PDFP: GPU-Accelerated Feasibility Pump via PDHG

Abstract

The feasibility pump (FP) is among the most widely used primal heuristics for mixed-integer linear programming. It alternates between rounding an LP-feasible point and projecting the rounded point back onto the feasible region of the LP relaxation. Recent pump-based heuristics compute the projection with the primal--dual hybrid gradient method (PDHG), which is scalable on modern GPUs. They pose it as a linear program, which needs auxiliary variables and constraints for general integers. Once the projection runs on the GPU, the constraint-propagation rounding (CPR) of FP~2.0 takes a large share of each iteration. For the projection, we propose PDFP, a custom first-order method that solves the pump's projection problem directly, without auxiliary primal variables or constraints. We prove that it keeps the accelerated linear rate of restarted Halpern PDHG. For the rounding, we propose a new procedure that is more efficient than CPR and, under certain assumptions, still returns a CPR rounding. It also chooses rounded values by constraint violation, which can produce feasible roundings where nearest rounding cannot. Finally, our pump runs two independent trajectories concurrently on one GPU through CPU--GPU synchronization. This exploits the variance in trajectory length and lets the pump terminate sooner on average. Computational experiments on MIPLIB~2017 instances show early, promising results: these contributions speed up the discovery of the first incumbent solution. The code is publicly available at https://github.com/MIT-Lu-Lab/PDFP.