# borealis—A generalized global update algorithm for Boolean optimization problems

@article{Zhu2016borealisAGG, title={borealis—A generalized global update algorithm for Boolean optimization problems}, author={Zheng Zhu and Chao Fang and Helmut G. Katzgraber}, journal={Optimization Letters}, year={2016}, volume={14}, pages={2495 - 2514} }

Optimization problems with Boolean variables that fall into the nondeterministic polynomial (NP) class when cast as decision problems are of fundamental importance in computer science, mathematics, physics and industrial applications. Most notably, solving constraint-satisfaction problems, which are related to spin-glass-like Hamiltonians in physics, remains a difficult numerical task. As such, there has been great interest in designing efficient heuristics to solve these computationally…

## 18 Citations

### Combining simulated annealing with local search heuristic for MAX-SAT

- Computer ScienceJ. Heuristics
- 2019

An adapted version of KL for the maximum satisfiability problem is introduced and embedded into the simulated annealing algorithm and suggests an intriguing idea which is based on replacing the search of one favorable move by a search for a favorable sequence of moves.

### The Houdayer Algorithm: Overview, Extensions, and Applications

- Computer Science
- 2022

This work investigates the Houdayer algorithm, a cluster Monte-Carlo method with small numerical overhead which improves the exploration of conﬁgurations by preserving the energy of the system and proposes a generalization capable of reaching exponentially many con-gurations at the same energy.

### Physics-Inspired Optimization for Quadratic Unconstrained Problems Using a Digital Annealer

- Computer ScienceFront. Phys.
- 2019

The results show that the Digital Annealer currently exhibits a time-to-solution speedup of roughly two orders of magnitude for fully connected spin-glass problems with bimodal or Gaussian couplings, over the single-core implementations of simulated annealing and parallel tempering Monte Carlo used in this study.

### 3-regular three-XORSAT planted solutions benchmark of classical and quantum heuristic optimizers

- Environmental ScienceQuantum Science and Technology
- 2022

With current semiconductor technology reaching its physical limits, special-purpose hardware has emerged as an option to tackle specific computing-intensive challenges. Optimization in the form of…

### Embedding penalties for quantum hardware architectures and performance of simulated quantum annealing

- Computer Science
- 2019

This research suggests that there might be an exponential penalty when using these embeddings for finding the embedded ground-state, since a classical simulation of quantum annealing has no real world constraints and can realize all-to-all connectivity without any embedding necessary.

### Effects of setting temperatures in the parallel tempering Monte Carlo algorithm.

- Computer SciencePhysical review. E
- 2019

It is demonstrated that there is no performance advantage for the methods that promote nonuniform swapping probabilities on spin-glass problems where the order parameter has a smooth transition between phases at the critical temperature, but on Wishart problems that have a first-order phase transition at low temperatures, the feedback-optimized method exhibits a time-to-solution speedup.

### Wishart planted ensemble: A tunably rugged pairwise Ising model with a first-order phase transition.

- PhysicsPhysical review. E
- 2020

An analytical expression for the location of the hardness peak is proposed and it is shown that at fixed precision, the number of constraints in the integer program must increase with system size to yield truly hard problems.

### NAE-SAT-based probabilistic membership filters

- Computer ScienceArXiv
- 2018

An improved SAT filter approach with a focus on reducing the filter building times, as well as query times is presented, based on using not-all-equal (NAE) SAT formulas to build the filters, solving these via a mapping to random SAT using traditionally-fast random SAT solvers, aswell as bit packing and the reduction of the number of hash functions.

### Benchmarking Quantum(-inspired) Annealing Hardware on Practical Use Cases

- Computer ScienceIEEE Transactions on Computers
- 2022

Experiments suggest that both quantum(-inspired) annealers are effective on problems with small size and simple settings, but lose their utility when facing problems in practical size and settings, and decomposition methods extend the scalability of annesalers, but they are still far away from practical use.

### Quantum Annealing Approaches to the Phase-Unwrapping Problem in Synthetic-Aperture Radar Imaging

- Computer Science2020 IEEE International Conference on Quantum Computing and Engineering (QCE)
- 2020

This work decomposes the problem of phase unwrapping of synthetic aperture radar (SAR) images as a quadratic unconstrained binary optimization (QUBO) problem, which can be solved using a quantum annealer, and achieves high-quality solutions comparable to state-of-the-art phase-unwrapping solvers.

## References

SHOWING 1-10 OF 83 REFERENCES

### Simplest random K-satisfiability problem

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

We study a simple and exactly solvable model for the generation of random satisfiability problems. These consist of gammaN random boolean constraints which are to be satisfied simultaneously by N…

### Extremal Optimization for Graph Partitioning

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

Numerical results demonstrate that extremal optimization maintains consistent accuracy for increasing system sizes, with an approximation error decreasing over run time roughly as a power law t(-0.4).

### Reducibility Among Combinatorial Problems

- Computer Science50 Years of Integer Programming
- 1972

Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.

### Approximation algorithms for combinatorial problems

- Computer Science, MathematicsSTOC
- 1973

For the problem of finding the maximum clique in a graph, no algorithm has been found for which the ratio does not grow at least as fast as 0(nε), where n is the problem size and ε> 0 depends on the algorithm.

### Optimization with Extremal Dynamics

- Computer ScienceComplex.
- 2003

This work uses extremal optimization to elucidate the phase transition in the 3-coloring problem, and provides independent confirmation of previously reported extrapolations for the ground-state energy of +/-J spin glasses in d = 3 and 4.

### From Spin Glasses to Hard Satisfiable Formulas

- Computer Science, MathematicsSAT
- 2004

We introduce a highly structured family of hard satisfiable 3-SAT formulas corresponding to an ordered spin-glass model from statistical physics. This model has provably “glassy” behavior; that is,…

### A quantum annealing approach for fault detection and diagnosis of graph-based systems

- Computer Science
- 2015

This work is the first research utilizing the route Problem → QUBO → Direct embedding into quantum hardware, where it is able to implement and tackle problem instances with sizes that go beyond previously reported toy-model proof-of-principle quantum annealing implementations; this is a significant leap in the solution of problems via direct-embedding adiabatic quantum optimization.

### On Solving the Partial MAX-SAT Problem

- Computer ScienceSAT
- 2006

Two solvers are implemented for the Partial MAX-SAT problem; the relative strengths and thus applicability of the two solvers for different solution scenarios are discussed and how both techniques benefit from the persistent learning techniques of incremental SAT.

### Local search strategies for satisfiability testing

- Computer ScienceCliques, Coloring, and Satisfiability
- 1993

The power of local search for satissability testing can be further enhanced by employing a new strategy, called mixed random walk, for escaping from local minima, which allows us to handle formulas that are substantially larger than those that can be solved with basic local search.

### Glassy Chimeras could be blind to quantum speedup: Designing better benchmarks for quantum annealing machines

- Physics
- 2014

The results show that a careful design of the hardware architecture and benchmark problems is key when building quantum annealing machines, and proposes alternative benchmarks by embedding potentially harder problems on the Chimera topology.