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

Algorithm 1

Greedy transform method.

Input: 𝐗=(𝑥₁,𝑥₂,…,𝑥_𝑛)∈{0,1}^𝑛

Step1: sort

The items are sorted according to the value-to-weight ratio 𝑝_𝑖/𝑤_𝑖  (𝑖=1,2,3,…,𝑛) in

descending order, then a queue {𝑠₁,𝑠₂,…,𝑠_𝑛} of length n is formed.  It means that:

𝐩_𝑠1/𝐰_𝑠1≥𝐩_𝑠2/𝐰_𝑠2,   for 𝑠₁<𝑠₂

Step2: repair stage

𝑖=1; Tempc = 𝑤_𝑠1;

While  (Tempc ≤ C)

 if  (𝑥_𝑠𝑖=1) then

  𝑦_𝑠𝑖=1;𝑖=𝑖+1; Tempc = Tempc + 𝑤_𝑠𝑖;

 end if

end while

Step 3: optimize stage

For  𝑗=𝑖 to 𝑛

 Tempc  =  Tempc  +  𝑤_𝑠𝑗;

 if  (Tempc  ≤  C)   then

  𝑦_𝑠𝑗=1;

 Else

 𝑦_𝑠𝑗=0;

 end if

end for

Output:   𝐘=(𝑦₁,𝑦₂,…,𝑦_𝑛), computation is terminated.