EXPEDIS: An Exact Penalty Method over Discrete Sets

TL;DR

The paper introduces EXPEDIS, an exact penalty method that transforms quadratic binary constrained problems into max-cut instances, enabling the use of max-cut solvers for exact solutions, with promising numerical results.

Contribution

It presents a novel transformation technique for quadratic binary problems into max-cut problems, leveraging existing solvers for exact solutions.

Findings

Successful application on various problem classes

Effective transformation into max-cut instances

Utilization of BiqMac solver for exact solutions

Abstract

We address the problem of minimizing a quadratic function subject to linear constraints over binary variables. We introduce the exact solution method called EXPEDIS where the constrained problem is transformed into a max-cut instance, and then thewhole machinery available for max-cut can be used to solve the transformed problem. We derive the theory in order to find a transformation in the spirit of an exact penalty method; however, we are only interested in exactness over the set of binary variables. In order to compute the maximum cut we use the solver BiqMac. Numerical results show that this algorithm can be successfully applied on various classes of problems.