> For the complete documentation index, see [llms.txt](https://docs.ithacaprotocol.io/docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.ithacaprotocol.io/docs/architecture/pre-match-processing/mixed-integer-linear-programming-milp-optimization.md).

# Mixed Integer Linear Programming (MILP) Optimization

Mixed Integer Linear Programming (MILP) allows for the searching of clearing prices and associated sets of consistent orders that maximize executed volume and satisfy best execution requirements. The optimization incorporates conditional orders and automatic replication.

MILP utilizes advanced heuristics to perform an efficient search of the solution space using the branch-and-bound algorithm for binary integer constraints.