## 1 Introduction
On the other hand, [PERSON], [PERSON], and [PERSON] [16] presented the heterogeneous vehicle routing problem that determines a set of vehicle routes that satisfies customer demands and vehicle capacities and minimize the sum of variable operating costs. An integer programming model was used, and for more complex problems, Tabu Search algorithms were developed to find solutions within a reasonable computational time. The results show that the amount of carbon emissions could be reduced by carbon trading without increasing the total costs. Regarding the study of biobjective vehicle routing problems considering the customer-centric approach, few contributions can be found in the literature: the traveling repairman problem with profits (TRPP) [17], the \(k\)-Traveling Repairmen Problem with Profits (\(k\)-TRPP) under uncertainty [18], and a biobjective study of the minimum latency problem [19]. In the first work [17], the authors considered the \(k\)-TRP with the objective function that monotonically decreases over time. For this problem, they proposed a mathematical formulation. However, since the model should be solved separately for each path, the solution framework can be time-consuming, motivating the development of a Tabu-search procedure. The second research [18] addresses the \(k\)-TRP but enables the decision-maker to manage and control risk. For this, the authors proposed a mean-risk formulation and a heuristic approach based on an adaptive neighborhood search for the \(k\)-TRPP under uncertainty, providing high-quality results for small and medium-size instances. Finally, the most recent work [19] studies the Minimum Latency-Distance Problem (MLDP), analyzing the conflict between the total distance traveled by the vehicles and the total waiting time of the customers. The authors proposed a mathematical formulation and two heuristic procedures inspired on evolutionary algorithms, obtaining optimal results for instances up to 40 customers and extending the computational experimentation over the metaheuristics for instances up to 256 customers. Considering the aforementioned discussion, to the best of our knowledge, no tailored approach has been proposed in the literature for the problem considering the risk-averse perspective. For this reason, in this paper,we study the Biobjective Cumulative Capacitated Vehicle Routing Problem considering Profits (BCCVRP-Pr). To handle this new problem, we propose a mixed-integer formulation and a MA-RK procedure to efficiently deal with instances of reasonable size. [PERSON] and [PERSON] [20] studied the diversity of variants of vehicle routing problems solved using metaheuristics, where eleven papers were identified using memetic algorithms. In a recent example, [PERSON] et al. [21] proposed a hybrid metaheuristic that combines a memetic algorithm, sequential variable neighborhood descent, and a revised 2-opt method, for the plug-in hybrid electric vehicle routing problem. In addition, [PERSON] et al. [22] developed a multiobjective memetic algorithm for the vehicle routing problem with time windows. To our knowledge, only [PERSON] et al. [2] applied memetic algorithms to the cumulative capacitated vehicle routing problem. They created two versions of their procedures to solve a single objective problem to minimize the sum of arrival times at the customers. On the other side, memetic algorithms have been combined with random keys in some applications. One example is the hybridization of [PERSON] et al. [23], where memetic algorithms were combined with a biased random key genetic algorithm and adaptive large neighbourhood search to solve a scheduling problem. Other applications to scheduling problems using memetic algorithms and random keys were proposed by [PERSON] and [PERSON] [24] and [PERSON] and [PERSON] [25], among others.