The Chebyshev center as an alternative to the analytic center in the feasibility pump

Abstract As a heuristic for obtaining feasible points of mixed integer linear problems, the feasibility pump (FP) generates two sequences points: one solutions relaxed problem; and another obtained by rounding solutions. In previous work, present authors proposed variant FP, named analytic center which obtains in segment between solution polyhedron problem. This work introduces new FP that replaces with Chebyshev center. Two benefits using are: (i) it requires optimization problem (unlike center, involves convex nonlinear its exact solution); (ii) is invariant to redundant constraints may not be well centered within problems highly rank-deficient matrices). The computational results set more than 200 MIPLIB2003 MIPLIB2010 instances show competitive can serve as an alternative other variants.