Scylla: a matrix-free fix-propagate-and-project heuristic for mixed-integer optimization

TL;DR

Scylla is a novel heuristic for mixed-integer optimization that leverages matrix-free LP relaxations and fix-propagate techniques to efficiently find feasible solutions, especially for challenging instances.

Contribution

It introduces a new primal heuristic combining matrix-free LP solves with fix-and-propagate methods for improved mixed-integer optimization performance.

Findings

Effective on instances with hard linear relaxations

Outperforms existing heuristics in computational experiments

Provides high-quality feasible solutions efficiently

Abstract

We introduce Scylla, a primal heuristic for mixed-integer optimization problems. It exploits approximate solves of the Linear Programming relaxations through the matrix-free Primal-Dual Hybrid Gradient algorithm with specialized termination criteria, and derives integer-feasible solutions via fix-and-propagate procedures and feasibility-pump-like updates to the objective function. Computational experiments show that the method is particularly suited to instances with hard linear relaxations.