This paper presents a solver, the PIMAGc, for optimization of constrained mixed integer programming problems based on the Compact Genetic Algorithm (cGA). As the cGA, the PIMAGc works with binary representation of variables. As comparison criteria and to measure the algorithm's performance, the PIMAGc was compared with the MI-LXPM, an appropriate algorithm for solving mixed integer programming problems. By using an appropriate number of problems, it was found that the PIMAGc outperformed the MI-LXPM with a greater success rate and a smaller number of evaluations on the majority of the problems, with equal performance on the others.