In the last decade, the new generation of software systems such as Internet of Things (IoT) and Artificial Intelligence (AI) systems has introduced several challenges to the computing infrastructure service providers. Specifically, such systems can be distributed, data-intensive, and latency-sensitive. Although computing infrastructures have been developing to meet such challenges, approaches are still needed to support efficient scheduling of precedence-constrained workflows, while balancing conflicting objectives, including time of execution and energy consumption. Metaheuristic optimization techniques, inspired by natural and evolutionary processes, have gained recognition for their ability to tackle such scheduling problems. Towards addressing this challenge, In this paper, we propose a framework for energy-aware workflow scheduling in heterogeneous edge-cloud infrastructures, taking into account energy consumption, execution time, resource capabilities, task dependencies, and resource contention. Within this framework, we evaluate multiple metaheuristic algorithms to compare their effectiveness in optimizing the trade-off between execution time and energy consumption. The experiments reveal that Evolutionary Optimization, Marine Predators Algorithm, and Differential Evolution consistently outperform other methods in both solution quality and stability.