A discrete multi-objective grey wolf optimizer for the home health care routing and scheduling problem with priorities and uncertainty

Abstract

In China, with the acceleration of the population aging, the demand for home health care is growing rapidly. However, the available caregivers are insufficient to serve all the customers who make an appointment in advance. Besides, there are actually some uncertain parameters such as travel and service times when implementing the given schedule. Hence, this paper presents a home health care routing and scheduling problem (HHCRSP) by considering customers’ priorities and times uncertainty. A fuzzy multi-objective optimization model is established to maximize the total priority of all visited customers and minimize the total service cost. Jimenez’s method is utilized to transform the fuzzy parameters in the model. A discrete multi-objective grey wolf optimizer (DMOGWO) is proposed to solve the model. In the DMOGWO, the heuristic rule of priority maximum-earliest service is designed to generate the initial solution. An individual position updating mechanism is developed to make the algorithm suitable for discrete search space. Subsequently, three neighborhood structures are designed to enhance the local search ability of the algorithm. Finally, the DMOGWO is compared with CPLEX, MOGWO, MOPSO, NSGA-II and NSGA-III. Experimental results indicate that the proposed DMOGWO is competitive in convergence, diversity and distribution of the solutions on many instances. This shows that the proposed DMOGWO can effectively solve the home care routing and scheduling problem.