**Acknowledgement**

This work has been partially supported by Spanish project TEC2010-21303-C04-04.

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**Chapter 0**

**Chapter 4**

**Simulated Annealing in Research and Applications**

Simulated annealing (SA) [16], [17], [14]), belongs among those algorithms which allow steps after which the value of the objective function will deteriorate. It can thus be seen again as the local extensions of classical methods of searching. The SA is similar to hill climbing, but differs in the fact that the individual is able to overcome local extremes. However, inspiration for this formulation of statistical mechanics had been found in the description of the physical annealing process of a rigid body. In this analogy, namely during annealing of metals with unstable crystal lattice, there is a stabilization of loose particles in an optimal state, i.e. the formation of a stable crystal lattice. Such a metal has much better properties. The process is carried out by heating the metal at high temperatures to the melting point and then very slowly cooling it. Cooling is done slowly enough to eliminate unstable particles and the metal has acquired the requisite optimal quality. In the early 1980s, Kirkpatrick, Gelatt and Vecchi (Watson Research Center of IBM, USA) and independently Cerny (Department of Theoretical Physics, Comenius University in Bratislava, former Czechoslovakia) proposed solutions to the problem of finding the global minimum of combinatorial optimization analogous to the

This chapter introduces simulated annealing in special applications focused on deterministic chaos control, synthesis and identification. The first one discusses the use of SA on evolutionary identification of bifurcations, i.e. positions of control parameters of the

The second application discusses the possibility of using SA for the synthesis of chaotic systems. The systems synthesized here were based on the structure of well-known logistic equations. For each algorithm and its version, repeated simulations were conducted and then averaged to guarantee the reliability and robustness of the proposed method. The third and last application is focused on deterministic spatiotemporal chaos realtime control by means of selected evolutionary techniques, with SA. Realtime-like behavior is specially defined and simulated with a spatiotemporal chaos model based on mutually nonlinear joined *n* equations, so-called Coupled Map Lattices (CML). Investigation consists of different case studies with increasing simulation complexity. For all algorithms each simulation was repeatedly evaluated in order to show and check the robustness of the methods used. All

> ©2012 Zelinka and Skanderova , licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original

©2012 Zelinka and Skanderova , licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Ivan Zelinka and Lenka Skanderova

procedure of the annealing rigid body.

investigated system related to that event.

work is properly cited.

http://dx.doi.org/10.5772/52094

**1. Introduction**

Additional information is available at the end of the chapter

Ursem, R.K. (2002). Diversity-guided Evolutionary Algorithms, *Proc. Int. Conf. on Parallel Problem Solving from Nature VII (PPSN VII),* (2002) Granada, Spain, 462–471.
