Algorithm Design

Opening — Why this matters now Mixed-Integer Linear Programming (MILP) sits quietly underneath a surprising amount of modern infrastructure: logistics routing, auctions, facility placement, chip layout, resource allocation. When it works, no one notices. When it doesn’t, the solver spins for hours, racks up nodes, and quietly burns money. At the center of this tension is branch-and-bound—an exact algorithm that is elegant in theory and painfully sensitive in practice. Its speed hinges less on raw compute than on where it looks first. For decades, that decision has been guided by human-designed heuristics: clever, brittle, and wildly inconsistent across problem families. ...

Opening — Why this matters now The academic world has been buzzing ever since a Nature paper claimed that large language models (LLMs) had made “mathematical discoveries.” Specifically, through a method called FunSearch, LLMs were said to have evolved novel heuristics for the classic bin packing problem—an NP-hard optimization task as old as modern computer science itself. The headlines were irresistible: AI discovers new math. But as with many shiny claims, the real question is whether the substance matches the spectacle. ...