A Novel Discrete Global-Best Harmony Search Algorithm for Solving 0-1 Knapsack Problems

Algorithm 4

The two-phase repair operator.

(1) Let 𝑣 represent a new generated harmony vector

 // Calculate the total weight of knapsack according to 𝑣

(2) 𝑡𝑜𝑡𝑊=𝑣∗𝑤^𝑇 // 𝑡𝑜𝑡𝑊 denotes the total weight

(3) if   𝑡𝑜𝑡𝑊>𝐶  then

(4) // The “DROP” phase

(5) for   𝑗=1 to 𝑁  do

(6)  𝜆_𝑗=𝑝_𝑗𝑤_𝑗𝑣_𝑗 // Compute the profit density value of items loaded

(7) end for

(8) Sort items in increasing order of 𝜆_𝑗, and let 𝜆_𝑗 represent the result sorted,

   and ind_𝑗 denotes the original index of each 𝜆_𝑗

(9) for   𝑗=1 to 𝑁  do

(10)  if   𝜆_𝑗==0  then

(11)   Continue

(12)  end if

(13)  𝑣_ind𝑗=0 // Unload the ind_𝑗th item from the knapsack

(14)  𝑡𝑜𝑡𝑊=𝑣∗𝑤^𝑇

(15)  if   𝑡𝑜𝑡𝑊⩽𝐶  then

(16)   Break // Terminate the “DROP” phase of repair process

(17)  end if

(18) end for

(19) end if

(20) 𝑡𝑜𝑡𝑊=𝑣∗𝑤^𝑇

(21) if   𝑡𝑜𝑡𝑊<𝐶  then

(22) // The “ADD” phase

(23) Calculate the profit density ratio 𝜇_𝑗 according to (4)

(24) Sort all the items in decreasing order of 𝜇_𝑗, and let 𝜇_𝑗 represent the result sorted,

   and ind_𝑗 denotes the original index of each 𝜇_𝑗

(25) for   𝑗=1 to 𝑁  do

(26)  if   𝑣_ind𝑗==0  then

(27)   Let 𝑣¹ represent a temporary harmony vector, and set 𝑣¹=𝑣

(28)   Set 𝑣¹_ind𝑗=1 //Try to load the ind_𝑗th item

(29)   if   𝑣¹∗𝑤^𝑇 ≤ 𝐶  then

(30)    𝑣_ind𝑗=1 // Load the ind_𝑗th item into knapsack

(31)   end if

(32)   end if

(33) end for

(34) end if