Vehicle Routing Problems (VRPs) have made significant strides in accuracy and computational efficiency through the adoption of Deep Learning (DL) techniques. However, previous studies have not fully addressed the symmetries inherent in VRPs, such as rotation, translation, permutation, and scaling. This paper introduces a novel training approach, GSE-VRPs, which employs a regularizer-based method to exploit universal symmetries present in various VRPs and their solutions. By leveraging symmetries like rotational, reflectional, and uniform scalability invariance, this approach substantially enhances the generalization capability of neural heuristic solvers. It enables learned solvers to effectively utilize common symmetries within the same class of VRPs. Our experiments demonstrate that GSE-VRPs significantly enhance the performance of deep heuristic methods in two VRP tasks—the Traveling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP)—all without relying on problem-specific domain expertise.