Branching with relaxation

Xpress Kalis defines predefined branching schemes and value and variable selection heuristics based on the optimal solution of a relaxation:

• KALIS_LARGEST_REDUCED_COST variable selection heuristic selects the variable with the largest reduced cost in the optimal solution of the relaxation used by the specified relaxation solver.
• KALIS_NEAREST_RELAXED_VALUE value selection heuristic selects the value in the domain of the variable that is the nearest (in L1) to the value of this variable in the optimal solution of the relaxation used by the specified relaxation solver.

Moreover, the fix_to_relaxed method can be called during the tree search process to instantiate all the continuous variables to their values in the optimal solution of a relaxation.

This can be useful with some specific problem structures and in combination with the KALIS_BILEVEL_RELAX_SOLVER configuration for the relaxation solver to obtain an automatic logical benders decomposition of the solving process.