One way to optimize a complex algorithm in R is to leverage vectorized operations and avoid using for-loops whenever possible. This allows for efficient use of memory and can significantly improve runtime performance. Additionally, using functions from the base R packages or specialized packages like data.table or dplyr can also enhance performance. Another approach is to profile the algorithm using tools like profvis or microbenchmark to identify the bottlenecks and optimize those specific parts of the code. By analyzing and fine-tuning the performance-critical sections, significant runtime improvements can be achieved.

In addition to the mentioned approaches, another optimization technique is the use of parallel processing in R. By parallelizing computationally intensive tasks across multiple cores or machines, the runtime can be greatly reduced. The parallel package can be used to implement parallel processing using different paradigms like forking, sockets, or message passing. Furthermore, leveraging external C/C++ libraries through packages like Rcpp can also improve performance by allowing critical parts of the algorithm to be executed at a lower-level language.

One alternative optimization technique is to transform the algorithm by applying domain-specific knowledge. This could involve simplifying the problem by reducing the dimensionality of the data, utilizing specific data structures, or exploiting known patterns or properties of the problem. By leveraging domain expertise, it is often possible to devise algorithms that are inherently faster or more efficient in the specific context. Additionally, outsourcing computationally intensive tasks to external tools or platforms, such as using Python for heavy number crunching or leveraging GPU computing, can also lead to significant performance gains.