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

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

Algorithm 2 Levy-WOA workflow scheduling optimization algorithm

Input: task_list, allocation obtained from HEFT, Dag = (T, E), VM_list, pre

(t_{i}),

data_size

(t_{i},

t_{j}),

bandwidth

(V M_{k}

, V M_{l}),

population_size = 50, max_iterations

T_{\max}

= 200,

α

= 0.01,

β

= 1.5,

η

= 1,

ω_{1}

= 0.5,

ω_{2}

= 0.5

Output: the best solution best_schedule

population = []
for i = 1 to population_size-1 do
        schedule = {}
        for task in task_list do
                vm = random_select(VM_list)
                Obtain the start time

{S t a_T}_{k, i}

using Equation (7)
Obtain end time

F i n_T_{k, i}

of the current task and Equation (9)
                schedule[task] = (vm, start_time, end_time)
        end for
                population.append(schedule)
end for
             population.append(allocation)
For each schedule in population do
      Calculate makespan

F_{N}

of the workflow by Equation (11)
Calculate total cost

T o t a l_Cos t

by Equation (12)
      Calculate fitness value using Equation (23)
  end for
  Return Initial “best_schedule” with the highest fitness value among the population
  Return Initial “best_fitness” with the hightest fitness value among the population

t

= 0
while

t

< T_{\max}

a \leftarrow

a = 2 - \frac{2 t}{T_{\max}}

p

= rand(),

φ

= rand().
for each schedule in population do
if

p

< 0.5 then
                        Obtain a new schedule by Encircling Prey of WOA using Equations (24)–(28)
                else
                     if

φ

< 0.5 then
l = rand (−1, 1)
for task

t_{i}

in task_list:
                                Obtain a new schedule by the spiral update in Bubble-net Attacking using Equations (29) and (30)
                     else
                             for task

t_{i}

in task_list:
                                        Obtain a new schedule by Levy Flight Perturbation using Equations (31)–(34)
                       end if
               end if
              Calculate” current_fitness” the fitness value of the current new schedule using Equation (23)
              If current_fitness > best_fitness then
              best_schedule

\leftarrow

the current new schedule
best_fitness

\leftarrow

the current_fitness
end if
end for

t

t

+ 1
end while
Return best_schedule