Optimizing Virtual Private Network Design Using a New Heuristic Optimization Method

Algorithm 1

Landscape smoothing search (LSS).

Procedure   algorithm LSS  (F,λ,X,G)

begin

create initial feasible solution 𝑋₀

set 𝑑_ℎ(X)= 0, (h = 1,…,H)

(set all initial smoothing factors to zero)

 for  i:   =  1   to max-iterations

 begin

  𝐹^(X) = F(X) + ∑_ℎ[𝜆_ℎ∗𝑑_ℎ(𝑋)]

  𝑋_𝑖 = Local search (𝐹^, 𝜆_ℎ, 𝑋_𝑖−1, G)

  for each h:   =  1 to H

  begin

   adjust 𝑑_ℎ(X);

      (𝑋_ℎ is the local optimum point)

   if  F(𝑋_𝑖) < 𝐹^best  then

    𝐹^best :  =  F(𝑋_𝑖);

    𝑋^best:   =   𝑋_𝑖;

   end

   adjust 𝜆_ℎ  for adaptive λ;

  end

 end procedure

 LSS  returns 𝑋^best where F(𝑋^best) is the minimum of all solutions so far.