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

Algorithm 5

The DGHS algorithm.

(1) Set the harmony memory size HMS, the number of maximum improvisations

  maxFEs, and other control parameters

(2) Initialize the harmony memory HM, and perform Algorithm 4 to repair

   the harmony vector of HM, then evaluate their objective function values

(3) Set FEs=1 // FEs represents the iterative variable

(4) while   FEs⩽maxFEs  do

(5) Record the position of the best harmony in the HM, and its index

  is represented by 𝑏𝑒𝑠𝑡, likewise, 𝑤𝑜𝑟𝑠𝑡 denotes the index of the worst

  harmony in the current HM

(6) Calculate the parameter HMCR(FEs) according to (5a)

(7) Perform Algorithm 3 to produce a new harmony vector 𝑥^→′

(8) Perform Algorithm 4 to repair the new harmony vector 𝑥^→′

  // Perform a new greedy selection scheme

(9) if   𝑥^→′ is better than or equal to 𝑥^→_{𝑏𝑒𝑠𝑡}  then

(10)   Replace 𝑥^→_{𝑏𝑒𝑠𝑡} with 𝑥^→′

(11) else if   𝑥^→′ is better than or equal to 𝑥^→_{𝑤𝑜𝑟𝑠𝑡}  then

(12)   Substitute 𝑥^→_{𝑤𝑜𝑟𝑠𝑡} with 𝑥^→′

(13) end if

(14) Memorize the best harmony achieved so far

(15) Set FEs=FEs+1

(16) end while