A biobjective home health care logistics considering the working time and route balancing: a self-adaptive social engineering optimizer

Home health care (HHC) logistics have become a hot research topic in recent years due to the importance of HHC services for the care of ageing population. The logistics of HHC services as a routing and scheduling problem can be defined as the HHC problem (HHCP) academically including a set of service centers and a large number of patients distributed in a specific geographic environment to provide various HHC services. The main challenge is to provide a valid plan for the caregivers, who include nurses, therapists, and doctors, with regard to different difficulties, such as the time windows of availability for patients, scheduling of the caregivers, working time balancing, the time and cost of the services, routing of the caregivers, and route balancing for their routes. This study establishes a biobjective optimization model that minimizes (i) the total service time and (ii) the total costs of HHC services to meet the aforementioned limitations for the first time. To the best of the authors' knowledge, this research is the first of its kind to optimize the time and cost of HHC services by considering the route balancing. Since the model of the developed HHCP is complex and classified as NP-hard, efficient metaheuristic algorithms are applied to solve the problem. Another innovation is the development of a new self-adaptive metaheuristic as an improvement to the social engineering optimizer (SEO), so-called ISEO. An extensive analysis is done to show the high performance of ISEO in comparison with itself and two well-known metaheuristics, i.e. FireFly algorithm and Artificial Bee Colony algorithm. Finally, the results confirm the applicability of new suppositions of the model and further development and investigation of the ISEO more broadly.