Let me end with a spoiler: The correct way to mow your lawn is to pay someone else to do it. Period. But I'm a data scientist so I'm going to show you how to spend all your time planning how to do it instead. You won't actually get to start mowing because this method takes more time than you'll spend mowing your lawn all summer. Possibly literally.
I hate mowing so I sat down to plan out how to minimize the amount of time I spent mowing. This planning time of course was a thinly veiled attempt at procrastination thus it's actually a multi-objective optimization problem and solution.
What interested me in this problem was finding a real world use case for solving some small versions of the Traveling Salesperson Problem. I also thought the wrinkle about minimizing turns was an interesting modification to figure out.
Controlled testing in modern systems is fairly straight-forward. There are many tools to handle statistical analysis, random population sampling, data collection, etc. With the number of web visitors routinely numbering in the millions, the statistical techniques are also greatly simplified because of the preponderance of data. What do we do though when data is very costly?
In this post, we'll take an overly simplified model and solve it using response surface modeling to find an approximate optimum with very little data. At the end of the post we'll discuss some possible caveats and some ideas for getting around those caveats.