ILOG CPLEX 11.0 User's Manual

Table 9.5 PPriInd Parameter Settings for Primal Simplex Pricing AlgorithmDescription Concert Callable Library-1 reduced-cost pricing PPriIndPartial CPX_PPRIIND_PARTIAL0 hybrid reduced-cost and devex PPriIndAuto CPX_PPRIIND_AUTO1 devex pricing PPriIndDevex CPX_PPRIIND_DEVEX2 steepest-edge pricing PPriIndSteep CPX_PPRIIND_STEEP3 steepest-edge, slack initial norms PPriIndSteepQStart CPX_PPRIIND_STEEPQSTART4 full pricing PriIndFull CPX_PPRIIND_FULLFor the dual simplex pricing parameter, the default value selects steepest-edge pricing. Thatis, the default (0 or CPX_DPRIIND_AUTO) automatically selects 2 or CPX_DPRIIND_STEEP.For the primal simplex pricing parameter, reduced-cost pricing (-1) is less computationallyexpensive, so you may prefer it for small or relatively easy problems. Try reduced-costpricing, and watch for faster solution times. Also if your problem is dense (say, 20-30nonzeros per column), reduced-cost pricing may be advantageous.In contrast, if you have a more difficult problem taking many iterations to complete Phase Iand arrive at an initial solution, then you should consider devex pricing (1). Devex pricingbenefits more from ILOG CPLEX linear algebra enhancements than does partial pricing, soit may be an attractive alternative to partial pricing in some problems. However, if yourproblem has many columns and relatively few rows, devex pricing is not likely to help much.In such a case, the number of calculations required per iteration will usually bedisadvantageous.If you observe that devex pricing helps, then you might also consider steepest-edgepricing (2). Steepest-edge pricing is computationally more expensive than reduced-costpricing, but it may produce the best results on difficult problems. One way of reducing thecomputational intensity of steepest-edge pricing is to choose steepest-edge pricing withinitial slack norms (3).ScalingPoorly conditioned problems (that is, problems in which even minor changes in data result inmajor changes in solutions) may benefit from an alternative scaling method. Scalingattempts to rectify poorly conditioned problems by multiplying rows or columns byconstants without changing the fundamental sense of the problem. If you observe that yourproblem has difficulty staying feasible during its solution, then you should consider analternative scaling method.ILOG CPLEX 11.0 — USER’ S MANUAL 181