An Improved Hybrid Encoding Cuckoo Search Algorithm for 0-1 Knapsack Problems

Algorithm 3

The main procedure of ICS.

Step1: Sorting.  According to value-to-weight ratio 𝑝_𝑖/𝑤_𝑖(𝑖=1,2,3,…,𝑛)  in descending order,

a queue {𝑠₁,𝑠₂,…,𝑠_𝑛} of length n is formed.

Step2: Initialization.  Generate m cuckoo nests randomly {𝐱_𝟏,𝐛_𝟏,𝐱_𝟐,𝐛_𝟐,…,𝐱_𝐦,𝐛_𝐦}.

Calculate the fitness for each individual, 𝑓(𝐛_𝐢), 1≤𝑖≤𝑚, determine 𝐱^{𝐛𝐞𝐬𝐭},𝐛^{𝐛𝐞𝐬𝐭}.

Set the generation counter 𝐺=1. Set mutation parameter 𝑝_𝑚.

Step3: While  (the stopping criterion is not satisfied)

   for  𝑖=1 to m

    for 𝑗=1 to n

     𝐱_𝐢(𝐣)=𝐱_𝐢(𝐣)+𝛼⊕𝐋𝐞𝐯𝐲(𝜆)

     Apply new position updating formula of ICS  (Algorithm 2)

     Repair the illegal individuals and optimize the legal individuals  (Algorithm 1)

    end for

   end for

Step4: Keep best solutions; Rank the solutions and find the current best (𝐛^{𝐛𝐞𝐬𝐭},𝑓(𝐛^{𝐛𝐞𝐬𝐭})).

   𝐺=𝐺+1

Step5: end while