The Feasibility Pump

In this paper we consider the NP-hard problem of finding a feasible solution (if any exists) for a generic MIP problem. Trivially, a feasible solution can be defined as an LP-feasible point x that is equal to its rounding. Replacing “equal” with “as close as possible” relative to a suitable distance function, suggests a new type of heuristic, that we call Feasibility Pump (FP). We report computational results on a set of 83 difficult 0-1 MIPs, using the commercial software ILOG-Cplex 8.1 as a benchmark. The outcome is that FP, in spite of its simple foundation, proves competitive with ILOG-Cplex both in terms of speed and quality of the first solution delivered. Interestingly, ILOG-Cplex could not find any feasible solution at the root node for 19 problems in our test-bed, whereas FP was unsuccessful in just 3 cases.