Constraint Programming to Discover One-Flip Local Optima of Quadratic Unconstrained Binary Optimization Problems

TL;DR

This paper introduces a constraint programming method to efficiently find one-flip local optima in QUBO problems, aiding in diverse solution generation and guiding optimization processes for combinatorial and quantum computing applications.

Contribution

It presents a novel approach leveraging constraint programming to identify one-flip local optima in QUBO problems, enhancing solution diversity and optimization guidance.

Findings

Effective generation of local optima sets

Analysis enables creation of soft guiding constraints

Improves initialization for quantum annealing and similar methods

Abstract

The broad applicability of Quadratic Unconstrained Binary Optimization (QUBO) constitutes a general-purpose modeling framework for combinatorial optimization problems and are a required format for gate array and quantum annealing computers. QUBO annealers as well as other solution approaches benefit from starting with a diverse set of solutions with local optimality an additional benefit. This paper presents a new method for generating a set of one-flip local optima leveraging constraint programming. Further, as demonstrated in experimental testing, analysis of the solution set allows the generation of soft constraints to help guide the optimization process.