Unused CF was recommended in the result

[Y-Wakuta]

Problem

Some recommended CFs are never used in any timestep

Cause

The numerical issue in Gurobi solver.

• the ration of max coefficient and min coefficient was too large > 10e+9
  • https://www.gurobi.com/pdfs/user-events/2016-frankfurt/Best-Practices.pdf
  • https://www.gurobi.com/documentation/9.0/refman/num_does_my_model_have_num.html
• the objective value was too large > 10e+4
  • https://www.gurobi.com/documentation/9.0/refman/num_recommended_ranges_for.html

Isn't the cause is constraints?

• I fixed index_vars by adding constraints to recommended the desired result. However, the desirable result was recommended without any problem. Therefore, there is no collision of constraints.
• I added CF num constraint not to recommend unnecessary CF. e.g. If there are 11 CFs and one of them is not used, force CF num <= 10. This recommended the desired result without any Exception.

Therefore, this bug is not produced by constraints. Therefore, this possibly produced by the objective function.

• The optimization is executed by three steps, cost, cost + index num, cost + index num + size. Gurobi outputs this warning when optimization is executed.

    Warning: Model contains large matrix coefficient range
         Consider reformulating model or setting NumericFocus parameter
         to avoid numerical issues.

Solutions

• fork mipper and set parameters.

        # strict gap
        Gurobi.GRBsetintparam @ptr, Gurobi::GRB_INT_PAR_OUTPUTFLAG, 0
        # strict gap
        Gurobi.GRBsetintparam @ptr, Gurobi::GRB_DBL_ATTR_MIPGAP, 0
        Gurobi.GRBsetintparam @ptr, Gurobi::GRB_DBL_PAR_MIPGAPABS, 0

• some coefficients in the objective function were multiplied by Interval
  • setting interval not in seconds but in minutes (3600 -> 60) fixed this problem
• increased coefficient for CF creation cost and the coefficient for migration support query to reduce the coefficient range