scholarly journals An Optimal Cooling Schedule Using a Simulated Annealing Based Approach

2017 ◽  
Vol 08 (08) ◽  
pp. 1195-1210 ◽  
Author(s):  
Alex Kwaku Peprah ◽  
Simon Kojo Appiah ◽  
Samuel Kwame Amponsah
Keyword(s):  
Simulated Annealing ◽  
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.

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

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.

Constructal Design of Double-T Shaped Cavity with Stochastic Methods Luus-Jaakola and Simulated Annealing

2017 ◽  
Vol 370 ◽  
pp. 152-161 ◽  
Author(s):  
Gill Velleda Gonzales ◽  
Elizaldo Domingues dos Santos ◽  
Liércio André Isoldi ◽  
Luiz Alberto Oliveira Rocha ◽  
Antônio José da Silva Neto ◽  
...  
Keyword(s):  
Simulated Annealing ◽  
Degrees Of Freedom ◽  
Hybrid Methods ◽  
Transfer Problem ◽  
Geometric Optimization ◽  
Stochastic Methods ◽  
Statistical Tool ◽  
Constructal Design ◽  
Cooling Schedule ◽  
Complete Optimization

In this paper it is proposed a comparison between two stochastic methods, Simulated Annealing and Luus-Jaakola algorithms, applied in association with Constructal Design to the geometric optimization of a heat transfer problem. The problem consists in a solid body with an internal uniform heat generation, which is cooled by an intruded cavity that is maintained at a minimal temperature. The other surfaces are kept as adiabatic. The objective is to minimize the maximum excess of temperature (θmax) in the solid domain through geometric optimization of the isothermal double-T shaped cavity. The problem geometry has five degrees of freedom, but in this study four degrees of freedom are evaluated, keeping fixed the ratio H/L (ratio between the height and length of the solid domain) as well as the cavity constraints. The search for the optimal geometry is performed by Simulated Annealing and the Luus-Jaakola algorithm with different configurations or set of main parameters. Each algorithm is executed twenty times and the results for θmax, and corresponding geometry ratios, are recorded. Results of two heuristics are compared in order to select the best method for future studies about the complete optimization of the cavity, as well as, the evaluation of constraints over the thermal performance of the problem. The method employed to compare and rank the different versions of the two algorithms is a statistical tool called multi-comparison of Kruskal-Wallis. With this statistical method it is possible to classify the algorithms in three main groups. Results showed that the Simulated Annealing with hybrid parameters of Cooling Schedule (BoltzExp and ConstExp2) and traditional ones (Exponential) led to the highest probability to find the global optimal shape, while the results obtained with the Luus-Jaakola algorithm reached to several local points of minimum far from the best shape for all versions of the algorithm studied here. However, the Luus-Jaakola algorithm led to the lowest magnitude of maximum excess of temperature, showing that the implementation of hybrid methods of optimization can be an interesting strategy for evaluation of this kind of problem.

Restarting search algorithms with applications to simulated annealing

2001 ◽  
Vol 33 (1) ◽  
pp. 242-259 ◽  
Author(s):  
F. Mendivil ◽  
R. Shonkwiler ◽  
M. C. Spruill
Keyword(s):  
Simulated Annealing ◽  
Energy Levels ◽  
Search Algorithms ◽  
Fixed Number ◽  
Stochastic Search ◽  
Goal State ◽  
Numerical Comparisons ◽  
Cooling Schedule ◽  
Local Generation

Some consequences of restarting stochastic search algorithms are studied. It is shown under reasonable conditions that restarting when certain patterns occur yields probabilities that the goal state has not been found by the nth epoch which converge to zero at least geometrically fast in n. These conditions are shown to hold for restarted simulated annealing employing a local generation matrix, a cooling schedule Tn ∼ c/n and restarting after a fixed number r + 1 of duplications of energy levels of states when r is sufficiently large. For simulated annealing with logarithmic cooling these probabilities cannot decrease to zero this fast. Numerical comparisons between restarted simulated annealing and several modern variations on simulated annealing are also presented and in all cases the former performs better.

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