This paper proposes Decomposed Retrieval of Constraints (DRoC), a novel framework aimed at enhancing large language models (LLMs) in exploiting solvers to tackle vehicle routing problems (VRPs) with intricate constraints. While LLMs have shown promise in solving simple VRPs, their potential in addressing complex VRP variants is still suppressed, due to the limited embedded internal knowledge that is required to accurately reflect diverse VRP constraints. Our approach mitigates the issue by integrating external knowledge via a novel retrieval-augmented generation (RAG) approach. More specifically, the DRoC decomposes VRP constraints, externally retrieves information relevant to each constraint, and synergistically combines internal and external knowledge to benefit the program generation for solving VRPs. The DRoC also allows LLMs to dynamically select between RAG and self-debugging mechanisms, thereby optimizing program generation without the need for additional training. Experiments across 48 VRP variants exhibit the superiority of DRoC, with significant improvements in the accuracy rate and runtime error rate delivered by the generated programs. The DRoC framework has the potential to elevate LLM performance in complex optimization tasks, fostering the applicability of LLMs in industries such as transportation and logistics.