An Optimal Constraint for QUBO Models

TL;DR

This paper introduces a method to incorporate a fixed-size constraint into QUBO models, which are inherently unconstrained, enabling more precise control over solution size.

Contribution

It presents a novel approach to add size constraints to QUBO models, expanding their applicability for fixed-size binary solutions.

Findings

Successfully integrates size constraints into QUBO models

Enables fixed-size solution selection in unconstrained optimization

Potentially improves solution quality for specific applications

Abstract

A quadratic binary unconstrained optimization model, hereafter QUBO, by definition is unconstrained. This, however, is not ideal if one needs to select a model containing only a fixed size binary vector. In this work we show how to add a constraint to a QUBO to force a particular size solution.