Empirically Tractable Antibiotics Time Machines

Suppose we have a population of bacteria and for each bacterium of a given genotype, an antibiotic alters it to another type with some probability. Our aim is to apply a set of antibiotics (K in number) with a specified precedence (in N steps) so as to maximize the fraction of bacteria (with d number of distinct genotypes) becoming a certain type. A straightforward approach would be to explicitly enumerate all the permutations with repetitions, which is computationally expensive. In this project, we propose to use mixed-integer programming techniques to model and solve this challenging problem.
 
The tasks of the students will include data analysis, modelling and coding. Students with strong computing and optimization background will be preferred.