Enumeration Relaxation

The enumeration Relaxation lists the values that can be taken by the parameter FeasOptMode. This parameter controls several aspects of how the method feasOpt performs its relaxation.

The method feasOpt works in two phases. In its first phase, it attempts to find a minimum-penalty relaxation of a given infeasible model. If you want feasOpt to stop after this first phase, choose a value with Min in its symbolic name. If you want feasOpt to continue beyond its first phase to find a solution that is optimal with respect to the original objective function, subject to the constraint that the penalty of the relaxation must not exceed the value found in the first phase, then choose a value with Opt in its symbolic name.

In both phases, the suffixes Sum, Inf, and Quad specify the relaxation metric:

• Sum tells feasOpt to mimimize the weighted sum of the required relaxations of bounds and constraints according to the formula penalty = sum (penalty_i times relaxation_amount_i)
• Inf tells feasOpt to minimize the weighted number of bounds and constraints that are relaxed according to the formula penalty = sum (penalty_i times relaxation_indicator_i)
• Quad tells feasOpt to mimimize the weighted sum of the squares of required relaxations of bounds and constraints according to the formula penalty = sum (penalty_i times relaxation_amount_i times relaxation_amount_i)

Weights are determined by the preference values you provide as input to the method feasOpt.

When IloAnd is used to group constraints as input to feasOpt, the relaxation penalty is computed on groups instead of on individual constraints. For example, all constraints in a group can be relaxed for a total penalty of one unit under the various Inf metrics.