Any evolutionary algorithm tends to end up in a local optimum. A new approach based on an evolutionary algorithm named as Diversity Driven Multi-Parent Evolutionary Algorithm with Adaptive non-uniform mutation is presented. In the proposed algorithm, Non-uniform mutation is used to maintain diversity in the explored solutions. Fitness variance, which signifies solution space aggregation, is used to detect the premature convergence of the population to a local optimum. The term multi-parent is used in the context of more than two parents participating in crossover operation. After multi-parent selection for cross-over to generate new solutions, the non-uniform adaptive mutation is performed, which in turn is triggered by the diminishing value of fitness variance of candidate solutions and pushes solutions out of local optimum. Hence, it can be said that the algorithm is driven by the diversity of the population and overcomes the tendency of evolutionary algorithms to stuck in local optimum. The performance of this algorithm is tested on 23 basic benchmarks, CEC05 functions, and CEC17 functions. As CEC17 benchmark functions include constraint problems, a constraint-handling technique is proposed based on the fuzzy set theory. In the proposed constrained handling strategy, constraint violation is also taken as another objective along with the main objective. The decision to accept or discard the solution is based on the fuzzy set theory. The values of constraint violation and objective function are calculated and fuzzified by calculating membership values by considering the main objective and constraint violation as triangular fuzzy functions. The best solutions are selected based on cardinal priority ranking. The obtained results from the proposed algorithm are compared with the results available in the literature. The result indicates that this algorithm is competitive, even with a smaller number of function evaluations.