ILOG CPLEX 11.0 User's Manual

Too Much Time at Node 0If you observe that a very long time passes before the search begins processing nodes, it maybe that the root relaxation problem itself is taking a long time. The standard screen displaywill print a line telling "Root relaxation solution time =" once this root solve iscomplete, and a large solution time would be an indicator of an opportunity for tuning. Ifyou set the MIPDisplay parameter to 4, you may get a further indication of the difficultiesthis root solve has run into. Tuning techniques found in Solving LPs: Simplex Optimizers onpage 171, Solving Problems with a Quadratic Objective (QP) on page 227, and SolvingProblems with Quadratic Constraints (QCP) on page 239 are applicable to tuning the rootsolve of a MIP model, too. In particular, it is worth considering setting the RootAlgparameter to a nondefault setting, such as the barrier optimizer, to see if a simple change inalgorithm will speed up this step sufficiently.For some problems, ILOG CPLEX will spend a significant amount of time performingcomputation at node 0, apart from solving the continuous LP, QP, or QCP root relaxation.While this investment of time normally saves in the overall branch & cut, it does not alwaysdo so. Time spent at node 0 can be reduced by two parameters.First, you can try turning off the node heuristic by setting the parameter HeurFreq to -1.Second, try a less expensive variable selection strategy by setting the parameter VarSel to4, pseudo reduced costs.It is worth noting that setting the MIPEmphasis parameter to 1, resulting in an emphasis onfeasibility instead of optimality, often also speeds up the processing of the root node. If yourpurposes are compatible with this emphasis, consider using it.Trouble Finding More than One Feasible SolutionFor some models, ILOG CPLEX finds an integer feasible solution early in the process andthen does not find a better one for quite a while. One possibility, of course, is that the firstfeasible solution is optimal and will eventually be proven optimal. In that case, there are nobetter solutions.One possible approach to finding more feasible solutions is to increase the frequency of thenode heuristic, by setting the heuristic frequency parameter (HeurFreq,CPX_PARAM_HEURFREQ) to a value such as 10 or 5 or even 1. This heuristic can beexpensive, so exercise caution when setting this parameter to values less than 10.Another approach to finding more feasible solutions is to try a node selection strategyalternative. Setting the node selection parameter (NodeSel , CPX_PARAM_NODESEL) to 2invokes a best-estimate search, which sometimes does a better job of locating good qualityfeasible solutions than the default node selection strategy.The settings 1 (one) and 4 of the MIP emphasis parameter (MIPEmphasis,CPX_PARAM_MIPEMPHASIS) both address the issue of finding feasible solutions. TheseILOG CPLEX 11.0 — USER’ S MANUAL 289