A benchmark generator for boolean quadratic programming

TL;DR

This paper introduces a benchmark generator for boolean quadratic programming that creates random problems solvable in polynomial time, and analyzes duality gaps under certain conditions using Lagrangian duality.

Contribution

The paper presents a novel benchmark generator for BQP problems and explores duality properties under specific conditions, enhancing understanding and testing of BQP algorithms.

Findings

No duality gap under certain conditions

Generated problems can be solved in polynomial time

Numerical examples demonstrate method effectiveness

Abstract

For boolean quadratic programming (BQP), we will show that there is no duality gap between the primal and dual problems under some conditions by using the classical Lagrangian duality. A benchmark generator is given to create random BQP problems which can be solved in polynomial time. Several numerical examples are generated to demonstrate the effectiveness of the proposed method.