## 1 Introduction  
In this paper, we study the biobjective variant of the Cumulative Capacitated Vehicle Routing Problem (CCVRP), a \"customer-centric\" variant of the classical Capacitated Vehicle Routing Problem (CVRP) [1] in which a fleet of \(k\) vehicles serves a set of customers by respecting their priority, defined as an index assigned to each node to indicate the preference to be served. Unlike the traditional VRP, which focuses on the impact that routing costs have on logistics and, in particular, in the transportation activities within the supply chain, the CCVRP rises as a particularization that covers broad objectives centered around service level issues. This problem is relevant in contexts where both customer satisfaction and company profits are prioritized. Due to the importance of sustainable business practices nowadays, there is a need to develop distribution strategies aimed at reducing the negative impact that transportation activities have on the environment. An important application can also be found in the context of emergency logistics, where the distribution of medical aid becomes crucial,particularly when the distribution of different types of drugs or supplementary medical equipment have different levels of importance. The CCVRP was introduced by [PERSON] et al. [2] as a generalization of the well known \(k\)-Traveling Repairmen Problem (\(k\)-TRP), with the objective of addressing problems in which customer metrics reflect the need for fast, equity and fair services. Since then, a diverse number of scenarios have been addressed: where a single vehicle can travel multiple trips [3,4], considering stochastic demand and split/unsplit deliveries [5], or when multiple depots are available [6]. Specifically, the CCVRP with priorities arises in the context of modeling situations in which customers have a differentiated level of attention and has attracted the interest of researchers over the past years due to its applicability in fields such as emergency logistics (i.e., level of damage), delivery logistics (i.e., delivery of different perishable items), personnel transportation, school bus transportation, machine scheduling considering due dates, maintenance operations including delivery dates, receiver wireless communications, etc. As in the traditional VRP and its known variants, exact solution methods, heuristics, and metaheuristic algorithms are proposed to solve the CCVRP. [PERSON] et al. [7] pointed out that optimal solutions are possible to obtain in small-scale problems using exact solution methods. However, large-scale problems are difficult and time-consuming to solve to optimality. Hence, when it comes to real-life optimization, where problems are complex and deal with a significant amount of data, sometimes it is enough to find approximate solutions through the use of heuristic and metaheuristic methods. Before the formal introduction of the problem in 2010, [PERSON] et al. [8] developed a preliminary research studying a particular version of the CCVRP, named as CumVRP, in which the objective consists of minimizing the sumproduct of the arrival times and the demand of the node. Additionally, the CCVRP has been mainly studied from the monobjective function perspective. For this, several contributions involving mathematical models [9,10], exact algorithms [9,11], and heuristic and metaheuristic approaches [2,4,12,13,14] have been developed. Previously, [PERSON] and [PERSON] [15] dealt with the time-dependent routing problem (TDVRP) and applied this approach to green logistics. They established that the use of time-dependent models could obtain optimal solutions that produce less pollution by directing vehicles to roads where they can travel at faster speeds, which means away from congestion zones. However, this could represent traveling longer distances. Another benefit of this model is that it allows time window constraints to be satisfied more reliably.