## 1 Introduction
The use of this kind of approach has well-known drawbacks: (a) finding the appropriate weights is not trivial; (b) multiple runs are needed to provide the decision maker with enough solutions; (c) non-supported solutions cannot be found whatever the selected weights. Regarding vehicle routing problems, several authors have been interested in algorithms based on Pareto optimality to solve different combinatorial optimization problems. For example, [PERSON] et al. (2009) proposed a Non-dominated Sorting Genetic algorithm (_NSGAII_) for solving the vehicle routing problem with route balancing. In the same context, [PERSON] et al. (2009) tested several local search procedures within the _NSGAII_ framework for the capacitated arc routing problem, and more recently, [PERSON] et al. (2010) adapted this previous local search for solving the pick-up and delivery problem. To the best of our knowledge, [PERSON] et al. (2010) and the more recent papers [PERSON] et al. (2010); [PERSON] et al. (2010) are the only ones that consider the routing and planning problem in HHC as a multi-objective variant. In the first one, the compromise relations were between minimizing travel costs and maximizing the level of satisfaction of patients in home care structures. A metaheuristic based on multi-directional local search was proposed to build an approximated front. The latter was compared to the optimal Pareto front obtained by using an \(\epsilon\)-constraint method. The study of [PERSON] et al. (2010) considered also a multicriteria problem with three objectives: (1) minimizing the total working time of the caregivers, (2) optimizing the quality of service by minimizing the patients time window and the synchronized visits non-satisfaction, (3) and minimizing the maximal working time difference among nurses and auxiliary nurses. To solve the problem, these authors designed a Memetic Algorithm for Multi-objective Optimization (MAMO), which uses an NSGAII structure combined with multi-directional local searches. In [PERSON] et al. (2010), a bi-objective optimization model aimed to make a tradeoff between transportation cost and environmental pollution. \begin{table}
\begin{tabular}{l c} \hline \hline \multicolumn{1}{c}{**Exact Linear Solver**} & **Metaheuristic** \\ \hline [PERSON] et al. (2010) & \(\times\) \\ [PERSON] et al. The authors proposed various versions of heuristics, metaheuristic, and modified/hybrid methods. Metaheuristics are simulated annealing and swarm algorithms. Their evaluation is made through four assessment metrics and the Pareto-optimal solutions of the employed metaheuristics by the epsilon constraint method. Overall, it can be seen that most implementations can be found in the category of metaheuristics, and the majority of them use local search procedures. However, the papers [38; 44; 47; 48; 51] may be the only ones that proposed a population-based metaheuristic for solving a vehicle routing problem in the HHC field. In addition, only [38; 51] tackled a multicriteria problem through this kind of solution approach. The last trends seem to focus either on uncertainties or dynamic data ([62] studied a pick-up and delivery version of HHC with travel time uncertainty; [63] worked on the caregiver routing problem solved in a dynamic context with uncertainties and random events by a multi-agent system; [53] proposed a dynamic method to handle sudden incidents in practice; and [54] considered the dynamic arrival and departure of patients and nursing staff to solve the daily scheduling and routing problem in a long-term perspective). However, none of those dealt with multi-objective functions. Summarizing the literature review, most works on vehicle routing problems raised in HHC, either considering simultaneous/precedence synchronization or not, have tackled the multi-criteria issue by a weighted sum of the considered criteria.