A Variable Neighborhood Search Algorithm for the Leather Nesting Problem

Algorithm 1

 Input:

  𝑡_max neighborhood structures 𝑁_𝑡, 𝑡=1,…,𝑡_max;

  A stopping criterion;

(1) Initialization:

   𝑥∶=findInitialSolution ();

(2) Repeat the following steps until the stopping criterion is met:

   (a) 𝑡∶=1;

  (b) Repeat the following steps until 𝑡=𝑡_max:

𝑥^′∶=shaking(x, t );

𝑥^′′∶=localSearch(𝑥^′,𝑡);

if 𝑣(𝑥^′′)<𝑣(𝑥) then

𝑥∶=𝑥^′′;

𝑡∶=1;

else

𝑡∶=𝑡+1;