An Efficient Algorithm for Unconstrained Optimization

Algorithm 2

PSO-3P algorithm.

(1) Begin.

(2) while  Termination criterion is not satisfied  do

(3)  Set variables , , , , and .

(4)  Create a population of nPop random particles.

(5)  Set and . Evaluate each position of the particles according to the fitness function.

(6)  If the current position of a particle is better (respect to the fitness function) than the previous update it.

(7)  Determine the best particle (according to the best previous positions against the optimization criterion).

     If a better particle cannot be founded, let .

(8)  Update the particle velocities according to (4).

(9)  (Phase 1: Stabilization) if    then

(10)   go to Step (34).

(11)    end

(12)   (Phase 2: Breadth-first search) if    then

(13)   if cont = c  then

(14)    Set . while    do

(15)     Create a random particle and, with a probability bigger than 0.5 substitute randomly a particle in the swarm.

(16)     Set .

(17)    end

(18)    Set .

(19)   end

(20)  go to Step (34).

(21)   end

(22) end

(23) (Phase 3: Depth-first search). if    then

(24)  if    then

(25)   Set . while  . do

(26)    Create a random particle in a variable neighborhood of and substitute randomly a particle in the swarm.

(27)    Set .

(28)   end

(29)  end

(30)  Set .

(31)   go to Step (34).

(32) end

(33) Select the best particles according to optimization criterion.

(34) Set . Go to Step (3) until the termination criterion is satisfied.