In this project you will be exploring a response surface involving the yield of a plot of land as a function of six nutrients added to the soil, and one proprietary additive recommended by an outside consultant. Measurements of the yield are noisy, and the noise level will vary throughout the experiment period. You will be limited in the number of observations you can gather by a (rolling over) weekly budget. Your primary goal will to find settings of the inputs that maximize yield, although there will be several secondary objectives having to do with the robustness of the optima you find, relevance of the seven factors, and the dynamics of the noise process. These details are outlined in more detail below.
You will obtain runs through a Shiny app hosted at http://gramacylab.shinyapps.io/yield.
Through this interface you will be able to download your cache of runs, perform new runs, and inspect your run budget.
Through the interface you will see numeric fields for seven inputs, and a sliding bar for a number of repetitions. The inputs are levels of nutrients, save the last one which is a level of a proprietary additive.
The range for all inputs is [0,100].
The output is yield (units irrelevant) and it is noisy. This means you won’t get the same responses as your friends even if you colluded to try the same inputs.
There are no do-overs.
In each week you get 100 units to spend on runs, and these units roll over from one week to the next.
You could, in theory, save your entire budget until the end of the class, thereby banking on learning something key from now until then that will allow you to spend more resourcefully. But there are two built-in discouragements against that.
The cost of runs depends on the number of replicates.
So there is a certain economy of scale to performing replication.
The interface will let you overspend your budget for the week
The recent runs are shown in a table on the interface page, and you can cycle through to see more runs if desired.
You are not expected to use the data directly in this tabular view format. It is mostly provided as a visual confirmation that new runs have been successfully obtained. A button at the bottom of the page allows you to download a CSV file with your runs.
Your primary goal, over the course of the rest of the semester, is to optimize yield, with larger yields being better. This was designed to be a challenging problem.
Secondary goals include the following.
Here are some rules which are not directly enforced by the interface, but which you are responsible for obeying.