A Dynamic Multistage Hybrid Swarm Intelligence Optimization Algorithm for Function Optimization

Pseudocode 1

Pseudocode of DM-PSO-ABC.

A dynamic Multi-stage hybrid swarm intelligence optimization algorithm

𝑚: Each swarm’s population size

𝑆: Swarms’ number

𝐿: Regrouping period

Max_gen: Max generations, stop criterion

Step 1 Generate initial 𝑚∗𝑛 particles and set up parameters for each particle;

   Initialize the position of all particles 𝑋=(𝑋₁,𝑋₂,…,𝑋_𝑁), and their fitnesses, and

   the velocity of all particles 𝑉= (𝑉₁,𝑉₂,…,𝑉_𝑁); the best local position of all particles

   pbest=(pbest₁,pbest₂,…,pbest_𝑁);

Step 2 Update all particles using local version PSO with Dynamic multi-group

   For 𝑖=1∶0.95∗Max_gen

      Update each swarm using (2.2), (2.3) local version PSO, pbests and lbests updating

   If mod(𝑖,𝐿)==0

   Regroup the swarms randomly

   End

Step 3 local search carried out in each small swarm by the artificial bee colony

   the population of food sources (solutions) is initialized by the current lbests in each

   sub-swarm

   For each component 𝑗∈(1,2,…,𝐷)

Employed Bees’ Phase

 For each employed bee 𝑖

  Replace the 𝑗 component of the lbest by using the 𝑗 component of bee 𝑖

  Calculate the [𝑓_newlbest (lbest₁, lbest₂,…,𝑥_𝑖𝑗,…,lbest_𝐷)]

  If (𝑓_newlbest_ better than 𝑓_lbest)

Then newlbest replaced lbest

  For employed bee 𝑖 produce new food source positions 𝑉_𝑖 by using (2.4)

  Calculate the value fitness by using (2.5)

  Apply greedy selection mechanism

  End For.

End For

  Calculate the probability values 𝑝_𝑖 for the solutions 𝑋_𝑖 by (2.6) and (2.7) using the

  roulette wheel selection rule;

Onlooker Bees’ Phase

 For each onlooker bee 𝑖

 Chooses a food source depending on 𝑝_𝑖

 Replace the 𝑗 component of the lbest by using the  𝑗  component of bee 𝑖

 Calculate the 𝑓[newlbest](lbest₁, lbest₂,…,𝑥_𝑖𝑗,…,lbest_𝐷)

 If 𝑓(newlbest) better than 𝑓(lbest)

 Then newlbest replaced lbest

 For onlooker bee 𝑖 produce new food source positions 𝑉_𝑖 by using (2.4)

 Calculate the value fitness

 Apply greedy selection mechanism

 End For

End For

Scout Bees’ Phase

 If there is an employed bee becomes scout

 Then replace it with a new random source positions by using (2.8)

 Memorize the best solution achieved so far

 Compare the best solution with lbest and Memorize the better one.

Step 4 Update all particles using global version PSO

 For 𝑖=0.95∗Max_gen∶Max_gen

 Update all particles using global version PSO, pbests and gbest updating

End