A Novel Self-Adaptive Harmony Search Algorithm

Algorithm 1

Pseudo code of the NSHS algorithm.

NSHS Algorithm

Initialise the problem and algorithm parameters:

   Define a standard fitness function 𝑓(𝑥),𝑥_𝑖∈[𝑙𝑏_𝑖,𝑢𝑏_𝑖](𝑖=1,2,…,𝑛) by (1)

   Define the parameters HMCR by (10), Bw by (11), HMS and NI

   Generate randomly an initial HM and calculate fstd

Search the best solution:

While (𝑘≤NI) do

  Generate a new harmony vector by the following loop

  While (𝑖≤𝑛) do

    First, generate a new value for every variable by the following rules:

    If (𝑟≤HMCR,𝑟∼𝑈[0,1]), then choose uniformly a value from the current memory for variable

     𝑥^′_𝑖=𝑥^𝑗_𝑖;𝑗∈{1,2,…,HMS}

    Else, generate randomly

        If 𝑓std>0.0001, then generate randomly in the range of [𝑙𝑏_𝑖,𝑢𝑏_𝑖]

       𝑥^′_𝑖=𝑙𝑏_𝑖+𝑟1∗𝑢𝑏_𝑖−𝑙𝑏_𝑖;𝑟1∼𝑈[0,1]

        Else, generate randomly in the range of [min_𝑗𝑥^𝑗_𝑖,max_𝑗𝑥^𝑗_𝑖]

       𝑥^′_𝑖=min_𝑗𝑥^𝑗_𝑖+𝑟1∗(max_𝑗𝑥^𝑗_𝑖−min_𝑗𝑥^𝑗_𝑖);𝑟1∼𝑈[0,1]

        End if

    End if

    Second, adjust the new value of every variable by the following rules:

    If 𝑓std>0.0001, then

       𝑥_𝑖^′′=𝑥^′+𝑢𝑏_𝑖−𝑙𝑏_𝑖∗𝑘1001−NI∗𝑟2;𝑟2∼𝑈[−1,1]

    Else, generate randomly in the range of [min_𝑗𝑥^𝑗_𝑖,max_𝑗𝑥^𝑗_𝑖]

       𝑥_𝑖^′′=𝑥^′_𝑖+0.0001∗𝑟2;𝑟2∼𝑈[−1,1]

    End if

  End while

  Assess the merit of the new harmony vector and update the current harmony memory

  If 𝑓(𝑥^new)<𝑓(𝑥^worst)=max_𝑗𝑓(𝑥^𝑗), then

    Accept the new harmony vector and replace the worst vector in the HM with it.

    Recalculate the standard deviation of the fitness function values fstd.

  End if

End while

Determine the optimal solution in the HM by the minimum fitness.