A Variable Neighborhood Search Algorithm for the Leather Nesting Problem

Algorithm 2

 Input:

   For each 𝑁_𝑖, 𝑖=1,…,4, 𝑡_𝑁𝑖 sets of parameters (𝑢^𝑗_min,𝑖,𝑢^𝑗_max,𝑖), 𝑞^𝑗_𝑖 and 𝑟^𝑗_𝑖, 𝑗=1,…,𝑡_𝑁𝑖,

   such that 𝑡_max=∑⁴_𝑖=1𝑡_𝑁𝑖 (the resulting neighborhood structures will be indexed with the

   index 𝑡, with 𝑡=1,…,𝑡_max);

   A limit 𝑡_limit on the total computing time;

(1) Initialization:

  𝐿∶=findInitialSolution();

(2) Repeat the following steps until cpuTime()≥𝑡_limit:

      (a) 𝑡∶=1;

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

      𝐿^′∶=shaking(L, t );

       𝐿^′′∶= first Improvement (𝐿^′,𝑡);

if 𝑣(𝐿^′′)<𝑣(𝐿) then

𝐿∶=𝐿^′′;

 𝑡∶=1;

else

𝑡∶=𝑡+1;