How do I modify the branch-and-bound algorithm or create a branch-price-and-cut algorithm?

Gurobi does not support to apply your own branching rules or dynamically add new variables in some branch-and-bound node, as it is required in algorithms based on column generation, e.g., branch-and-price(-and-cut) algorithms. Instead, you have to build your own branch-and-bound algorithm, use Gurobi to solve the node relaxation, and modify the model in-between to implement column and cut generation, custom branching rules, etc.

In general, if you want to significantly intervene in Gurobi's branch-and-bound algorithm, you need to:

• terminate the optimization (in a callback or based on some termination criteria),
• modify the model and/or parameters, and
• restart optimization (that usually is able to warmstart from previous results).

Further information

• How do I change parameters in a callback?