We introduce a GPU‐based parallel vertex substitution (pVS) algorithm for the p‐median problem using the CUDA architecture by NVIDIA. pVS is developed based on the best profit search algorithm, an implementation of vertex substitution (VS), that is shown to produce reliable solutions for p‐median problems. In our approach, each candidate solution in the entire search space is allocated to a separate thread, rather than dividing the search space into parallel subsets. This strategy maximizes the usage of GPU parallel architecture and results in a significant speedup and robust solution quality. Computationally, pVS reduces the worst case complexity from sequential VS’s O(p·n
2) to O(p·(n−p)) on each thread by parallelizing computational tasks on GPU implementation. We tested the performance of pVS on two sets of numerous test cases (including 40 network instances from OR‐lib) and compared the results against a CPU‐based sequential VS implementation. Our results show that pVS achieved a speed gain ranging from 10 to 57 times over the traditional VS in all test network instances.
