Edge computing has emerged as a promising solution for delivering services that demand low latency, high bandwidth, and stringent privacy requirements in numerous data- and compute-intensive applications, such as those in Smart Cities. Heterogeneity in edge computing resources and diverse application requirements demand adaptive optimization techniques, such as service placement, to conform to changing conditions. A service placement model must optimize the selection of edge nodes for deploying and executing services, thereby improving application QoS and maximizing resource utilization. Numerous optimization techniques for adaptive service placement problem have been proposed in the recent past. However, in most cases, the results have been evaluated in limited scenarios. This paper presents a comprehensive comparative study evaluating representative optimization algorithms applied to the problem of dynamic service placement across various application scenarios. The study covers nature-inspired approaches, including both meta-heuristics and reinforcement learning. Our experimental findings offer valuable insights into the strengths and weaknesses of the selected nature-inspired algorithms for service placement optimization, evaluated for applications with different QoS requirements. In our analysis, the Genetic Algorithm shows superior performance in achieving lower average distance and the average number of servers selected. Particle Swarm Optimization excels in minimizing average waiting time and placement decision time. The Artificial Bee Colony maintains low average latency, whereas the RL Proximal Policy Optimization demonstrates superior performance in terms of balancing the utilization of network resources.