Direct comparison of stochastic driven nonlinear dynamical systems for combinatorial optimization

• URL: http://arxiv.org/abs/2503.15427v2
• Date: Fri, 28 Mar 2025 17:58:28 GMT
• Title: Direct comparison of stochastic driven nonlinear dynamical systems for combinatorial optimization
• Authors: Junpeng Hou, Amin Barzegar, Helmut G. Katzgraber,
• Abstract summary: Combinatorial optimization problems are ubiquitous in industrial applications.<n>Tremendous effort has been devoted to developing solvers for Ising-type problems over the past decades.<n>Recent advances in controlling and manipulating both quantum and classical systems have enabled novel computing paradigms.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Combinatorial optimization problems are ubiquitous in industrial applications. However, finding optimal or close-to-optimal solutions can often be extremely hard. Because some of these problems can be mapped to the ground-state search of the Ising model, tremendous effort has been devoted to developing solvers for Ising-type problems over the past decades. Recent advances in controlling and manipulating both quantum and classical systems have enabled novel computing paradigms such as quantum simulators and coherent Ising machines to tackle hard optimization problems. Here, we examine and benchmark several physics-inspired optimization algorithms, including coherent Ising machines, gain-dissipative algorithms, simulated bifurcation machines, and Hopfield neural networks, which we collectively refer to as stochastic-driven nonlinear dynamical systems. Most importantly, we benchmark these algorithms against random Ising problems with planted solutions and compare them to simulated annealing as a baseline leveraging the same software stack for all solvers. We further study how different numerical integration techniques and graph connectivity affect performance. This work provides an overview of a diverse set of new optimization paradigms.

Related papers

• Quantum Optimization Benchmark Library -- The Intractable Decathlon [27.362963067036087]
  We present ten optimization problem classes that are difficult for existing classical algorithms. The individual properties of the problem classes vary in terms of objective and variable type, coefficient ranges, and density. We introduce the Quantum Optimization Benchmark Library (QOBLIB) where the problem instances and solution track records can be found.
  arXiv  Detail & Related papers  (2025-04-04T18:00:00Z)
• Integrating Optimization Theory with Deep Learning for Wireless Network Design [38.257335693563554]
  Traditional wireless network design relies on optimization algorithms derived from domain-specific mathematical models.<n>Deep learning has emerged as a promising alternative to overcome complexity and adaptability concerns.<n>This paper introduces a novel approach that integrates optimization theory with deep learning methodologies to address these issues.
  arXiv  Detail & Related papers  (2024-12-11T20:27:48Z)
• Learning to optimize with convergence guarantees using nonlinear system theory [0.4143603294943439]
  We propose an unconstrained parametrization of algorithms for smooth objective functions. Notably, our framework is directly compatible with automatic differentiation tools.
  arXiv  Detail & Related papers  (2024-03-14T13:40:26Z)
• Analyzing and Enhancing the Backward-Pass Convergence of Unrolled Optimization [50.38518771642365]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an optimization problem, which often lacks a closed form. This paper provides theoretical insights into the backward pass of unrolled optimization, showing that it is equivalent to the solution of a linear system by a particular iterative method. A system called Folded Optimization is proposed to construct more efficient backpropagation rules from unrolled solver implementations.
  arXiv  Detail & Related papers  (2023-12-28T23:15:18Z)
• Federated Conditional Stochastic Optimization [110.513884892319]
  Conditional optimization has found in a wide range of machine learning tasks, such as in-variant learning tasks, AUPRC, andAML. This paper proposes algorithms for distributed federated learning.
  arXiv  Detail & Related papers  (2023-10-04T01:47:37Z)
• Let the Flows Tell: Solving Graph Combinatorial Optimization Problems with GFlowNets [86.43523688236077]
  Combinatorial optimization (CO) problems are often NP-hard and out of reach for exact algorithms. GFlowNets have emerged as a powerful machinery to efficiently sample from composite unnormalized densities sequentially. In this paper, we design Markov decision processes (MDPs) for different problems and propose to train conditional GFlowNets to sample from the solution space.
  arXiv  Detail & Related papers  (2023-05-26T15:13:09Z)
• Backpropagation of Unrolled Solvers with Folded Optimization [55.04219793298687]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. One typical strategy is algorithm unrolling, which relies on automatic differentiation through the operations of an iterative solver. This paper provides theoretical insights into the backward pass of unrolled optimization, leading to a system for generating efficiently solvable analytical models of backpropagation.
  arXiv  Detail & Related papers  (2023-01-28T01:50:42Z)
• On the Convergence of Distributed Stochastic Bilevel Optimization Algorithms over a Network [55.56019538079826]
  Bilevel optimization has been applied to a wide variety of machine learning models. Most existing algorithms restrict their single-machine setting so that they are incapable of handling distributed data. We develop novel decentralized bilevel optimization algorithms based on a gradient tracking communication mechanism and two different gradients.
  arXiv  Detail & Related papers  (2022-06-30T05:29:52Z)
• Optimization of Robot Trajectory Planning with Nature-Inspired and Hybrid Quantum Algorithms [0.0]
  We solve robot trajectory planning problems at industry-relevant scales. Our end-to-end solution integrates highly versatile random-key algorithms with model stacking and ensemble techniques. We show how the latter can be integrated into our larger pipeline, providing a quantum-ready hybrid solution to the problem.
  arXiv  Detail & Related papers  (2022-06-08T02:38:32Z)
• Neural Improvement Heuristics for Graph Combinatorial Optimization Problems [49.85111302670361]
  We introduce a novel Neural Improvement (NI) model capable of handling graph-based problems where information is encoded in the nodes, edges, or both. The presented model serves as a fundamental component for hill-climbing-based algorithms that guide the selection of neighborhood operations for each.
  arXiv  Detail & Related papers  (2022-06-01T10:35:29Z)
• Neural Combinatorial Optimization: a New Player in the Field [69.23334811890919]
  This paper presents a critical analysis on the incorporation of algorithms based on neural networks into the classical optimization framework. A comprehensive study is carried out to analyse the fundamental aspects of such algorithms, including performance, transferability, computational cost and to larger-sized instances.
  arXiv  Detail & Related papers  (2022-05-03T07:54:56Z)
• Particle Swarm Optimization: Fundamental Study and its Application to Optimization and to Jetty Scheduling Problems [0.0]
  The advantages of evolutionary algorithms with respect to traditional methods have been greatly discussed in the literature. While particle swarms share such advantages, they outperform evolutionary algorithms in that they require lower computational cost and easier implementation. This paper does not intend to study their tuning, general-purpose settings are taken from previous studies, and virtually the same algorithm is used to optimize a variety of notably different problems.
  arXiv  Detail & Related papers  (2021-01-25T02:06:30Z)
• Cross Entropy Hyperparameter Optimization for Constrained Problem Hamiltonians Applied to QAOA [68.11912614360878]
  Hybrid quantum-classical algorithms such as Quantum Approximate Optimization Algorithm (QAOA) are considered as one of the most encouraging approaches for taking advantage of near-term quantum computers in practical applications. Such algorithms are usually implemented in a variational form, combining a classical optimization method with a quantum machine to find good solutions to an optimization problem. In this study we apply a Cross-Entropy method to shape this landscape, which allows the classical parameter to find better parameters more easily and hence results in an improved performance.
  arXiv  Detail & Related papers  (2020-03-11T13:52:41Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.