Algorithm 1 Pseudo-code for chaotic and QRL population initialization

Step 1: Generate starting population $P_{start}$ of $N/2$ solutions with standard initialization expression: $X_i=LB+(UB-LB)·rand(0,1),i=1,\dots ,N/2$, where $rand(0,1)$ represents pseudo-random number drawn from the range $[0,1]$. Step 2: Randomly select 2 subsets of $N/4$ from $P_{start}$ for chaotic and QRL initialization, denoted as $P^c$ and $P^{qrl}$, respectively. Step 3: Extend $P^c$ by applying chaotic sequences to each individual in $P^c$ using expressions (19) and (20). The size of $P^c$ after extension is $N/2$. Step 4: Extend $P^{qrl}$ by applying QRL mechanism to each individual in $P^{qrl}$ using expression (21). The size of $P^{qrl}$ after extension is $N/2$. Step 5: Calculate fitness of all individuals from $P^c$ and $P^{qrl}$. Step 6: Sort all solutions from $P^c\cup P^{qrl}$ according to fitness. Step 7: Select N best solutions as the initial population P.