I'm new to machine learning and am trying to use it to solve a specific problem related to seating students in a classroom. I want to take a list of students and allocate them each to a seat, such that a certain output value is maximised.
Students (each one containing all the data from which a compatibility score can be calculated): A B C D E F
Seats: 1 2 3 4 5 6 7 8
Each pair of students has a predefined 'compatibility score' and each pair of seats has a geometric distance between them. After sorting students into seats, I would calculate a ratio between those two values, the average of which would be my outcome to be optimised.
A class of 25 students and 25 seats has something like 15,000,000,000,000,000,000,000,000 possible arrangements, so a brute force method is rather unfeasible. My ideal outcome here is that machine learning can develop an optimised algorithm for sorting them.
Any ideas for what kind of ML algorithm I want?