Choosing an Optimizer

Solving the extracted model with ILOG CPLEX involves solving one or a series of LPs or QPs:

Only one LP or QP needs to be solved if the extracted model is continuous itself, that is, if it does not contain integer, Boolean, semi-continuous or semi-integer variables, SOS, or piecewise linear functions. Chapter 5, Solving Linear Programming Problems discusses the algorithms available for solving LPs. Similarly, Chapter 7, Solving Quadratic Programming Problems, discusses the algorithms available for solving QPs.
In all other cases, the extracted problem that ILOG CPLEX sees is indeed a MIP and, in general, a series of LPs or QPs needs to be solved. Method cplex.isMIP() returns IloTrue in such a case. Chapter 8, Solving Mixed Integer Programming Problems discusses the algorithms applied.

The optimizer option used for solving the first LP or QP (whether it is the only one or just the first in a series of problems) is controlled by setting the root algorithm parameter:

cplex.setParam(IloCplex::RootAlg, alg);

where alg is a member of the nested enumeration type:

  enum IloCplex::Algorithm { 
    Primal, 
    Dual, 
    Barrier, 
    Network, 
    Sifting, 
    Concurrent
  };

Note that the last two choices, Sifting and Concurrent, are not available for QP models. As a nested enumeration type, the fully qualified names that must be used in the program are IloCplex::Primal, IloCplex::Dual, and so on. Table 1.2 displays the meaning of the optimizer options defined by IloCplex::Algorithm



Table 1.2    Optimizer Options


IloCplex::Primal  use the primal simplex algorithm 
IloCplex::Dual  use the dual simplex algorithm 
IloCplex::Barrier   use the barrier algorithm. The type of crossover performed after the barrier algorithm is determined by parameter IloCplex::BarCrossAlg. 
IloCplex::Network  use the primal network simplex algorithm on an embedded network followed by the dual simplex algorithm for LPs and the primal simplex algorithm for QPs on the entire problem 
IloCplex::Sifting  use the sifting algorithm 
IloCplex::Concurrent  use multiple algorithms concurrently on a multiprocessor system

.

If the extracted model requires the solution of more than one LP or QP, the algorithm for solving all but the first is controlled by the NodeAlg parameter:

  cplex.setParam(IloCplex::NodeAlg, alg).

Controlling ILOG CPLEX Optimizers

Though ILOG CPLEX defaults will prove sufficient to solve most of the problems, ILOG CPLEX offers a variety of parameters to control various algorithmic choices. ILOG CPLEX parameters can assume values of type bool, num, int, and string. IloCplex provides four categories of parameters that are listed in the nested enumeration types IloCplex::BoolParam, IloCplex::IntParam, IloCplex::NumParam, IloCplex::StringParam.

To access the current value of a parameter that interests you from the Concert Technology Library, use the method getParam. To access the default value of a parameter, use the method getDefault. Use the methods getMin and getMax to access the minimum and maximum values of num and int type parameters.

Some integer parameters are tied to nested enumerations that define symbolic constants for the values the parameter may assume.

In particular, these enumeration types are: IloCplex::MIPEmphasisType, , IloCplex::VariableSelect, IloCplex::NodeSelect, IloCplex::PrimalPricing, IloCplex::DualPricing., and IloCplex::BranchDirection. They are used for parameters IloCplex::MIPEmphasis, IloCplex::VarSel, IloCplex::NodeSel, IloCplex::PPriInd, IloCplex::DPriInd, and IloCplex::BrDir, respectively. Only the parameter IloCplex::MIPEmphasis may be of importance for general use.

There are, of course, routines in the Concert Technology Library to set these parameters. Use the following methods to set the values of ILOG CPLEX parameters:

  IloCplex::setParam(BoolParam, value);
  IloCplex::setParam(IntParam, value);
  IloCplex::setParam(NumParam, value);
  IloCplex::setParam(StringParam, value);

For example, the numerical parameter IloCplex::EpOpt controlling the optimality tolerance for the simplex algorithms can be set to 0.0001 by calling

  cplex.setParam(IloCplex::EpOpt, 0.0001);

The ILOG CPLEX Reference Manual documents the type of each parameter (bool, int, num, string) along with the Concert Technology enumeration value, symbolic constant, and reference number representing the parameter.

The method setDefaults resets all parameters (except the log file) to their default values, including the ILOG CPLEX callback functions. This routine resets the callback functions to NULL.

When solving MIPs, additional controls of the solution process are provided. Priority orders and branching directions can be used to control the branching in a static way. These are discussed in Heuristics. These controls are static in the sense that they allow you to control the solution process based on data that does not change during the solution and can thus be set up before solving the model.

Dynamic control of the solution process of MIPs is provided through goals or control callbacks. They are discussed in Goals in IloCplex, and in Using Callbacks. Goals and callbacks allow you to control the solution process based on information that is generated during the solution process.

`IloCplex::Primal`	use the primal simplex algorithm
`IloCplex::Dual`	use the dual simplex algorithm
`IloCplex::Barrier`	use the barrier algorithm. The type of crossover performed after the barrier algorithm is determined by parameter `IloCplex::BarCrossAlg`.
`IloCplex::Network`	use the primal network simplex algorithm on an embedded network followed by the dual simplex algorithm for LPs and the primal simplex algorithm for QPs on the entire problem
IloCplex::Sifting	use the sifting algorithm
IloCplex::Concurrent	use multiple algorithms concurrently on a multiprocessor system