Algorithm 3 Optimisation based on SA algorithm

1: Let $\mathcal{T}$> 0 as initial parameter 2: Let $\mathcal{N}$($\mathcal{T}$) as maximum number of iterations 3: while stop criterion has not been met do 4:  Randomly generate a fasible solution $t_{sched}$ 5:  Evaluate $t_{sched}^i$, $\mathcal{D}$ = f($t_{sched}^i$) 6:  n = 1 7:  while while n $<=$ $\mathcal{N}$($\mathcal{T}$) do 8:   Generate solution $t_{sche{d}^{\prime }}^i$ based on $t_{sched}^i$ 9:   Evaluation of $t_{sche{d}^{\prime }}^i$; ${\mathcal{D}}^{\prime }$ = f($t_{sche{d}^{\prime }}^i$); $\delta$ =  f($t_{sche{d}^{\prime }}^i$)–f($t_{sched}^i$) 10:   if f($t_{osi}^{\prime }$) < f($t_{sched}^i$) then 11:    $t_{sched}^i$ = $t_{sche{d}^{\prime }}^i$ 12:   else 13:    if$\delta$ >= 0 and u< exp((f($t_{sche{d}^{\prime }}^i$)–f($t_{sched}^i$))/$\mathcal{T}$) then 14:     $t_{sched}^i$ = $t_{sche{d}^{\prime }}^i$ 15:    end if 16:   end if 17:   n = n+1 18:  end while 19:  $\mathcal{T}$ reduction and update $t_{sched}^i$ at each reduction 20: end while