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The problem of computing the bandwidth-delay-constrained least-cost QoS multicast routing is an NP-complete problem. We present a new efficient heuristic algorithm for the QoS multicast routing that depends on bounded end-to-end delay and link bandwidth along the path from the source to each destinations, and minimum cost of Steiner tree. In this algorithm, the modified determinant encoding is used for genotype representation. The major objectives of this study are: to modify the determinant encoding to be suitable for the QoS-constrained Steiner tree problems; to propose a new algorithm for repairing determinant codes for Steiner tree algorithms; to develop a new heuristic GA-based solution to the QoS multicast routing problem with modified determinant encoding and new proposed repair function. To compare the performance of the proposed algorithm with some existing GA-based algorithms, we simulate our algorithm for several networks with different network and multicast sizes. These results show that our proposed algorithm can generate a smaller average tree cost than the mentioned existing algorithms within a reasonable time.