Algorithm 1: The framework of the ASDSSA.

Input: Population size, N; Proportion of discoverers, PD; Proportion of vigilantes SD; Upper bounds ub; Lower bounds lb; The maximum number of iterations $T_{max}$; Weights, w; Output: The optimal solution, $F_{best}$; The best fitness value, $f_g$; 1: Initialize the position of N sparrows using Equation (5), and calculating the individual sparrow fitness value $f_i$; 2: Initialize the position of $r_i$ sparrows using Equation (6), and recalculating the individual sparrow fitness value; 3: According to the fitness value, the top N sparrows with better fitness value are selected as the initial population; 4: Get the optimal position and its corresponding optimal fitness value, the worst position and its corresponding worst fitness value; 5: while (t < $T_{max}$) 6: for j = 1: ND 7: Update the positions of the discoverers using Equation (8); 8: end for 9: for j = PD: N 10: Update the positions of the followers using Equation (2); 11: end for 12: for j = 1: SD 13: Update the positions of the vigilantes using Equation (3); 14: end for 15: Selecting the best individual for the current iteration and implement the adaptive Cauchy mutation for it by Equation (9); 16: If the position of the mutated individual is better than the original individual position, it will be replaced by Equation (11); 17: t = t + 1; 18: end while 19: return $F_{best}$, $f_g$