In recent years, healthcare robotics has emerged as a promising solution to address the challenges of nurse burnout and shortages, while simultaneously enhancing patient care. Non-contact vitals monitoring has gained significance in reducing the spread of infectious diseases, exemplified by its role during the COVID-19 pandemic. Among various types of healthcare robots, wheeled mobile robots stand out due to their versatility and potential for autonomous navigation. However, achieving efficient and intelligent navigation in dynamic healthcare environments remains a complex problem. This paper examines behavior-based algorithms and evolutionary algorithms, which take inspiration from biological systems and swarm intelligence. Using these algorithms, the aim is to enhance the capabilities of healthcare robots, allowing them to navigate complex environments with ease and efficiency. This study encompasses an evaluation of popular healthcare robots, such as Dr. Spot, a non-contact vitals monitoring robot, and the versatile Temi robot. Through simulations using the Webots platform and the E-puck robot, we compare the performance of behavior-based and evolutionary algorithms. The results conclude the advantages of evolutionary algorithms in static environments. However, their limitations are observed in dynamic settings, where adaptation is crucial. The findings of this research offer guidance for designing and implementing autonomous wheeled mobile robots in real-world healthcare settings, where efficient and safe navigation is vital to ensure quality patient care.