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Nowadays, object recognition based on local invariant features is widely acknowledged as one of the best paradigms for object recognition due to its robustness for solving image matching across different views of a given scene. This paper proposes a new approach for learning invariant region descriptor operators through genetic programming and introduces another optimization method based on a hill-climbing algorithm with multiple re-starts. The approach relies on the synthesis of mathematical expressions that extract information derived from local image patches called local features. These local features have been previously designed by human experts using traditional representations that have a clear and, preferably mathematically, well-founded definition. We propose in this paper that the mathematical principles that are used in the description of such local features could be well optimized using a genetic programming paradigm. Experimental results confirm the validity of our approach using a widely accepted testbed that is used for testing local descriptor algorithms. In addition, we compare our results not only against three state-of-the-art algorithms designed by human experts, but also, against a simpler search method for automatically generating programs such as hill-climber. Furthermore, we provide results that illustrate the performance of our improved SIFT algorithms using an object recognition application for indoor and outdoor scenarios.