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 provides retrospectively my relevant contributions to the theoretical and utilized elements of optimization. whilst I had accomplished my thesis I took an interest in enhancing a quantity on the topic of a brand new increasing zone of utilized optimization. I thought of numerous methods: simulated annealing, tabu seek, genetic algorithms, neural networks, heuristics, professional platforms, generalized multipliers, and so forth. ultimately, i made a decision to edit a quantity on the topic of simulated annealing. My major 3 purposes for this selection have been the subsequent: (i) over the past 4 years my colleagues at IMSOR and i've vehicle­ ried out a number of utilized tasks the place simulated annealing used to be a necessary. point within the problem-solving strategy. many of the avail­ capable reviews and papers were written in Danish. After a brief evaluation 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 stated functions of simulated annealing (1983- 1985), an enormous volume of theoretical and utilized paintings were released inside of many alternative disciplines. hence, i think that simulated annealing is an method that merits to be within the curricula of, e.g. Engineering, Physics, Operations examine, Math­ ematical Programming, Economics, procedure Sciences, and so on. (iii) A touch to a world community of famous researchers confirmed that numerous contributors have been keen to give a contribution to this sort of volume.

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5 and an iterative equilibrium identification algorithm. In our implementation we used a dynamic annealing algorithm, where the initial temperature and length of Markov chains were determined as described in the last section. l. ------------------------. 42 Figure 3: Number of Accessible States of running time. Figure 4 shows the corresponding values of internal energy at the end of each Markov chain. We would like to point out that, after intensive experimentation, a poker expert colleague found a configuration with score value 146000.

L. ------------------------. 42 Figure 3: Number of Accessible States of running time. Figure 4 shows the corresponding values of internal energy at the end of each Markov chain. We would like to point out that, after intensive experimentation, a poker expert colleague found a configuration with score value 146000. However, given that as initial configuration, our algorithm was able to find another one with 146296 points. We also 'observed the occurrence of several equally good solutions. In fact, by using the configuration with 146296 score as initial solution our algorithm found 13 other maximal configurations in a single run.

The basic concept of our Par-Chain algorithm consists of the clustering of processors. In each cluster a number of processors are working together on the evaluation of one Markov chain according to the One-Chain algorithm. The clusters work in parallel, calculating different sub-chains. After a certain number of steps a global synchronization is performed and the actual configurations of all clusters are sent to a certain processor (the "chief"). This processor selects one of the configurations as the 38 new starting solution of the next sub-chain calculation and sends it back to the processors of all clusters (cf.

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