Achieving an effective balance between solution convergence and diversity remains a key challenge when solving multi-objective optimization problems. However, the performance of existing algorithms continues to degrade on many-objective optimization problems. Additionally, the genetic operators commonly utilized in many-objective evolutionary algorithms require extensive tuning of control parameters, without which solution quality suffers. To address these limitations, several new techniques are proposed. First, an adaptive penalty mechanism that leverages population and weight vector distribution information to assign specialized penalty factors to each sub-problem is developed by us. Second, the Jaya optimization algorithm is extended by us to improve its efficacy in many-objective spaces. Finally, Levy mutation is incorporated to help escape local optima and enhance population diversity. The proposed MJaya/D algorithm is assessed on standard DTLZ benchmark problems to evaluate the performance improvements stemming from the Jaya operator and adaptive penalty scheme. Experiments demonstrate that MJaya/D obtains superior Pareto front approximations compared to current state-of-the-art techniques for several many-objective optimization formulations.