## 1 Introduction
[PERSON] and [PERSON] [15] introduce two parallel two-phase hybrid metaheuristics using TS and SA, designated as the HM4 and HM4C methods, improving the solution quality of several problems generated by the authors. [PERSON] and [PERSON] [16] propose one parallel master-slave co-evolutionary approach using two populations with different fitness functions: The first minimizing the total travel distance and the second reducing the time window constraints violations. [PERSON] and [PERSON] [17] implement a combination of TS and GA running in several cooperative threads and using the population as shared memory. One GA in each thread is used to evolve the population using different selection and crossover operators, and TS is a local search method applied to improve the offspring quality. [PERSON] and [PERSON] [18] apply the adaptive large neighborhood search (ALNS) heuristic to solve five different VRP variants. First, each variant is transformed in a rich pickup and delivery problem with time windows (RPDPTW), and then the ALNS is used to solve it. This algorithm was able to improve the best-known solution in 183 of 486 benchmark problems. Furthermore, [PERSON] and [PERSON] [19] propose several thread-cooperation schemes to solve VRPTW instances: Two use a constant cooperation frequency rate, and the others use two adaptive cooperation rates. Experimental results with several Gehring and Homberger benchmark problems show that, for harder instances, the cooperation frequency increases, and higher solution accuracy is obtained, and this behavior is contrary for less hard instances. [PERSON] and [PERSON] [20] propose an island-model-based approach for a parallel memetic algorithm (PMA-VRPTW) applying refinements to a population of candidate solutions evolving in a parallel scheme. Experimental tests with a symmetric-multiprocessor cluster report better solutions than the best-known solutions of 19 Gehring and Homberger benchmark problems with 1000 customers. [PERSON] et al. [21] present another island-based parallel method to solve the capacitated VRPTW named multiple temperature Pareto simulated annealing (MT-PSA). Experimental results with several Solomon benchmark problems show that the parallel version produces better solutions than those obtained by the sequential version of the algorithm. [PERSON] [22] proposes one cooperative population learning algorithm (CPLA) using several search heuristics implemented as software agents cooperating in a two-stage procedure that first learn and then promote the best solutions. CPLA is evaluated using 56 Solomon benchmark problems with 100 customers, and its results are comparable to those produced by other methods. [PERSON] and [PERSON] [23] apply the bee colony optimization (BCO) with one sequential insertion heuristic maintaining an acceptable population diversification rate to solve several Solomon benchmark problems. They apply a self-adapting tuning strategy to decide the search behavior of each bee in the swarm. [PERSON] and [PERSON] [24] implement a multi-objective GA with a stochastic partially optimized cyclic shift crossover operator to build feasible candidate solutions in its evolutionary process guiding using the distance route and the number of vehicles as fitness functions. The performance of this method is evaluated using 56 Solomon benchmarks problems, and the results indicate that this approach produces 16 solutions comparable with the best-known solutions. [PERSON] and [PERSON] [25] propose a hybrid algorithm combining ACO and TS to solve the capacitated VRPTW. In this approach, a set of ants is used to find promising candidate solutions, and TS is applied to improve the quality of these solutions in each step of its iterative process. [PERSON] et al. [26] implement a message-passing communication scheme with a parallel SA (p-SA) algorithm, including one insertion-based heuristic to solve a VRP variant with simultaneous pickup and delivery with time windows.