Algorithm 3. Tour improvement.
Input: $G=(V,E)$, initial charging tour $P$, traveling distance constraint $L$;
Output: An improved charging tour $P$
1:	repeat
2:		$R:=\varphi$
3:		for each vertex $v_i\in V$ and $v_i\notin P$ do
4:			$c_i^{″}:=\underset{v_x,v_y\in P}{\min }{c}_{ix}+c_{iy}-c_{xy}$
5:			if $c_i^{″}+C_{LKH}(P)\le L$ then
6:				$R(i,P):={\widehat{r}}_i/c_i^{″}$
7:				$R:=R\cup \{R(i,P)\}$
8:			else
9:				continue
10:			end if
11:		end for
12:		$v_i:=\arg \underset{R(i,P)\in R}{\max }R(i,P)$
13:		insert $v_i$ into $P$ at the location with minimum insertion cost
14:	until no more feasible vertices in $V\backslash P$
15:	return$P$