ILOG CPLEX 11.0 User's Manual

These limits are controlled by the parameters StrongCandLim and StrongItLim,respectively.Other parameters to consider trying, in the case of slow movement of the Best Node value,are non-default levels for Probe (try the aggressive setting of 3 first, and then reduce it if theprobing step itself takes excessive time for your purposes), and MIPEmphasis set to a valueof 3.Time Wasted on Overly Tight Optimality CriteriaSometimes ILOG CPLEX finds a good integer solution early, but must examine manyadditional nodes to prove the solution is optimal. You can speed up the process in such acase if you are willing to change the optimality tolerance. ILOG CPLEX supports two kindsof tolerance:◆Relative optimality tolerance guarantees that a solution lies within a certain percentageof the optimal solution.◆ Absolute optimality tolerance guarantees that a solution lies within a certain absoluterange of the optimal solution.The default relative optimality tolerance is 0.0001. At this tolerance, the final integersolution is guaranteed to be within 0.01% of the optimal value. Of course, manyformulations of integer or mixed integer programs do not require such tight tolerance, sorequiring ILOG CPLEX to seek integer solutions that meet this tolerance in those cases iswasted computation. If you can accept greater optimality tolerance in your model, then youshould change the parameter EpGap.If, however, you know that the objective values of your problem are near zero, then youshould change the absolute gap because percentages of very small numbers are less useful asoptimality tolerance. Change the parameter EpAGap in this case.To speed up the proof of optimality, you can set objective difference parameters, bothrelative and absolute. Setting these parameters helps when there are many integer solutionswith similar objective values. For example, setting the ObjDif parameter to 100.0 makesILOG CPLEX skip any potential solution with its objective value within 100.0 units of thebest integer solution so far. Or, setting the RelObjDif to 0.01 would mean thatILOG CPLEX would skip any potential new solution that is not at least 1% better than theincumbent solution. Naturally, since this objective difference setting may makeILOG CPLEX skip an interval where the true integer optimum may be found, the objectivedifference setting weakens the guarantee of optimality.Cutoff parameters can also be helpful in restricting the search for optimality. If you knowthat there are solutions within a certain distance of the initial relaxation of your problem,then you can readily set the upper cutoff parameter for minimization problems and the lowercutoff parameter for maximization problems. Set the parameters CutUp and CutLo,respectively, to establish a cutoff value.ILOG CPLEX 11.0 — USER’ S MANUAL 291