Clonal Selection Algorithm is a very powerful Nature Inspired Algorithm that has been applied in a number of different kind of optimization problems since the time it was first published. Also, in recent years a growing number of optimization models have been proposed that are trying to reduce the energy consumption in vehicle routing. In this paper, a new variant of Clonal Selection Algorithm, the Parallel Multi-Start Multiobjective Clonal Selection Algorithm (PMS-MOCSA) is proposed for the solution of a Vehicle Routing Problem variant, the Multiobjective Energy Reduction Multi-Depot Vehicle Routing Problem (MERMDVRP). In the formulation four different scenarios are proposed where the distances between the customers and the depots are either symmetric or asymmetric and the customers have either demand or pickup. The algorithm is compared with two other multiobjective algorithms, the Parallel Multi-Start Non-dominated Sorting Differential Evolution (PMS-NSDE) and the Parallel Multi-Start Non-dominated Sorting Genetic Algorithm II (PMS-NSGA II) for a number of benchmark instances.