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Filterless optical networks (FON) are attracting attention because of their low-cost characteristics. However, removing active devices forces the signal to be broadcast on all output ports, wasting a significant amount of spectrum resources. In order to maintain the low-cost advantage and save more spectrum resources, this paper studies the routing, modulation, and spectrum assignment (RMSA) problem in semi-filterless optical networks. For this problem, we propose a spectrum assignment algorithm based on adaptive modulation scheme with minimum link and boundary distance (ML-M-MTBD). The algorithm selects the path that occupies the minimal number of links (ML) for spectrum assignment during the routing process and combines it with a variable adaptive modulation scheme (VAMS) between fiber trees. During the spectrum assignment process, the algorithm divides the frequency spectrum resources into two regions, calculates the distance from the frequency spectrum block to the two boundaries of the spectrum resources to be assigned, and selects the position corresponding to the shorter distance to the boundary for spectrum assignment. We conducted simulations on German-Net and Henan-Net, and compared our algorithm with two existing algorithms, the first-fit algorithm and the best-fit algorithm. The simulation results show that the proposed algorithm has a lower blocking probability. • Combining two optimization metrics of routing and spectrum assignment: (1) L: Link occupancy; (2) BD: Boundary distance of the spectrum block, we propose an algorithm for minimum link and boundary distance spectrum assignment. • Reduced the request blocking probability in the semi-filterless network. [ABSTRACT FROM AUTHOR]