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A feasible rounding approach is a novel technique to compute good feasible points for mixed-integer optimization problems. The central idea of this approach is the construction of a continuously described inner parallel set for which any rounding of any of its elements is feasible in the original mixed-integer problem. It is known that this approach is promising for problems in which no equality constraints on integer variables appear. Yet, so far the potential of incorporating equality constraints with integer variables into this approach remained unclear. In this article, we close this gap by developing a reduction scheme that enables the application of feasible rounding approaches to problems in which such equality constraints occur. Our computational study on a large test bed of MIPLIB instances shows that this reduction is applicable to a relevant share of practical problems. Moreover, our results illustrate that a non-empty inner parallel set is possible, but less likely to occur for practical problems with equality constraints on integer variables. Finally, our results indicate that the application of a feasible rounding approach can be beneficial for the computation of good feasible points even under the occurrence of equality constraints on integer variables.

Feasible rounding approaches for equality constrained mixed-integer optimization problems