Discrete and Continuous Optimization Based on Hierarchical Artificial Bee Colony Optimizer

Algorithm 1

Pseudocode for the HABC algorithm.

HABC algorithm

Set 𝑡∶=0;

INITIALIZE.

   Randomly divide the whole population into N species (𝑃_𝑖) each possesses 𝐾 sub-populations (𝑃_𝑖𝑗), each possesses 𝑀 bees;

Randomize 𝑃_𝑖𝑗’s D-dimensions food source positions 𝑃_𝑖𝑗⋅𝑋_𝑘; 𝑖∈[1∶𝑁], 𝑗∈[1∶𝐾], 𝑘∈[1∶𝑀].

   Each sub-population 𝑃_𝑖𝑗 with S dimensions (where S is randomly chosen from a set G, and 𝐷=𝐾∗𝑆).

WHILE (the termination conditions are not met)

      for each species i, 𝑖=[1∶𝑁]

      Initialize D-dimensions complete vector 𝐺𝑏𝑒𝑠𝑡=(𝑃_𝑖1⋅𝑔,𝑃_𝑖2⋅𝑔,…,𝑃_𝑖l−1⋅𝑔,𝑧, 𝑃_𝑖l+1⋅𝑔,…,𝑃_𝑖𝐾⋅𝑔),

      which consists of the S-dimensions

      best solution 𝑃_𝑖𝑙 𝑦.

      Randomly all D dimension indices;

      WHILE (the termination conditions are not met)

          for each sub-population 𝑃_𝑖𝑗,𝑗=[1∶𝐾] do

             repeat

             Employed Bees’ Phase:

             For each employed bee 𝑃_𝑖𝑗⋅𝑥_𝑘∶

              Produce a new solution by using (2)

              Evaluate the new solution

              Apply Greedy selection choosing the better solution

                  end

                  Calculate the probability values Pi for the solution by using (2)

                Onlooker Bees’ Phase:

             for each employed bee 𝑃_𝑖𝑗⋅𝑥_𝑘

              Probabilistically choose a solution according to 𝑃_𝑖

              Produce a new solution by (2)

              Evaluate the new solution

              Apply Greedy selection choosing the better solution

                  end

             Re-initialize solutions not improved for Limit cycles

             Memorize the best solution 𝑃_𝑖𝑗⋅𝑥

             for each individual of 𝑃_𝑖𝑗⋅𝑥_𝑘, 𝑘=[1∶𝑀] do

                    Place best solution in the complete solution newGbest by:

                       𝑛𝑒𝑤𝐺𝑏𝑒𝑠𝑡= (𝑃_𝑖1⋅𝑔, 𝑃_𝑖2⋅𝑔,…,𝑃_𝑖𝑗⋅𝑥_𝑘,…,𝑃_𝑖𝐾⋅𝑔)

                    Update complete solution if it improves:

                    If (newGbest) <  f  (Gbest))

                       Then 𝑃_𝑖𝑗⋅𝑔=𝑃_𝑖𝑗·𝑥_𝑘

                  end

          end

      end WHILE

      Select elites form neighborhood of 𝑃_𝑖

      BPL = the top 𝑀 best individuals of the ring topology {𝑃_𝑖−1,𝑃_𝑖,𝑃_𝑖+1}

      Crossover and Mutation 𝑃_𝑖^′ by (4)

      Update 𝑃_𝑖 with applying Greedy selection mechanism from 𝑃_𝑖^′

      end

      find the global best solution gbest from the whole population P

      memorize the best solution of each 𝑃_𝑖𝑗

      Set 𝑡∶=𝑡+1;

 end WHILE