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This paper explores a surprising equivalence between two seemingly-distinct convex optimization methods. We show that simulated annealing, a well-studied random walk algorithms, is directly equivalent, in a certain sense, to the central…

Optimization and Control · Mathematics 2015-11-06 Jacob Abernethy , Elad Hazan

Simulated annealing is an effective and general means of optimization. It is in fact inspired by metallurgy, where the temperature of a material determines its behavior in thermodynamics. Likewise, in simulated annealing, the actions that…

Machine Learning · Computer Science 2020-07-01 Avrim Blum , Chen Dan , Saeed Seddighin

Global optimization heuristics are popular to optimize hard non-convex problems. Despite their irrefutably large cost-to-solution, in the lack of other working greedy or convex approaches, global optimization algorithms remain the…

Optimization and Control · Mathematics 2025-02-24 Kayo Gonçalves-e-Silva , Samuel Xavier-de-Souza

We present a modified simulated annealing method with a dynamical choice of the cooling temperature. The latter is determined via a closed-loop control and is proven to yield exponential decay of the entropy of the particle system. The…

Optimization and Control · Mathematics 2026-02-18 Michael Herty , Mattia Zanella

We study the simulated annealing algorithm based on the kinetic Langevin dynamics, in order to find the global minimum of a non-convex potential function. For both the continuous time formulation and a discrete time analogue, we obtain the…

Probability · Mathematics 2022-06-14 Xuedong He , Xiaolu Tan , Ruocheng Wu

Algorithms for simulating complex physical systems or solving difficult optimization problems often resort to an annealing process. Rather than simulating the system at the temperature of interest, an annealing algorithm starts at a…

Computational Physics · Physics 2015-04-02 Michael Habeck

This study combines simulated annealing with delta evaluation to solve the joint stratification and sample allocation problem. In this problem, atomic strata are partitioned into mutually exclusive and collectively exhaustive strata. Each…

Artificial Intelligence · Computer Science 2021-11-23 Mervyn O'Luing , Steven Prestwich , S. Armagan Tarim

In this paper we propose a modified version of the simulated annealing algorithm for solving a stochastic global optimization problem. More precisely, we address the problem of finding a global minimizer of a function with noisy…

Machine Learning · Statistics 2017-03-02 Clément Bouttier , Ioana Gavra

This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…

Quantum Physics · Physics 2015-12-16 Sergio Boixo , Rolando D. Somma

The planted coloring problem is a prototypical inference problem for which thresholds for Bayes optimal algorithms, like Belief Propagation (BP), can be computed analytically. In this paper, we analyze the limits and performances of the…

Disordered Systems and Neural Networks · Physics 2023-06-29 Maria Chiara Angelini , Federico Ricci-Tersenghi

A new approach to combinatorial optimization based on systematic move-class deflation is proposed. The algorithm combines heuristics of genetic algorithms and simulated annealing, and is mainly entropy-driven. It is tested on two problems…

Statistical Mechanics · Physics 2007-05-23 Reimer Kuehn , Yu-Cheng Lin , Gerhard Poeppel

We propose a variant of the Simulated Annealing method for optimization in the multivariate analysis of differentiable functions. The method uses global actualizations via the Hybrid Monte Carlo algorithm in their generalized version for…

Statistical Mechanics · Physics 2009-10-30 R. Salazar , R. Toral

This paper gives a straightforward implementation of simulated annealing for solving maximum cut problems and compares its performance to that of some existing heuristic solvers. The formulation used is classical, dating to a 1989 paper of…

Optimization and Control · Mathematics 2015-05-13 Tor G. J. Myklebust

Recently authors have introduced the idea of training discrete weights neural networks using a mix between classical simulated annealing and a replica ansatz known from the statistical physics literature. Among other points, they claim…

Machine Learning · Computer Science 2021-03-17 Vincent Gripon , Matthias Löwe , Franck Vermet

I propose a "quantum annealing" heuristic for the problem of combinatorial search among a frustrated set of states characterized by a cost function to be minimized. The algorithm is probabilistic, with postselection of the measurement…

Quantum Physics · Physics 2009-11-07 Carlo A. Trugenberger

Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a…

Machine Learning · Statistics 2007-09-20 A. Lecchini-Visintini , J. Lygeros , J. Maciejowski

Simulated annealing (SA) is a stochastic global optimisation technique applicable to a wide range of discrete and continuous variable problems. Despite its simplicity, the development of an effective SA optimiser for a given problem hinges…

Machine Learning · Computer Science 2024-06-27 Alvaro H. C. Correia , Daniel E. Worrall , Roberto Bondesan

We provide a set of conditions which ensure the almost sure convergence of a class of simulated annealing algorithms on a bounded set $\mathcal{X}\subset\mathbb{R}^d$ based on a time-varying Markov kernel. The class of algorithms considered…

Probability · Mathematics 2017-07-07 Mathieu Gerber , Luke Bornn

We develop an optimization algorithm, using simulated annealing for the quantification of patterns in astronomical data based on techniques developed for robotic vision applications. The methodology falls in the category of cost…

Instrumentation and Methods for Astrophysics · Physics 2020-09-09 Maria Chira , Manolis Plionis

We propose a new stochastic algorithm (generalized simulated annealing) for computationally finding the global minimum of a given (not necessarily convex) energy/cost function defined in a continuous D-dimensional space. This algorithm…

Condensed Matter · Physics 2015-06-25 Constantino Tsallis , Daniel A. Stariolo
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