Convergence theorems for a class of simulated annealing algorithms on ℝd

1992 ◽  
Vol 29 (4) ◽  
pp. 885-895 ◽  
Author(s):  
Claude J. P. Bélisle
Keyword(s):  
Simulated Annealing ◽  
Global Minimum ◽  
Almost Sure Convergence ◽  
Convergence In Probability ◽  
Global Minimization ◽  
Absolutely Continuous ◽  
Mild Conditions ◽  
Cooling Schedule ◽  
Annealing Algorithms ◽  
Uniformly Bounded

We study a class of simulated annealing algorithms for global minimization of a continuous function defined on a subset of We consider the case where the selection Markov kernel is absolutely continuous and has a density which is uniformly bounded away from 0. This class includes certain simulated annealing algorithms recently introduced by various authors. We show that, under mild conditions, the sequence of states generated by these algorithms converges in probability to the global minimum of the function. Unlike most previous studies where the cooling schedule is deterministic, our cooling schedule is allowed to be adaptive. We also address the issue of almost sure convergence versus convergence in probability.

Convergence theorems for a class of simulated annealing algorithms on ℝd

1992 ◽  
Vol 29 (04) ◽  
pp. 885-895 ◽  
Author(s):  
Claude J. P. Bélisle
Keyword(s):  
Simulated Annealing ◽  
Global Minimum ◽  
Almost Sure Convergence ◽  
Convergence In Probability ◽  
Global Minimization ◽  
Absolutely Continuous ◽  
Mild Conditions ◽  
Cooling Schedule ◽  
Annealing Algorithms ◽  
Uniformly Bounded

We study a class of simulated annealing algorithms for global minimization of a continuous function defined on a subset of We consider the case where the selection Markov kernel is absolutely continuous and has a density which is uniformly bounded away from 0. This class includes certain simulated annealing algorithms recently introduced by various authors. We show that, under mild conditions, the sequence of states generated by these algorithms converges in probability to the global minimum of the function. Unlike most previous studies where the cooling schedule is deterministic, our cooling schedule is allowed to be adaptive. We also address the issue of almost sure convergence versus convergence in probability.

Simple conditions for the convergence of simulated annealing type algorithms

1998 ◽  
Vol 35 (4) ◽  
pp. 885-892 ◽  
Author(s):  
J. R. Cruz ◽  
C. C. Y. Dorea
Keyword(s):  
Simulated Annealing ◽  
Global Minimum ◽  
Global Minimization ◽  
General Acceptance

We study a class of simulated annealing type algorithms for global minimization with general acceptance probabilities. This paper presents simple conditions, easy to verify in practice, which ensure the convergence of the algorithm to the global minimum with probability 1.

Simple conditions for the convergence of simulated annealing type algorithms

1998 ◽  
Vol 35 (04) ◽  
pp. 885-892 ◽  
Author(s):  
J. R. Cruz ◽  
C. C. Y. Dorea
Keyword(s):  
Simulated Annealing ◽  
Global Minimum ◽  
Global Minimization ◽  
General Acceptance

We study a class of simulated annealing type algorithms for global minimization with general acceptance probabilities. This paper presents simple conditions, easy to verify in practice, which ensure the convergence of the algorithm to the global minimum with probability 1.

scholarly journals A simulated annealing-based algorithm for selecting balanced samples

2021 ◽  
Author(s):  
Roberto Benedetti ◽  
Maria Michela Dickson ◽  
Giuseppe Espa ◽  
Francesco Pantalone ◽  
Federica Piersimoni
Keyword(s):  
Simulated Annealing ◽  
Optimization Problem ◽  
Sample Selection ◽  
Auxiliary Information ◽  
Real Data ◽  
Simulation Experiments ◽  
Balanced Sampling ◽  
Inclusion Probabilities ◽  
Random Method ◽  
Annealing Algorithms

AbstractBalanced sampling is a random method for sample selection, the use of which is preferable when auxiliary information is available for all units of a population. However, implementing balanced sampling can be a challenging task, and this is due in part to the computational efforts required and the necessity to respect balancing constraints and inclusion probabilities. In the present paper, a new algorithm for selecting balanced samples is proposed. This method is inspired by simulated annealing algorithms, as a balanced sample selection can be interpreted as an optimization problem. A set of simulation experiments and an example using real data shows the efficiency and the accuracy of the proposed algorithm.

Simulated annealing for airborne EM inversion

Geophysics ◽  
2007 ◽  
Vol 72 (4) ◽  
pp. F189-F195 ◽  
Author(s):  
Changchun Yin ◽  
Greg Hodges
Keyword(s):  
Simulated Annealing ◽  
Random Walk ◽  
Boltzmann Distribution ◽  
Model Parameters ◽  
Local Minima ◽  
Model Configuration ◽  
Airborne Electromagnetic ◽  
Starting Model ◽  
Airborne Em ◽  
Cooling Schedule

The traditional algorithms for airborne electromagnetic (EM) inversion, e.g., the Marquardt-Levenberg method, generally run only a downhill search. Consequently, the model solutions are strongly dependent on the starting model and are easily trapped in local minima. Simulated annealing (SA) starts from the Boltzmann distribution and runs both downhill and uphill searches, rendering the searching process to easily jump out of local minima and converge to a global minimum. In the SA process, the calculation of Jacobian derivatives can be avoided because no preferred searching direction is required as in the case of the traditional algorithms. We apply SA technology for airborne EM inversion by comparing the inversion with a thermodynamic process, and we discuss specifically the SA procedure with respect to model configuration, random walk for model updates, objective function, and annealing schedule. We demonstrate the SA flexibility for starting models by allowing the model parameters to vary in a large range (far away from the true model). Further, we choose a temperature-dependent random walk for model updates and an exponential cooling schedule for the SA searching process. The initial temperature for the SA cooling scheme is chosen differently for different model parameters according to their resolvabilities. We examine the effectiveness of the algorithm for airborne EM by inverting both theoretical and survey data and by comparing the results with those from the traditional algorithms.

scholarly journals Comparison between simulated annealing algorithms and rapid chain delineation in the construction of genetic maps

2010 ◽  
Vol 33 (2) ◽  
pp. 398-408 ◽  
Author(s):  
Moysés Nascimento ◽  
Cosme Damião Cruz ◽  
Luiz Alexandre Peternelli ◽  
Ana Carolina Mota Campana
Keyword(s):  
Simulated Annealing ◽  
Genetic Maps ◽  
Annealing Algorithms
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