Discretization of the Firefly Algorithm for Home Care

This paper aims to solve the problem of home-care routing by using a metaheuristic inspired by nature which is the firefly (FF) algorithm. A good discretization and correction of the solution was provided to maintain the advantages of such an algorithm on this combinatorial problem. Even if the problem is only an extension of the vehicle routing problem with time windows (TWVRP), the human aspect hardens it so that any abuse of a constraint can destroy the feasibility or reduce the services quality. Hard constraints concern the precedence between cares and a patient cares synchronization, while soft constraints concern time windows preferences. The problem in this paper also takes into account overtime and the painfulness of home workers. The main purpose is to minimize the routing total duration and to maximize the constraints satisfaction. The results on two examples show that the discrete version of the FF algorithm gives a better total travel time and better satisfies the constraints.