Over the last two decades, many Genetic Algorithms have been introduced for solving Constrained Optimization Problems (COPs). Due to the variability of the characteristics in different COPs, none of these algorithms performs consistently over a range of problems. In this paper, we introduce a Genetic Algorithm with a new multi-parent crossover for solving a variety of COPs. The proposed algorithm also uses a randomized operator instead of mutation and maintains an archive of good solutions. The algorithm has been tested by solving the 36 test instances, introduced in the CEC2010 constrained optimization competition session. The results show that the proposed algorithm performs better than the state-of-the-art algorithms.