Postsolve

Type

Selection

Range

The settings listed below

Default

Automatic

When solving a problem, solvers like CPLEX, Gurobi, COPT and CBC allow variables to slightly violate their bounds as specified by some (feasibility) tolerance. Additionally, when solving a MIP problem, solvers do not round the found integer variable values to the nearest integer value. Instead the solver returns values which are considered to be integer within some (integrality) tolerance. For these reasons AIMMS offers a postsolve step during which integer variables are fixed to the nearest integer or variables outside their bounds are fixed to the nearest bound. The resulting postsolve problem is then solved to obtain a truly integer solution or a solution in which all variable values are inside the bounds. Note that the postsolve problem is always a LP problem.

The postsolve step can also be used to calculate sensitivity information for a MIP problem.

This option specifies whether or not a postsolve step will be performed after solving a LP or MIP problem by CPLEX, Gurobi, COPT or CBC. Possible values of this option are:

  • Off

  • Automatic

  • On

With the default setting of ‘Automatic’ the postsolve step will be executed if CPLEX, Gurobi or COPT is used to solve the problem, and it will not be executed if CBC is used. However, if a lazy constraint callback procedure is installed, which is only supported by CPLEX and Gurobi, then the postsolve step will only be executed if this option is set to ‘On’.

During the postsolve step AIMMS will first check whether the solution returned by the solver is truly feasible and integer. If that is the case then the postsolve step is normally finished, i.e., AIMMS will then not solve the postsolve problem. Otherwise AIMMS will solve the postsolve problem using the same solver as was used to solve the original LP or MIP problem.

If the postsolve step should calculate sensitivity information for a MIP problem, as controlled by the option MIP Calculate Sensitivity Information, then AIMMS will always solve the postsolve problem to obtain this information (even if the solution returned by the solver is truly feasible and integer). Note that solvers like CPLEX, Gurobi, COPT and CBC do not provide sensitivity information for MIP problems because it is (in general) not available for MIP problems. The sensitivity information calculated during the postsolve step only represents the sensitivity information for the fixed MIP problem, obtained after fixing the integer variables.

Normally, the problem solved during the postsolve step will be feasible, and the objective value returned will be equal to the objective value that was found by solving the original problem. If the postsolve problem is infeasible then AIMMS will use the solution that was found before while solving the original problem. If the postsolve problem is feasible then AIMMS will use the solution found by solving the postsolve problem.

If the postsolve problem is infeasible then this implies that the solution found by the solver was not reliable although it was feasible according to the tolerances used by the solver. An infeasible postsolve, or a large gap between the objective values of the original problem and the postsolve problem, indicates that the problem is ill-conditioned. In either case AIMMS will generate a warning by default, as controlled by the option Warning Unreliable Solution. Ill conditioning can often be “resolved” by adjusting solver tolerances, e.g., by lowering the values of the options that control the feasibility or the integrality tolerance. But sometimes it can only be resolved by reformulating the problem to improve the numerical stability.

Other postsolve options

The option Postsolve Integer Variables determines how AIMMS will handle integer variables during the postsolve step, while the option Postsolve Continuous Variables determines how continuous variables are handled. The postsolve step can be used to calculate sensitivity information for the fixed MIP problem that is solved during the postsolve; this is controlled by the option MIP Calculate Sensitivity Information.

Note

  • In case of a user interrupt or when the iteration limit is exceeded, the postsolve step might be skipped, depending on the setting of the option Do Postsolve after Interrupt.

  • Switching off this option is equivalent to setting the options Postsolve Continuous Variables and Postsolve Integer Variables to ‘No rounding’, and the option MIP Calculate Sensitivity Information to ‘Off’.

  • In case of a MIP problem, solving the postsolve problem can be enforced by switching on the option MIP Calculate Sensitivity Information, even if the solution returned by the solver is truly feasible and integer.

  • The postsolve step will always be skipped if CPLEX or Gurobi is used to solve a multi-objective optimization model and a cut callback procedure is installed.

  • The postsolve step will always be skipped if CPLEX is used to solve a multi-objective optimization model and the model contains a cut pool or filter constraint.

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