This research focuses on the home health care optimization problem that involves staff routing and scheduling problems. The considered problem is an extension of multiple travelling salesman problem. It consists of finding the shortest path for a set of caregivers visiting a set of patients at their homes in order to perform various tasks during a given horizon. Thus, a mixed-integer linear programming model is proposed to minimize the overall service time performed by all caregivers while respecting the workload balancing constraint. Nevertheless, when the time horizon become large, practical-sized instances become very difficult to solve in a reasonable computational time. Therefore, a new Learning Genetic Algorithm for mTSP (LGA-mTSP) is proposed to solve the problem. LGA-mTSP is composed of a new genetic algorithm for mTSP, combined with a learning approach, called learning curves. Learning refers to that caregivers’ productivity increases as they gain more experience. Learning curves approach is considered as a way to save time and costs. Simulation results show the efficiency of the proposed approach and the impact of learning curve strategy to reduce service times.