11: Compare and select the one that generates the smaller value as the update position; 12: For i = 1 to N do; 13: Update the individual position using Equation (4); 14: Update the individual position using Equation (11); 15: Calculate the fitness values Fitness ($S_j^{\mathrm{Cadres}}$) and Fitness ($S_j^{\mathrm{Tu}}$); 16: If Fitness ($S_j^{\mathrm{Cadres}}$) < Fitness ($S_j^{\mathrm{Tu}}$), then 17: Obtain the best position and the best fitness value of the current iteration using Equation (4); 18: else; 19: Obtain the best position and the best fitness value of the current iteration using Equation (11); 20: end if; 21: end for; 22: end for; 23: Return the best solution.