At present, home health care (HHC) has been accepted as an effective method for handling the healthcare problems of the elderly. The HHC scheduling and routing problem (HHCSRP) attracts wide concentration from academia and industrial communities. This work proposes an HHCSRP considering several care centers, where a group of customers (i.e., patients and the elderly) require being assigned to care centers. Then, various kinds of services are provided by caregivers for customers in different regions. By considering the skill matching, customers' appointment time, and caregivers' workload balancing, this article formulates an optimization model with multiple objectives to achieve minimal service cost and minimal delay cost. To handle it, we then introduce a brain storm optimization method with particular multi-objective search mechanisms (MOBSO) via combining with the features of the investigated HHCSRP. Moreover, we perform experiments to test the effectiveness of the designed method. Via comparing the MOBSO with two excellent optimizers, the results confirm that the developed method has significant superiority in addressing the considered HHCSRP.