Improving the Randomization Step in Feasibility Pump

TL;DR

This paper enhances the Feasibility Pump heuristic for MILP by introducing a novel randomization step based on WalkSAT, supported by theoretical analysis and computational experiments demonstrating its practical benefits.

Contribution

It proposes a new WalkSAT-based randomization step for Feasibility Pump, providing the first theoretical analysis of its running-time and validating its effectiveness through computational experiments.

Findings

The new randomization step shows improved performance in experiments.

Theoretical analysis indicates potential efficiency gains.

Practical implementation enhances existing Feasibility Pump algorithms.

Abstract

Feasibility pump (FP) is a successful primal heuristic for mixed-integer linear programs (MILP). The algorithm consists of three main components: rounding fractional solution to a mixed-integer one, projection of infeasible solutions to the LP relaxation, and a randomization step used when the algorithm stalls. While many generalizations and improvements to the original Feasibility Pump have been proposed, they mainly focus on the rounding and projection steps. We start a more in-depth study of the randomization step in Feasibility Pump. For that, we propose a new randomization step based on the WalkSAT algorithm for solving SAT instances. First, we provide theoretical analyses that show the potential of this randomization step; to the best of our knowledge, this is the first time any theoretical analysis of running-time of Feasibility Pump or its variants has been conducted. Moreover, we also conduct computational experiments incorporating the proposed modification into a state-of-the-art Feasibility Pump code that reinforce the practical value of the new randomization step.