Multi-objective evolutionary approach based on K-means clustering for home health care routing and scheduling problem

This paper suggests a bi-objective mathematical model, called HHC-MOVRPTW for the home health care routing and scheduling problem. HHC-MOVRPTW aims to minimize the overall service time while minimizing the total tardiness compared to the visiting time preferences. The considered problem is a NP hard, combining the Personnel Scheduling Problem and the Vehicle Routing Problem with time windows. Three solution approaches are proposed to solve it. Firstly, the HHC-MOVRPTW is solved with a non-scalar method, called Lexicographical method, in order to obtain a first solution for the problem. It is subsequently solved by two well-known multi-objective evolutionary algorithms, namely the Non-dominated Sorting Genetic Algorithm (NSGA-II) and the Strength Pareto Evolutionary Algorithm (SPEA2). Afterwards, a new hybridization approach, combined the evolutionary algorithm with K-means clustering technique is also suggested to improve the quality of the obtained Pareto sets. This is achieved by dividing the population of NSGA-II and SPEA-2 into sub-populations (clusters) and all sub-solutions have to be combined to find the final Pareto front. The computational experiments are performed using Solomon’s bench- mark instances. Thus, results prove the effectiveness of the proposed approaches and their suitability with the problem.