Multi-Objective Approach for Energy-Aware Workflow Scheduling in Cloud Computing Environments

Pseudocode 1

DVFS-MODPSO based workflow scheduling.

// Swarm initialization with HEFT

(1)  For i = 1 to SNum (SNum is the size of particle swarm)

 (a)  For j = 1 to m (m the number of processors)

    (i) Randomly initialize VSL(j) (randomly choose the voltage/frequency of processor from the set of its operating points).

 (b) Initialize 𝑆[𝑖] with HEFT heuristic (S is the swarm of particles)

 (c) Initialize the velocity V of each particle

      𝑉[𝑖]=0(𝑆[𝑖])

 (d) Initialize the Personal Best (pBest) of each particle:

      𝑝𝐵𝑒𝑠𝑡[𝑖]=𝑆[𝑖];

 (e) Evaluate objectives of each particle:

      Evaluate S[i]

 (f) Initialize the Global Best particle (gBest) with the best one among the SNum particles:

      g𝐵𝑒𝑠𝑡= Best particle found in 𝑆

(2) End For

(3) Add the nondominated solutions found in S into EA (EA is the External Archive storing the pareto front)

(4) Initialize the iteration number 𝑡=0

(5)  Repeat until 𝑡>𝐺 (𝐺 is the maximum number of iterations)

 (a)  For 𝑖=1 to SNum (swarm size)

  (i) Randomly select the global best particle for S from the External Archive EA and store its position in gBest.

  (ii) Calculate the new velocity 𝑉[𝑖] according to (22)

  (iii) Compute the new position of 𝑆[𝑖] according to (23)

  (iv)  If (𝑡<𝐺 * PMUT ) then (PMUT is the probability of mutation)

    Perform mutation on 𝑆[𝑖].

  (v)  Evaluate S[i]

 (b) End For

 (c) Update the personal best solution of each particle 𝑆[𝑖]:

     if 𝑆[𝑖]≼𝑝𝐵𝑒𝑠𝑡𝑠[𝑖]∨(𝑆[𝑖]∼𝑝𝐵𝑒𝑠𝑡𝑠[𝑖])

     Then 𝑝𝐵𝑒𝑠𝑡𝑠[𝑖]=𝑆[𝑖]

 (d) Update the External Archive EA:

   (i) Add all new non-dominated solution in S into EA

   if 𝑆[𝑖]⪯^╱𝑥,∀𝑥∈𝐸𝐴 Then 𝐸𝐴=𝐸𝐴∪{𝑆[𝑖]}

   (ii) Remove all particles dominated by 𝑆[𝑖] in EA

      𝐸𝐴=𝐸𝐴−{𝑦∈𝐸𝐴∣𝑦<𝑆[𝑖]}

   (iii) If the archive is full then randomly select the article to be replaced from EA.

(6) Return the pareto front (the set of non-dominated solutions from S and EA)