Applied Simulated Annealing by Prof. Dr. René V. V. Vidal (auth.), Prof. Dr. René V. V.

By Prof. Dr. René V. V. Vidal (auth.), Prof. Dr. René V. V. Vidal (eds.)

In February 1992, I defended my doctoral thesis: Engineering Optimiza­ tion - chosen contributions (IMSOR, The Technical college of Den­ mark, 1992, p. 92). This dissertation offers retrospectively my valuable contributions to the theoretical and utilized features of optimization. whilst I had accomplished my thesis I took an interest in modifying a quantity relating to a brand new increasing quarter of utilized optimization. I thought of a number of methods: simulated annealing, tabu seek, genetic algorithms, neural networks, heuristics, professional platforms, generalized multipliers, and so on. ultimately, i made a decision to edit a quantity relating to simulated annealing. My major 3 purposes for this selection have been the next: (i) over the last 4 years my colleagues at IMSOR and i've motor vehicle­ ried out a number of utilized tasks the place simulated annealing was once an important. aspect within the problem-solving strategy. lots of the avail­ capable stories and papers were written in Danish. After a brief assessment i used to be confident that the majority of those works deserved to be pub­ lished for a much broader viewers. (ii) After the 1st mentioned purposes of simulated annealing (1983- 1985), an enormous volume of theoretical and utilized paintings were released inside many alternative disciplines. therefore, i feel that simulated annealing is an technique that merits to be within the curricula of, e.g. Engineering, Physics, Operations examine, Math­ ematical Programming, Economics, approach Sciences, and so on. (iii) A touch to a world community of recognized researchers confirmed that a number of members have been keen to give a contribution to the sort of volume.

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Fig. 8). The left part of Fig. 8 shows the average degree of moved nodes versus temperature of two runs of the One-Chain algorithm implemented for the k-partitioning problem. The average degree of all nodes of the graph is 10. 33 cost function value 80 x 103 . 10 average degree of moved nodes . 7 0 _ Random . -F""---.. 60 i . -. t I 50 ! "........ - First Wins ---... i i 1. . _.... 1 l_ .... _. ! I.. _.. ~ ; 100 temp. 1 1000 10000 temp. Figure 8: The effects of the different selection strategies.

In this schedule the initial temperature To and the temperature decrement ak between the temperature-steps k and k + 1 are chosen according to the mean value C and standard deviation (J' of the cost function C: To = c· (J' ).. Tk ak = exp( - (J'(Tk )) The start temperature To is chosen high enough, so that a deterioration of 3(J' is accepted with high probability (c = 10). The decrement ratio ak is chosen in such a manner that the expected mean value C of the cost function at Tk+l lies in a range of (J' around the attained mean value at Tk.

21, n2 6, June 1953. [10] L. J. Osborne, B. E. n2 3 Summer 1991. [11] F. Reif, Statistical Physics, Berkeley Physics Course, Vol. 5, McGraw-Hill, 1965. [12] J. Rose, W. Klebsch, J. Wolf, Temperature Measurement and Equilibrium Dynamics of Simulated Annealing Placements, IEEE Transactions on Computer Aided Design, Vol. 9, n2 3, March 1990.

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