The surge of artificial intelligence, particularly large language models, has driven the rapid development of large-scale machine learning clusters. Executing distributed models on these clusters is often constrained by communication overhead, making efficient utilization of available network resources crucial. As a result, the routing algorithm employed for collective communications (i.e., collective algorithms) plays a pivotal role in determining overall performance. Unfortunately, existing collective communication libraries for distributed machine learning are limited by a fixed set of basic collective algorithms. This limitation hinders communication optimization, especially in modern clusters with heterogeneous and asymmetric topologies. Furthermore, manually designing collective algorithms for all possible combinations of network topologies and collective patterns requires heavy engineering and validation efforts. To address these challenges, this paper presents TACOS, an autonomous synthesizer capable of automatically generating topology-aware collective algorithms tailored to specific collective patterns and network topologies. TACOS is highly flexible, synthesizing an All-Reduce algorithm for a heterogeneous 128-NPU system in just 1.08 seconds, while achieving up to a 4.27x performance improvement over state-of-the-art synthesizers. Additionally, TACOS demonstrates better scalability with polynomial synthesis times, in contrast to NP-hard approaches which only scale to systems with tens of NPUs. TACOS can synthesize for 40K NPUs in just 2.52 hours.