ILOG CPLEX 11.0 User's Manual

little variability in the righthand side coefficients but significant variability in the costcoefficients.Primal Simplex OptimizerILOG CPLEX's Primal Simplex Optimizer also can effectively solve a wide variety of linearprogramming problems with its default parameter settings. The primal simplex method isnot the obvious choice for a first try at optimizing a linear programming problem. However,this method will sometimes work better on problems where the number of variables exceedsthe number of constraints significantly, or on problems that exhibit little variability in thecost coefficients. Few problems exhibit poor numeric performance in both primal and dualform. Consequently, if you have a problem where numeric difficulties occur when you usethe dual simplex optimizer, then consider using the primal simplex optimizer instead.Network OptimizerIf a major part of your problem is structured as a network, then the ILOG CPLEX NetworkOptimizer may have a positive impact on performance. The ILOG CPLEX NetworkOptimizer recognizes a special class of linear programming problems with networkstructure. It uses highly efficient network algorithms on that part of the problem to find asolution from which it then constructs an advanced basis for the rest of your problem. Fromthis advanced basis, ILOG CPLEX then iterates to find a solution to the full problem.Solving Network-Flow Problems on page 217 explores this optimizer in greater detail.Barrier OptimizerThe barrier optimizer offers an approach particularly efficient on large, sparse problems (forexample, more than 100 000 rows or columns, and no more than perhaps a dozen nonzerosper column) and sometimes on other models as well. The barrier optimizer is sufficientlydifferent in nature from the other optimizers that it is discussed in detail in Solving LPs:Barrier Optimizer on page 197.Sifting OptimizerSifting was developed to exploit the characteristics of models with large aspect ratios (thatis, a large ratio of the number of columns to the number of rows). In particular, the method iswell suited to large aspect ratio models where an optimal solution can be expected to placemost variables at their lower bounds. The sifting algorithm can be thought of as an extensionto the familiar simplex method. It starts by solving a subproblem (known as the workingproblem) consisting of all rows but only a small subset of the full set of columns, byassuming an arbitrary value (such as its lower bound) for the solution value of each of theremaining columns. This solution is then used to re-evaluate the reduced costs of theremaining columns. Any columns whose reduced costs violate the optimality criterionbecome candidates to be added to the working problem for the next major sifting iteration.174 ILOG CPLEX 11.0 — USER’ S MANUAL