**Advances in SA**

**Chapter 0**

**Chapter 1**

**Adaptive Neighborhood Heuristics for Simulated**

Simulated annealing has been applied to a wide range of problems: combinatorial and continuous optimizations. This work approaches a new class of problems in which the objective function is discrete but the parameters are continuous. This type of problem arises in rotational irregular packing problems. It is necessary to place multiple items inside a container such that there is no collision between the items, while minimizing the items occupied area. A feedback is proposed to control the next candidate probability distribution, in order to increase the number of accepted solutions. The probability distribution is controlled by the so called crystallization factor. The proposed algorithm modifies only one parameter at a time. If the new configuration is accepted then a positive feedback is executed to result in larger modifications. Different types of positive feedbacks are studied herein. If the new configuration is rejected, then a negative feedback is executed to result in smaller modifications. For each non-placed item, a limited depth binary search is performed to find a scale factor that, when applied to the item, allows it to be fitted in the layout. The proposed algorithm was used to solve two different rotational puzzles. A geometrical cooling schedule is used. Consequently, the proposed algorithm can be classified as simulated quenching.

This work is structured as follows. Section 2 presents some simulated annealing and simulated quenching key concepts. In section 3 the objective function with discrete values and continuous parameters is explained. Section 4 explains the proposed adaptive neighborhood based on the crystallization factor. Section 5 explains the computational experiments and section 6 presents the results. Finally, section 7 rounds up the work with the conclusions.

Simulated annealing is a probabilistic meta-heuristic with a capacity of escape from local minima. It came from the Metropolis algorithm and it was originally proposed in the area of combinatorial optimization [9], that is, when the objective function is defined in a discrete

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©2012 Tsuzuki et al., 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 work is properly

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**Annealing over Continuous Variables**

T.C. Martins, A.K.Sato and M.S.G. Tsuzuki

http://dx.doi.org/10.5772/50302

**1. Introduction**

**2. Background**

cited.

Additional information is available at the end of the chapter
