“Optimization”

I model the NYC Subway Challenge as a time-expanded routing problem over the real MTA schedule. My current best validated route visits all 472 stations in 24:24:30.

Fix only your home airport, list the cities you want to visit, and let a time-expanded traveling-salesman model pick the cheapest order and dates. We use it to price two bucket-list trips: the world's 10 most-visited cities and the New 7 Wonders.

We use the Sudoku solver from the previous post to hunt for minimum-clue puzzles across different grid sizes — and bump into an open problem in mathematics.

In this post, we go from the seemingly simple interview question of "model Sudoku as an optimization problem" all the way to an open problem in mathematics.