Algorithm 1: Modified Crow Search Algorithm (MCSA)

//Problem Initialization ${\mathbf{O}\mathcal{B}\mathbf{j}}_{\left(\mathcal{F}\right)}:$ The objective function(minimize the distance error) ${\mathbf{F}\mathbf{i}\mathbf{t}}_{\left(\mathcal{F}\right)}$: The fitness Function ${\mathbf{D}\mathbf{e}\mathbf{c}\mathbf{i}}_{\mathcal{V}\mathbf{a}\mathbf{r}}$: Decision variable lir ${\mathbf{F}\mathcal{L}}_{\mathbf{s}\mathbf{i}\mathbf{z}\mathbf{e}}$: The flock size ${\mathbf{M}\mathbf{a}\mathbf{x}}_{\mathbf{i}\mathbf{t}\mathbf{r}}$: maximum number of iterations ${\mathit{x}}^{\mathit{i},\mathit{i}\mathit{t}\mathit{e}\mathit{r}}$: A vector for the position of crow i at time iter in the search space obtained from the mathematical approach ${{\mathcal{F}}_{\mathbf{L}\mathbf{e}\mathbf{n}}\left(\mathit{i}\right)}^{\mathit{i}\mathit{t}\mathit{r}}$: The length of flight of crow $\mathit{i}$ in specific iteration $\mathbf{P}\left(\mathbf{Å}\mathbf{w}\right)$: The probability of awareness ${\mathit{C}\mathit{r}\mathit{o}\mathit{w}}_{\mathit{n}\mathit{u}\mathit{m}}$: Number of crows of the flock ${\mathcal{F}\mathcal{S}}_{\mathit{v}\mathit{e}\mathit{c}\mathit{t}\mathit{o}\mathit{r}}$: The feasible solution vector(the intermediate area obtained from the CBA) ${\mathcal{r}}_{\mathit{i}}$: A random number with uniform distribution between 0 and 1 ${\mathcal{F}\mathit{e}\mathit{a}\mathit{s}\mathit{b}}_{\mathbb{T}\mathbb{H}}:\mathbf{T}\mathbf{h}\mathbf{e} \mathbf{f}\mathbf{e}\mathbf{a}\mathbf{s}\mathbf{a}\mathbf{b}\mathbf{i}\mathbf{l}\mathbf{i}\mathbf{t}\mathbf{y} \mathbf{t}\mathbf{h}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{h}\mathbf{o}\mathbf{l}\mathbf{d}$ 1. Positions and memories Initialization           For Each $\mathit{i}$ in ${\mathit{C}\mathit{r}\mathit{o}\mathit{w}}_{\mathit{n}\mathit{u}\mathit{m}}$           Generate (${\mathcal{F}\mathcal{S}}_{\mathbf{v}\mathbf{e}\mathbf{c}\mathbf{t}\mathbf{o}\mathbf{r}}$)           Fill(${\mathbf{P}\mathbf{o}\mathbf{s}}_{\mathbf{i}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}}⟶\mathbf{M}\mathbf{e}\mathbf{m}\mathbf{o}\mathbf{r}\mathbf{y}$) //2. Fitness function Evaluation           Calculate (${\mathbf{F}\mathbf{i}\mathbf{t}}_{\left(\mathcal{F}\right)}$) //3. New position Generation           For Each $\mathit{i}$ in ${\mathit{C}\mathit{r}\mathit{o}\mathit{w}}_{\mathit{n}}$           Rand_Select ($\mathit{j}$$\in {\mathit{C}\mathit{r}\mathit{o}\mathit{w}}_{\mathit{n}\mathit{u}\mathit{m}}$)           If ${\mathcal{r}}_{\mathit{j}}$ > ${\mathbf{P}\left(\mathbf{Å}\mathbf{w}\right)}_{\mathit{j}}$            Generate $\left({\mathit{N}\mathit{e}\mathit{w}}_{\mathit{P}\mathit{o}\mathit{s}}\right)$           ${\mathit{x}}^{\mathit{i},\mathit{i}\mathit{t}\mathit{e}\mathit{r}+1}={\mathit{x}}^{\mathit{i},\mathit{i}\mathit{t}\mathit{e}\mathit{r}}+{\mathcal{r}}_{\mathit{j}}\times {{\mathcal{F}}_{\mathit{L}\mathit{e}\mathit{n}}\left(\mathit{i}\right)}^{\mathit{i}\mathit{t}\mathit{r}}\times \left({\mathit{m}}^{\mathit{j},\mathit{i}\mathit{t}\mathit{e}\mathit{r}}-{\mathit{x}}^{\mathit{i},\mathit{i}\mathit{t}\mathit{e}\mathit{r}}\right)$           $\mathit{e}\mathit{l}\mathit{s}\mathit{e}$ Generate $\left({\mathit{R}\mathit{a}\mathit{n}\mathit{d}}_{\mathit{P}\mathit{o}\mathit{s}}\right)$ //4. Check feasibility of new positions           For Each $\mathit{i}$ in ${\mathit{C}\mathit{r}\mathit{o}\mathit{w}}_{\mathit{n}\mathit{u}\mathit{m}}$           Check-Feasibility $\left({\mathit{N}\mathit{e}\mathit{w}}_{\mathit{P}\mathit{o}\mathit{s}}\right)$           If ${\mathit{N}\mathit{e}\mathit{w}}_{\mathit{P}\mathit{o}\mathit{s}}$ $\ge$ ${\mathcal{F}\mathit{e}\mathit{a}\mathit{s}\mathit{b}}_{\mathbb{T}\mathbb{H}}$                 ${\mathit{N}\mathit{e}\mathit{w}}_{\mathit{P}\mathit{o}\mathit{s}}⟶\mathbf{U}\mathbf{p}\mathbf{d}\mathbf{a}\mathbf{t}\mathbf{e}\left(\mathbf{P}\mathbf{o}\mathbf{s}\right)$           $\mathit{e}\mathit{l}\mathit{s}\mathit{e}$ No-$\mathbf{U}\mathbf{p}\mathbf{d}\mathbf{a}\mathbf{t}\mathbf{e}\left(\mathbf{P}\mathbf{o}\mathbf{s}\right)$ //5. Evaluate fitness function for new positions           For Each $\mathbf{i}$ in ${\mathit{C}\mathit{r}\mathit{o}\mathit{w}}_{\mathit{n}\mathit{u}\mathit{m}}$           Calculate (${\mathbf{F}\mathbf{i}\mathbf{t}}_{\left(\mathcal{F}\right)}$) //6. Update memory           For Each $\mathbf{i}$ in ${\mathit{C}\mathit{r}\mathit{o}\mathit{w}}_{\mathit{n}\mathit{u}\mathit{m}}$           If ${{\mathbf{F}\mathbf{i}\mathbf{t}}_{\left(\mathcal{F}\right)}}_{\mathit{i}+1}>{{\mathbf{F}\mathbf{i}\mathbf{t}}_{\left(\mathcal{F}\right)}}_{\mathit{i}}$           ${\mathit{N}\mathit{e}\mathit{w}}_{\mathit{P}\mathit{o}\mathit{s}}⟶\mathbf{U}\mathbf{p}\mathbf{d}\mathbf{a}\mathbf{t}\mathbf{e}\left(\mathbf{P}\mathbf{o}\mathbf{s}\right)$           Else No-$\mathbf{U}\mathbf{p}\mathbf{d}\mathbf{a}\mathbf{t}\mathbf{e}\left(\mathbf{P}\mathbf{o}\mathbf{s}\right)$ //7. Check termination criterion           If i $\le {\mathbf{M}\mathbf{a}\mathbf{x}}_{\mathbf{i}\mathbf{t}\mathbf{r}}$ Repeat step 1