ILOG CPLEX C++ API 9.0 Reference Manual

IloCplex
classes that allow the user to monitor solution progress at each level. Callbacks derived
from IloCplex::ContinuousCallbackI or one of its derived classes are called
regularly during the solution of a node relaxation (including the root), and callbacks
derived from IloCplex::MIPCallbackI or one of its derived callbacks are
called regularly during branch & cut search. All callbacks provide the option to abort the
current optimization.
Branch Priorities and Directions
When a branch occurs at a node in the branch & cut tree, usually there is a set of
fractional-valued variables available to pick from for branching. IloCplex has several
built-in rules for making such a choice, and they can be controlled by the parameter
IloCplex::VarSel. Also, the method setPriority allows the user to specify
a priority order. An instance of IloCplex branches on variables with an assigned
priority before variables without a priority. It also branches on variables with higher
priority before variables with lower priority, when the variables have fractional values.
Frequently, when two new nodes have been created (controlled by the parameter
IloCplex::BtTol), one of the two nodes is processed next. This activity is known
as diving. The branch direction determines which of the branches, the up or the down
branch, is used when diving. By default, IloCplex automatically selects the branch
direction. The user can control the branch direction by the method setDirection.
As mentioned before, the greatest flexibility for controlling the branching during branch
& cut search is provided through goals (see IloCplex::Goal) or through the
callbacks (see IloCplex::BranchCallbackI). With these concepts, you can
control the branching decision based on runtime information during the search, instead
of statically through branch priorities and directions, but the default strategies work well
on many problems.
Cuts
An instance of IloCplex can also generate certain cuts in order to strengthen the
relaxation, that is, in order to make the relaxation a better approximation of the original
MIP. Cuts are constraints added to a model to restrict (cut away) noninteger solutions
that would otherwise be solutions of the relaxation. The addition of cuts usually reduces
the number of branches needed to solve a MIP.
When solving a MIP, IloCplex tries to generate violated cuts to add to the problem
after solving a node. After IloCplex adds cuts, the subproblem is re-optimized.
IloCplex then repeats the process of adding cuts at a node and reoptimizing until it
finds no further effective cuts.
An instance of IloCplex generates its cuts in such a way that they are valid for all
subproblems, even when they are discovered during analysis of a particular node. After
a cut has been added to the problem, it will remain in the problem to the end of the
optimization. However, cuts are added only internally; that is, they will not be part of
the model extracted to the IloCplex object after the optimization. Cuts are most
ILOG CPLEX C++ API 9.0 REFERENCE M ANUAL 50