An Effective QoS-Aware Hybrid Optimization Approach for Workflow Scheduling in Cloud Computing

. 2025 Jul 30;25(15):4705. doi: 10.3390/s25154705

Algorithm 1 Workflow scheduling Based on HEFT

Input: the workflow

D a g = (T, E)

, W[i][k], B[k][l]
Output: A task_list sorted in descending order of Upward rank, the allocation of task to VM
for each task

t_{i}

T

do
rank_u

[t_{i}

] ← 0
end for
for each task

t_{i}

in reverse topological order of Dag do
Obtain the average computation time

\bar{w_{i}}

using Equation (17)
if

s u c c (t_{i})

is empty then
rank_u

[t_{i}]

\leftarrow \bar{w_{i}}

else
Obtain the

\max_{t_{j} \in s u c c (t_{i})} (\bar{c_{i, j}} + r a n k_{u} (t_{j}))

by Equations (18)–(20)
Update the

r a n k_{u} (t_{j})

by Equation (21)
               end if
          end for
       task_list ← []
       temp_list ← sort

T

r a n k_{u} (t_{j})

in descending order
while temp_list is not empty do
for each task

t_{i}

in temp_list do
all_pred_scheduled ← true
for each predecessor task

t_{k}

t_{i}

do
if

t_{k}

not in task_list then
                                    all_pred_scheduled ← false
                                    break
                               end if
                       end for
                       if all_pred_scheduled then
                               task_list.append

(t_{i}

)
temp_list.remove

(t_{i}

)
                               break
                       end if
               end for
       end while
return task_list
       allocation ← {}
       machine_ready_time ← [0, 0, …, 0]
       for each task

t_{i}

in task_list do
               earliest_finish_time ← ∞
               selected_machine ← −1
               for each machine k in Machines do
                       Calculate

{S t a_T}_{k, i}

t_{i}

V M_{k}

Calculate

F i n_T_{k, i}

t_{i}

V M_{k}

                       Update the selected_machine based on earliest completion time
               end for
               Assign

t_{i}

to the selected_machine

V M_{k}

Add this assignment to the allocation
update the ready time of

V M_{k}

end for
return allocation