An adaptive cooling schedule for simulated annealing with application to multiple‐constraint time‐domain beamforming

1990 ◽  
Vol 88 (S1) ◽  
pp. S29-S29
Author(s):  
Nolan R. Davis ◽  
Jonathan M. Berkson ◽  
John S. Perkins ◽  
Michael D. Collins ◽  
W. A. Kuperman
Keyword(s):  
Simulated Annealing ◽  
Time Domain ◽  
Multiple Constraint ◽  
Cooling Schedule

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.

A fast simulated‐annealing algorithm for time‐domain beamforming

1990 ◽  
Vol 87 (S1) ◽  
pp. S154-S154
Author(s):  
W. A. Kuperman ◽  
Michael D. Collins ◽  
John S. Perkins ◽  
N. R. Davis
Keyword(s):  
Simulated Annealing ◽  
Time Domain ◽  
Simulated Annealing Algorithm ◽  
Annealing Algorithm

MEMBRANE ALGORITHM WITH BROWNIAN SUBALGORITHM AND GENETIC SUBALGORITHM

2007 ◽  
Vol 18 (06) ◽  
pp. 1353-1360 ◽  
Author(s):  
TAISHIN Y. NISHIDA
Keyword(s):  
Simulated Annealing ◽  
Approximate Solutions ◽  
Search Space ◽  
Traveling Salesman ◽  
Benchmark Problems ◽  
Wide Range ◽  
Membrane Algorithm ◽  
Thermal Movement ◽  
The Traveling Salesman Problem ◽  
Cooling Schedule

Membrane algorithms with subalgorithms inspired by simulated annealing are treated in this paper. Simulated annealing is inherently a kind of local search but it modifies a solution to a worse one with a probability determined by "temperature". The temperature of simulated annealing is changed according to "cooling schedule". On the other hand, the subalgorithm introduced here has constant temperature which is determined by the region where the subalgorithm is. It is called Brownian subalgorithm since the subalgorithm incorporates "thermal movement" of a solution in the search space but does not simulate "annealing". Computer simulations show that a membrane algorithm which has three regions and has a Brownian subalgorithm in each region can obtain very good approximate solutions for several benchmark problems of the traveling salesman problem. However, the algorithm, occasionally, gets quite bad solutions (twice as large as the optimum) for a problem. A membrane algorithm which has both Brownian and genetic subalgorithms never gets such a bad solution (only 8% worse than the optimum) for all problems examined, although, in average, it is not as good as the algorithm with Brownian only. The result indicates that membrane algorithm with subalgorithms under different approximate mechanisms may be robust under a wide range of problems.

scholarly journals List-Based Simulated Annealing Algorithm for Traveling Salesman Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Shi-hua Zhan ◽  
Juan Lin ◽  
Ze-jun Zhang ◽  
Yi-wen Zhong
Keyword(s):  
Simulated Annealing ◽  
Traveling Salesman Problem ◽  
Simulated Annealing Algorithm ◽  
Solution Space ◽  
Traveling Salesman ◽  
Maximum Temperature ◽  
Acceptance Criterion ◽  
Wide Range ◽  
Key Factor ◽  
Cooling Schedule

Simulated annealing (SA) algorithm is a popular intelligent optimization algorithm which has been successfully applied in many fields. Parameters’ setting is a key factor for its performance, but it is also a tedious work. To simplify parameters setting, we present a list-based simulated annealing (LBSA) algorithm to solve traveling salesman problem (TSP). LBSA algorithm uses a novel list-based cooling schedule to control the decrease of temperature. Specifically, a list of temperatures is created first, and then the maximum temperature in list is used by Metropolis acceptance criterion to decide whether to accept a candidate solution. The temperature list is adapted iteratively according to the topology of the solution space of the problem. The effectiveness and the parameter sensitivity of the list-based cooling schedule are illustrated through benchmark TSP problems. The LBSA algorithm, whose performance is robust on a wide range of parameter values, shows competitive performance compared with some other state-of-the-art algorithms.

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.

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