The convergence of cloud and edge computing in smart manufacturing offers significant potential for improving efficiency in Industry 4.0. However, task scheduling in this context remains a complex, multi-objective challenge. This study introduces a novel Cloud-Edge Smart Manufacturing Architecture (CESMA), leveraging a hybrid approach that integrates NSGA-II and the Improved Monarch Butterfly Optimization (IMBO) algorithms. The combination utilizes NSGA-II's global search and non-dominated solution capabilities with IMBO's fine-tuning and local optimization strengths to enhance task scheduling performance. Where CESMA combines the scalability and analytics power of cloud computing with edge-based real-time decision-making to address the dynamic demands of smart manufacturing. Through extensive simulations and experiments, the feasibility and effectiveness of CESMA are validated, showing improved task scheduling quality, resource utilization, and adaptability to changing conditions. This research establishes a robust platform for managing the complexities of task scheduling in cloud-edge environments, advancing intelligent manufacturing processes, and contributing to the integration of evolutionary algorithms for real-time industrial decision-making