New concave penalty functions for improving the Feasibility Pump

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 non-differentiable penalty functions for measuring solution integrality. We present computational results on binary MILP problems from the MIPLIB library showing the effectiveness of our approach