This article solves the order batching, batch assignment, and sequencing problem (JOBASP) given multiple objectives and heterogeneous picking vehicles in multi-parallel-aisle warehouse systems. A multi-objective grouping genetic algorithm (GGA) is developed to minimize total travel time and total tardiness by implementing an encoding scheme where a gene represents orders grouped in a batch and the assignment of the batch to a picking vehicle. Computer simulations show that the proposed algorithm performs 25.4% better than a first come, first served (FCFS) rule–based heuristic and 10.2% better than an earliest due date (EDD) rule–based heuristic. The proposed GGA provides significant savings of up to 46.8% and 28.4% on travel time and tardiness, respectively, for these benchmark heuristics. Therefore, this article introduces a GGA to solve the JOBASP with a reasonable computing time, making this approach interesting for warehouse operators using heterogeneous picking vehicles and addressing multiple objectives. © 2021 International Society of Management Science and Engineering Management.