## Comparison of Different Neighbourhood Sizes in Simulated Annealing (1993)

Venue: | Proc. of Fourth Australian Conf. on Neural Networks |

Citations: | 6 - 3 self |

### BibTeX

@INPROCEEDINGS{Yao93comparisonof,

author = {Xin Yao},

title = {Comparison of Different Neighbourhood Sizes in Simulated Annealing},

booktitle = {Proc. of Fourth Australian Conf. on Neural Networks},

year = {1993},

pages = {216--219}

}

### OpenURL

### Abstract

Neighbourhood structure and size are important parameters in local search algorithms. This is also true for generalised local search algorithms like simulated annealing. It has been shown that the performance of simulated annealing can be improved by adopting a suitable neighbourhood size. However, previous studies usually assumed that the neighbourhood size was fixed during search. This paper presents a simulated annealing algorithm with a dynamic neighbourhood size which depends on the current "temperature" value during search. A method of dynamically deciding the neighbourhood size by approximating a continuous probability distribution is given. Four continuous probability distributions are used in our experiments to generate neighbourhood sizes dynamically, and the results are compared. 1 Introduction Simulated Annealing (SA) algorithms can find very good near optimal solutions to a wide range of hard problems, but at the high computational cost. Various methods have been proposed...

### Citations

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(Show Context)
Citation Context ...; \Delta \Delta \Delta ; x n ), where x i 2 X i , i = 1; 2; \Delta \Delta \Delta ; n. An excellent discussion of combinatorial optimisation and its complexity can be found in Garey and Johnson's book =-=[8]-=-. A general model of SA, which is applicable to both continuous and discrete problems, can be described by Figure 1, where function generate (X; T n ) is decided by the generation probabilitysg XY (T ... |

3527 | Optimization by Simulated Annealing
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Citation Context ...3]; and (3) Parallelising SA [4]. This paper falls into the above first category. Section 2 of this paper describes a general SA algorithm [5, 6] which unifies different variants of the classical one =-=[7]-=-. Section 3 presents SA with a dynamic neighbourhood size and its application in Published in Proc. of Fourth Australian Conf. on Neural Networks, ed. P. Leong and M. Jabri, pp.216--219, 1993, Melbour... |

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Citation Context ...b) the exponential function E (T n ), i.e., f (d XY ) = 1 T n exp ` \Gamma dXY T n ' (c) the Cauchy function C (T n ), i.e., f (d XY ) = 1 �� T n d 2 XY + T 2 n (d) the stable function with index =-=1 2 [13], i.-=-e., f (d XY ) = 1 q 2��d 3 XY exp ` \Gamma 1 2dXY ' Then the SA algorithm converges to global minima if the cooling rate is T n = ln n + n 0 ; n = 1; 2; \Delta \Delta \Delta (7) wheresand n 0 are ... |

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A Connectionist Machine for Genetic Hillclimbing
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Citation Context ...ds have been proposed to speed up its convergence, which can roughly be divided into three categories: (1) Optimising functions and parameters in SA [1]; (2) Combining SA with other search algorithms =-=[2, 3]-=-; and (3) Parallelising SA [4]. This paper falls into the above first category. Section 2 of this paper describes a general SA algorithm [5, 6] which unifies different variants of the classical one [7... |

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Citation Context ... its convergence, which can roughly be divided into three categories: (1) Optimising functions and parameters in SA [1]; (2) Combining SA with other search algorithms [2, 3]; and (3) Parallelising SA =-=[4]-=-. This paper falls into the above first category. Section 2 of this paper describes a general SA algorithm [5, 6] which unifies different variants of the classical one [7]. Section 3 presents SA with ... |

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Citation Context ...ixed-size neighbourhood clearly does not conform with the basic search strategy behind SA. It is appealing to have a neighbourhood size which can adjust itself in the different search stages. Fast SA =-=[12]-=- can be regarded as an example of SA with a dynamic neighbourhood size, but it is only used in the continuous case. The application of dynamic neighbourhood size in combinatorial optimisation, to our ... |

21 | Simulated annealing with extended neighbourhood
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(Show Context)
Citation Context ...in SA [1]; (2) Combining SA with other search algorithms [2, 3]; and (3) Parallelising SA [4]. This paper falls into the above first category. Section 2 of this paper describes a general SA algorithm =-=[5, 6]-=- which unifies different variants of the classical one [7]. Section 3 presents SA with a dynamic neighbourhood size and its application in Published in Proc. of Fourth Australian Conf. on Neural Netwo... |

15 | Optimization by genetic annealing
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(Show Context)
Citation Context ...ds have been proposed to speed up its convergence, which can roughly be divided into three categories: (1) Optimising functions and parameters in SA [1]; (2) Combining SA with other search algorithms =-=[2, 3]-=-; and (3) Parallelising SA [4]. This paper falls into the above first category. Section 2 of this paper describes a general SA algorithm [5, 6] which unifies different variants of the classical one [7... |

5 | General simulated annealing - Yao, Li - 1991 |

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A note on the effect of neighborhood structure in simulated annealing
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Citation Context ... size of NX , i.e., the number of configurations in NX , and is the same for all X in S. Moreover, jNX j is fixed during search once defined for a problem. Goldstein and Waterman [10] and Cheh et al. =-=[11]-=- carried out some experiments on comparing SA with different neighbourhood sizes, but the sizes are still fixed once decided. A limitation of SA with a fixed neighbourhood size is its inability to per... |

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Citation Context ...configuration Y after it has been generated at temperature T n , and functionsupdate (T n ) decides the rate of the temperature decrease. These three functions determine the convergence of general SA =-=[5, 6, 9]-=-, but parameters in general SA, such as the initial temperature, initial configuration, inner-loop stop criterion, and outer1 generate initial configuration X at random; generate initial temperature T... |

2 |
Neighborhood size in the simulated annealing algorithm
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Citation Context ...j, where jNX j is the size of NX , i.e., the number of configurations in NX , and is the same for all X in S. Moreover, jNX j is fixed during search once defined for a problem. Goldstein and Waterman =-=[10]-=- and Cheh et al. [11] carried out some experiments on comparing SA with different neighbourhood sizes, but the sizes are still fixed once decided. A limitation of SA with a fixed neighbourhood size is... |