Program Synthesis is a challenging problem in Artificial Intelligence. An important element of a program synthesizer is the objective function that guides the combinatorial search for a program that satisfies a given user intent. Given multiple I/O example transformations that correspond to the intended behavior of the program, this function evaluates the performance of a generated program based on the distance of its output to the correct output. In this study, we consider the possibility of using a Genetic algorithm for the evolution of such a function as a means to partially automate the design process. In particular, we propose the GeneticObjective algorithm that evolves domain-specific objective functions by combining user-defined local distance functions in an algebraic expression. Using the Brute synthesizer, we conducted experiments in the Robot Planning and the String transformation domains, the results of which showed that such an approach evolves informative functions. The best evolved function reached the effectiveness of a manually-designed function in the Robot domain, while it outperformed the effectiveness of a hand-crafted function in the String domain.