An Effective Heuristic-Based Approach for Partitioning

Algorithm 1

Annealing algorithm.

(1) Initialize the parameters of the annealing algorithm;

(2) Randomly generate an initial state as the 𝑐𝑢𝑟𝑟𝑒𝑛𝑡_𝑠𝑡𝑎𝑡𝑒;

(3) K ≔ 1;

(4) while (system has been frozen) do

(5)  while (system equilibrium at 𝑇_𝑘) do

(6)   call generation strategy for the 𝑛𝑒𝑥𝑡_𝑠𝑡𝑎𝑡𝑒_𝑗;

(7)   Δ𝐸_𝑖𝑗 = cost(𝑛𝑒𝑥𝑡_𝑠𝑡𝑎𝑡𝑒_𝑗) − cost(𝑐𝑢𝑟𝑟𝑒𝑛𝑡_𝑠𝑡𝑎𝑡𝑒);

(8)   𝑃_𝑟=𝐴_𝑖𝑗;

(9)   if (𝑃_𝑟>𝑟𝑎𝑛𝑑𝑜𝑚[0,1)) then

(10)   𝑐𝑢𝑟𝑟𝑒𝑛𝑡_𝑠𝑡𝑎𝑡𝑒≔ 𝑛𝑒𝑥𝑡_𝑠𝑡𝑎𝑡𝑒_𝑗;

(11)    end if

(12)  end while

(13)  𝑇_𝑘+1∶=𝑇_𝑘⋅𝛼;

(14) end while

(15) return  𝑐𝑢𝑟𝑟𝑒𝑛𝑡_𝑠𝑡𝑎𝑡𝑒;