Algorithm 4. Solution promotion algorithm.

Input: ${\mathit{x}}^{\mathbf{\ast }}$ , ${\mathit{x}}^{\mathit{s}}$ , differential set $\mathit{T}$

Output: ${\mathit{x}}^{\mathbf{\ast }}$

1: While $\mathit{T}\mathbf{=}\mathit{\varphi }$

2: Change ${\mathit{x}}^{\mathit{s}}(\mathit{i})$ in ${\mathit{x}}^{\mathit{s}}$ as $\mathbf{1}\mathbf{-}{\mathit{x}}^{\mathit{s}}(\mathit{i})$;

3: Compute $\mathit{f}({\mathit{x}}^{\mathit{s}})$ , ${\mathit{x}}^{\mathit{s}}\mathbf{=}\mathbf{\{}{\mathit{x}}^{\mathit{s}}(\mathbf{1})\mathbf{,}{\mathit{x}}^{\mathit{s}}(\mathbf{2})\mathbf{,}\mathbf{\dots }\mathbf{,}\mathbf{1}\mathbf{-}{\mathit{x}}^{\mathit{s}}(\mathit{i})\mathbf{,}\mathbf{\dots }\mathbf{,}{\mathit{x}}^{\mathit{s}}(\mathit{n})\mathbf{\}}\mathbf{;}$

4: If ($\mathit{f}({\mathit{x}}^{\mathit{s}})\mathbf{>}\mathit{B}\mathbf{=}\mathit{f}({\mathit{x}}^{\mathbf{\ast }})$)

5: ${\mathit{x}}^{\mathbf{\ast }}\mathbf{=}{\mathit{x}}^{\mathit{s}}$;

6: Else if ($\mathit{f}({\mathit{x}}^{\mathit{s}})\mathbf{\le }\mathit{B}\mathbf{=}\mathit{f}({\mathit{x}}^{\mathbf{\ast }})$)

7: $\mathit{T}\mathbf{=}\mathit{T}\mathbf{-}\mathbf{\{}{\mathit{x}}^{\mathit{s}}(\mathit{j})\mathbf{\}}$;

8: End while

9: Return ${\mathit{x}}^{\mathbf{\ast }}$;