Algorithm 2. Hyper-matheuristic algorithm.

REQUIRE: Hyper-matheuristic parameters, MILP Problem

ENSURE: Hi, Best metaheuristic.

1  Fix limits for all the parameters in the scheme (upper and lower bound);

2  for i = 1 to NIM do

3    Generate matheuristic Hi;

4  End

5  for i = 1 to NIM do

6   Solve problem using the matheuristic in Hi;

7   for k = 1 to i do

8    if (Hi solution quality) < (Hk solution quality) then

9     Compare parameters between the metaheuristics;

10     Improve the matheuristic Hi modifying the parameters with more differences;

11    end

12   end

13  end

14  for i = NIM to NIM + NFM do

15   Select two matheuristics randomly from those generated in step 3;

16   Combine their parameters to create a new metaheuristic;

17   Execute steps from line 6 to 12;

18  end

19  Classify all the solutions by quality and time;

20  Select the best matheuristic (which maximize fitness/time), and save parameters;