New concave penalty functions for improving the Feasibility Pump

Abstract Mixed-Integer optimization represents a powerful tool for modeling many optimization problems arising from real-world applications. The Feasibility pump is a heuristic for finding feasible solutions to mixed integer linear problems. In this work, we propose a new feasibility pump approach using concave nondifferentiable penalty functions for measuring solution integrality. We present computational results on binary MILP problems from the MIPLIB library showing the effectiveness of our approach.