Artificial Bee Colony Algorithm Merged with Pheromone Communication Mechanism for the 0-1 Multidimensional Knapsack Problem

Algorithm 1

ABC.

1. Initialization: Initialize parameters K, N, Limit, 𝐶_𝑖=0 (𝑖=1,…, K );

2. Initial solutions: Randomly generated K food sources {𝑆_𝑖(0)∣𝑖=1,…, K};

3. Loop:

 For 𝑡=1 to N do:

 {

  (1) For 𝑖=1 to K do: (employed bees select food sources and perform local searches respectively)

    {Associate each employed bee with a food source 𝑆_𝑖(𝑡) and compute its nectar amount;

   Find a new 𝑆^′_𝑖(𝑡) in the neighborhood of 𝑆_𝑖(𝑡) and compute its nectar amount;

   Take the better one in {𝑆^′_𝑖(𝑡), 𝑆_𝑖(𝑡)} as a new location of the employed bee;}

  (2) For 𝑗=1 to K do: (onlooker bees help employed bees to perform further local searches)

    {Select a food source 𝑆_𝑗(𝑡) from {𝑆_𝑖(𝑡)} for every onlooker bee;

   Find a new 𝑆^′_𝑗(𝑡) in the neighborhood of 𝑆_𝑗(𝑡) and compute its nectar amount;

   Take the better one in {𝑆^′_𝑗(𝑡), 𝑆_𝑗(𝑡)} as a new location of the corresponding bees;}

  (3) Exploiting new food sources (scout bees randomly carry out global searches)

   For 𝑖=1 to K do: (food sources)

    {If 𝑆_𝑖(𝑡)=𝑆_𝑖(𝑡−1) then 𝐶_𝑖=𝐶_𝑖+1;

    If 𝐶_𝑖 = Limit then

     {Abandon the 𝑆_𝑖(𝑡) and the associated employed bee becomes a scout;

      Randomly generate a new 𝑆_𝑖(𝑡) and the scout becomes an employed bee again;

       𝐶_𝑖=0;}}

  (4) Memorize the best food source 𝑆_best found so far;

    𝑡=𝑡+1;

 }

4. Output: Return 𝑆_best while the predefined end condition is met.