A memetic algorithm for multi-objective optimization of the home health care problem

Home health care structures provide cares for the elderly, people with disabilities or patients with chronic conditions. Since the increase in demand, organizations providing home health care are eager to optimize their activities. The planning of caregivers' activities must optimize several objectives, often conflicting, that requires an extensive time to obtain a fair and valid schedule. In this paper, we address the multi-objective home health care problem with the aim of ensuring the applicability of the planning. To that end, the objectives considered in the proposed model are the minimization of the total working time of the caregivers, while maximizing the quality of service and minimizing the maximal working time difference among nurses and auxiliary nurses. A memetic algorithm for multi-objective optimization is proposed to solve the problem. Computational results on benchmark instances from the literature highlight the efficiency of the proposed algorithm in comparison with other existing metaheuristics thanks to four comparison metrics. As well, an analysis of the results exposes the trade-off between the three objectives. As a result, requiring a minimum caregivers' travel time solution leads to scarcity of the available solutions and so, cannot be demanding on the quality of the other objectives.