A Feasible Active Set Method with Reoptimization for Convex Quadratic Mixed-Integer Programming

TL;DR

This paper introduces a feasible active set method tailored for convex quadratic mixed-integer programming, enhancing branch-and-bound algorithms with efficient reoptimization and preprocessing, leading to improved performance on certain instances.

Contribution

The paper presents a novel active set method integrated into branch-and-bound for convex quadratic MIQP, leveraging preprocessing and reoptimization for faster solutions.

Findings

Outperforms CPLEX 12.6 MIQP solver on small constrained instances

Efficient reoptimization accelerates branch-and-bound process

Preprocessing phase enables fast enumeration of nodes

Abstract

We propose a feasible active set method for convex quadratic programming problems with non-negativity constraints. This method is specifically designed to be embedded into a branch-and-bound algorithm for convex quadratic mixed integer programming problems. The branch-and-bound algorithm generalizes the approach for unconstrained convex quadratic integer programming proposed by Buchheim, Caprara and Lodi to the presence of linear constraints. The main feature of the latter approach consists in a sophisticated preprocessing phase, leading to a fast enumeration of the branch-and-bound nodes. Moreover, the feasible active set method takes advantage of this preprocessing phase and is well suited for reoptimization. Experimental results for randomly generated instances show that the new approach significantly outperforms the MIQP solver of CPLEX 12.6 for instances with a small number of constraints.