Opposition-Based Barebones Particle Swarm for Constrained Nonlinear Optimization Problems

Algorithm 1

The proposed OBPSO algorithm.

𝟏Uniform randomly initialize each particle in the swarm;

2 Initialize pbest and gbest;

3 While    FEs ≤ MAX_FEs   do

  /*  Barebones PSO                         */

4  for  𝑖=1 to 𝑁  do

5   Calculate the position of the 𝑖th particle 𝑃_𝑖 according to (2.2);

6   Calculate the fitness value of 𝑃_𝑖 according to (3.6);

7   FEs++;

8  end

  /*  Opposition-based learning                   */

9    if  rand(0,1)≤𝑝_𝑜  then  

10   Update the dynamic interval boundaries [𝑎_𝑗(𝑡),𝑏_𝑗(𝑡)] in 𝑃 according to (3.3);

11   for  𝑖=1 to 𝑁  do

12    Generate the opposite particle of 𝑃_𝑖 according to (3.2)

13    Calculate the fitness value of 𝑃_𝑖 according to (3.6)

14    FEs++;

15   end

16   Select 𝑁 fittest particles from {𝑃, 𝑂𝑃} as current population 𝑃;

17  end

   /*  Boundary search strategy                   */

18  if  𝑀<𝑁  then  

19   𝐾=min{𝑀,𝑁−𝑀}

20   for  𝑖=1 to 𝐾  do

21    Randomly select a feasible solution 𝑥 and an infeasible solution 𝑦;

22    Generate a new solution 𝑧 according to (3.11);

23    Calculate the fitness value of 𝑧 according to (3.6);

24    𝐹𝐸𝑠++;

25    if  𝑧 is feasible  then

26      𝑥=𝑧;

27    end

28    else

29      𝑦=𝑧;

30    end

31   end

32  end

33  Update pbest and gbest;

34  end