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The Vehicle Routing Problem (VRP) is an NP-hard scheduling problem for goods transportation with vehicle capacity and transportation cost constraints. This paper presents GPU-based parallel strategies for the Local Search Heuristic (LSH) algorithm to solve the large-scale Capacitated Vehicle Routing Problem (CVRP) instances. This work employs a combination of five improvement heuristic approaches to improve the constructed feasible solution. Typically, 99% of CPU execution time is spent in the feasible solution improvement phase. Two GPU-based parallel strategies, namely route level and customer level parallel designs, have been developed to reduce the execution time of the solution improvement phase. The proposed parallel LSH version has been tested on large-scale instances with up to 30,000 customers. When compared to the corresponding sequential version, the customer level parallel design offers a speedup of up to 147.19 times. [ABSTRACT FROM AUTHOR]