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.