Genetic programming techniques allow flexibility in the optimization process, making it possible to use them in different areas of knowledge and providing new ways for specialists to advance in their areas more quickly and more accurately.Parameter mapping approach is a numerical optimization method that uses genetic programming to find an appropriate mapping scheme among initial guesses to optimal parameters for a system. Although this approach yields good results for problems with trivial solutions, the use of large equations/trees may be required to make this mapping appropriate for more complex systems.In order to increase the flexibility and applicability of the method to systems of different levels of complexity, this thesis introduces a generalization by thus using multi-gene genetic programming to perform a multivariate mapping, avoiding large complex structures.Three sets of benchmark functions, varying in complexity and dimensionality, were considered. Statistical analyses carried out suggest that this new method is more flexible and performs better on average, considering challenging benchmark functions of increasing dimensionality.This thesis also presents an improvement of this new method for multimodal numerical optimization.This second algorithm uses some niching techniques based on the clearing procedure to maintain the population diversity. A multimodal benchmark set with different characteristics and difficulty levels to evaluate this new algorithm is used. Statistical analysis suggested that this new multimodal method using multi-gene genetic programming can be used for problems that requires more than a single solution. As a way of testing real-world problems for these methods, one application in nanotechnology is proposed in this thesis: the structural optimization of quantum well infrared photodetector from a desired energy.The results present new structures better than those known in the literature with improvement of 59.09 percent.