PUSH: a primal heuristic based on Feasibility PUmp and SHifting

TL;DR

PUSH is a novel primal heuristic that integrates Feasibility Pump and Shifting techniques, improving the solution process for mixed-integer programming by directly handling equality constraints and adapting rounding strategies.

Contribution

It introduces a new heuristic combining Feasibility Pump and Shifting, with strategies tailored to different partial solution states, and demonstrates effectiveness on benchmark instances.

Findings

Outperforms traditional start heuristics on MIPLIB2017 instances

Effectively handles equality constraints without row duplication

Parameter tuning based on Mip Competition 2022 instances

Abstract

This work describes PUSH, a primal heuristic combining Feasibility Pump and Shifting. The main idea is to replace the rounding phase of the Feasibility Pump with a suitable adaptation of the Shifting and other rounding heuristics. The algorithm presents different strategies, depending on the nature of the partial rounding obtained. In particular, we distinguish when the partial solution is feasible, infeasible with potential candidates, and infeasible without candidates. We used a threshold to indicate the percentage of variables to round with our algorithm and which other to round to the nearest integer. Most importantly, our algorithm tackles directly equality constraints without duplicating rows. We select the parameters of our algorithm on the 19 instances provided for the Mip Competition 2022. Finally, we compared our approach to other start heuristics, like Simple Rounding, Rounding, Shifting, and Feasibility Pump on the first 800 MIPLIB2017 instances ordered by the number of non-zeros.