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**9** 

*Brasil* 

Annibal Hetem Jr.

*Universidade Federal do ABC* 

**The Search for Parameters and Solutions:** 

Genetic Algorithms (GAs) can help solving a great variety of complex problems, and the characterization of these problems as possible subject for GA is the first step in applying this technique. After some years, we have used this strong tool to solve problems from astronomy and engineering, and both fields demand complex models and simulations.

With the aim of improving previous models and test new ones, we have developed a methodology generate solutions based on GAs. From a first analysis, one must establish the model input and output parameters, and then workout on the inversion of the problem, what we called the inverted model. This concept leads to the final formalism that can be

After a brief presentation of the main concerns and ideas, it will be described some applications and their results and discussions. Some details on implementation are also given together with the particularities of each model/solution. A special section regarding error bars estimates is also provided. The GA method gives a good quality of fit, but the range of input

GAs can also be used to verify if a given model is better than another for solving a problem. Even considering the limitation of the derived parameters, the automatic fitting process provides an interesting tool for the statistical analysis large samples of data and the models

In this section, the NP-Complete problems are presented as the main targets of GAs. Before starting to project a GA, it is of greatest importance to study and characterize the problem to

The early first notion of NP-completeness was proposed by Stephen Cook (1971), in his famous paper *The complexity of theorem proving procedures*. The main ideas presented in this section have their origins in the excelent works of Garey & Johnson (1979) and Papadimitriu

parameters must be chosen with caution, as unrealistic parameters can be derived.

**2. Characterization of NP-Complete problems** 

**1. Introduction** 

considered.

(1995).

justify the technique to use.

subject to the GA implementation.

**Applying Genetic Algorithms on** 

**Astronomy and Engineering** 

