How does docplex find the best bound?

Question

I really can't understand how does CPLEX compute the best bound in the first place. From my understanding CPLEX needs to explore all the nodes in order to find the best bound or the objective value that maximises or minimizes all feasible solutions. Knowing that exploring all nodes is infeasible in most cases, how can CPLEX find this best bound and in the first place? Any reference to papers or documentations is appreciated. Thank you in advance.

Answer 1

The best bound comes from the LP solution. It is the solution that would be possible if variables did not need to have integer values. No integer solution can possibly have a better objective value than this 'relaxed' solution, so it provides a valid bound on the objective. As CPLEX explores and eliminates parts of the B&B tree, it can update the bound with successively better values.