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

arXiv: https://arxiv.org/abs/2104.01709 · HTML: https://mlsanity.com/paper/2104.01709/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 23 references that are in the map.
- First posted on arXiv 4 Apr 2021.

## Builds on (most cited first, 2 of 2)

- [Local Optima Networks: A New Model of Combinatorial Fitness Landscapes](https://mlsanity.com/paper/1402.2959/) (2014)
- [When data mining meets optimization: A case study on the quadratic assignment problem](https://mlsanity.com/paper/1708.05214/) (2017)

## Built on by (most cited first, 3 of 3)

- [Efficient QUBO transformation for Higher Degree Pseudo Boolean Functions](https://mlsanity.com/paper/2107.11695/) (2021)
- [A Graph Neural Network-Based QUBO-Formulated Hamiltonian-Inspired Loss Function for Combinatorial Optimization using Reinforcement Learning](https://mlsanity.com/paper/2308.13978/) (2023)
- [A Graph Neural Network-Based QUBO-Formulated Hamiltonian-Inspired Loss Function for Combinatorial Optimization using Reinforcement Learning](https://mlsanity.com/paper/2311.16277/) (2023)

## Abstract (arXiv)

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.