The high-definition map is a cornerstone of autonomous driving. Unlike constructing a costly fleet of mapping vehicles, the crowdsourcing paradigm is a cost-effective way to keep an HD map up to date. Achieving practical success for crowdsourcing-based HD maps is contingent on addressing two critical issues: freshness and recruitment costs. Given that crowdsource vehicles are often heterogeneous in terms of operational costs and sensing capabilities, it is practical to recruit heterogeneous crowdsource vehicles to achieve the tradeoff between freshness and recruitment costs. However, existing works neglect this aspect. To solve it, we formulate this problem as a Markov decision process. We demonstrate that the optimal policy is threshold-type age-dependent. Additionally, our findings reveal some counter-intuitive insights. In some cases, the company should initiate vehicle recruitment earlier when vehicles arrive more frequently, or have higher operational costs or sensing capabilities.} Besides, we propose an efficient algorithm, called the bound-based relative value iteration (BRVI) algorithm, to overcome the technical challenge that finding an optimal policy is time-consuming. Numerical simulations show that (i) the optimal policy reduces the average cost by $19.04\%$ compared to the state-of-the-art mechanism}, and (ii) the proposed algorithm can reduce the convergence time by $13.66\%$ on average compared to the existing algorithm.

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