Architecture design and logistics mission planning are two important components of space campaign design. Given available architecture designs, multi-mission logistics mission planning problem typically can be solved for each mission independently. However, design of a multi-mission campaign considering the interactions among the missions is essential for optimal vehicle or other infrastructure designs; this campaign-level space mission design optimization problem over a long time horizon can become computationally prohibitive due to the curse of dimensionality. This paper proposed a lookahead-policy-based approximate dynamic programming (ADP) algorithm to design architectures effectively. It resolves the curse of dimensionality by considering the performance of architectures in the first few missions optimally and further future missions approximately. A case study of lunar exploration campaign design demonstrates the effectiveness of the proposed ADP algorithm. Results show that the ADP algorithm can provide a fast estimation of architecture designs. The solution approximates well traditional all-at-once mission planning optimization framework. Moreover, the proposed ADP algorithm is more scalable and flexible to balance the design fidelity and computational efficiency.