This paper presents a modified genetic algorithm (GA) using a new crossover operator (ADX) and a novel statistic correlation mutation algorithm (CAM). Both ADX and CAM work with population information to improve existing individuals of the GA and increase the exploration potential via the correlation mutation. Solution-based methods offer better local improvement of already known solutions while lacking at exploring the whole search space; in contrast, evolutionary algorithms provide better global search in exchange of exploitation power. Hybrid methods are widely used for constrained optimization problems due to increased global and local search capabilities. The modified GA improves results of constrained problems by balancing the exploitation and exploration potential of the algorithm. The conducted tests present average performance for various CEC’2015 benchmark problems, while offering better reliability and superior results on path planning problem for redundant manipulator and most of the constrained engineering design problems tested compared with current works in the literature and classic optimization algorithms.