Home health care faces new challenges day by day and it has become increasingly legitimate in the face of an aging population. Home healthcare centers are exposed to cumulative demands and academics are paying attention to the routing and scheduling matter, which is offered in literature as a Technician Routing and Scheduling Problem (TRSP) where the aim is to minimize the total cost subject to the time windows constraints to serve the patients respecting their priorities. In this paper, we develop a new distributed algorithm to resolve the home health care routing and scheduling problem (HHRSP). The principal idea of this algorithm is to apply artificial intelligence techniques in a distributed optimization method. The integration of automatic learning and search methods are applied to optimize the assignment of appointments to home caregivers. It allows us to gain time, effort, especially cost, and while complying with the problem constraints. The comparison results prove the efficacy of the recommended approach, which can offer decision support for medical executives of home health care.