ILOG CPLEX 11.0 User's Manual

If the solution to the relaxation still has one or more fractional-valued integer variables afterILOG CPLEX tries to add cuts, then ILOG CPLEX branches on a fractional variable togenerate two new subproblems, each with more restrictive bounds on the branching variable.For example, with binary variables, one node will fix the variable at 0 (zero), the other,at 1 (one).The subproblems may result in an all-integer solution, in an infeasible solution, or anotherfractional solution. If the solution is fractional, ILOG CPLEX repeats the process.◆ Applying Cutoff Values on page 266◆ Applying Tolerance Parameters on page 266◆ Applying Heuristics on page 267◆ When an Integer Solution Is Found: the Incumbent on page 267◆ Controlling Strategies: Diving and Backtracking on page 267◆ Selecting Nodes on page 268◆ Selecting Variables on page 269◆ Changing Branching Direction on page 269◆ Solving Subproblems on page 270◆ Using Node Files on page 270Applying Cutoff ValuesILOG CPLEX cuts off nodes when the value of the objective function associated with thesubproblem at that node is worse than the cutoff value.You set the cutoff value by means of the CutUp parameter (for a minimization problem) orthe CutLo parameter (for a maximization problem), to indicate to ILOG CPLEX that integerfeasible solutions worse than this cutoff value should be discarded. The default value of thelower cutoff is -1e+75; the default value of the upper cutoff is 1e+75. The defaults, ineffect, mean that no cutoff is to be supplied. You can supply any number that you findappropriate for your problem. It is never required that you supply a cutoff, and in fact formost applications is it not done.Applying Tolerance ParametersILOG CPLEX will use the value of the best integer solution found so far, as modified by thetolerance parameters ObjDif (absolute objective function difference) or RelObjDif(relative objective function difference) as the cutoff. Again, it is not typical that users setthese parameters, but they are available if you find them useful. Use care in changing thesetolerances: if either of them is nonzero, you may miss the optimal solution by as much asthat amount. For example, in a model where the true minimum is 100 and the absolute cutoffis set to 5, if a feasible solution of say, 103 is found at some point, the cutoff will discard allnodes with a solution worse than 98, and thus the solution of 100 would be overlooked.266 ILOG CPLEX 11.0 — USER’ S MANUAL