Alternatively, after a model have been proven infeasible, IloCplex::feasOpt performs an additional optimization that computes a minimal relaxation of the constraints over variables, of the bounds on variables, and of the righthand sides of constraints to make the model feasible. The parameter FeasOptMode lets you guide feasOpt in its computation of this relaxation.

IloCplex::feasOpt works in two phases. In its first phase, it attempts to minimize its relaxation of the infeasible model. That is, it attempts to find a feasible solution that requires minimal change. In its second phase, it finds an optimal solution among those that require only as much relaxation as it found necessary in the first phase.

Your choice of values for the parameter FeasOptMode indicates two aspects to CPLEX:

• whether to stop in phase one or continue to phase two:
  • Min means stop in phase one with a minimal relaxation.
  • Opt means continue to phase two for an optimum among those minimal relaxations.
• how to measure the minimality of the relaxation:
  • Sum means CPLEX should minimize the sum of all relaxations
  • Inf means that CPLEX should minimize the number of constraints and bounds relaxed.

The possible values of FeasOptMode are documented in the method IloCplex::feasOpt.

The status of the bounds and constraints of a relaxation returned by a call of IloCplex::feasOpt are documented in the enumeration IloCplex::Status.