Using C++ OR Python:

For this program were going to take a look at another type of stochastic optimization, simulated annealing.

The residence hall at Wassamatta U. is co-ed, with each floor being single-sex. We are going to deal with one gender, so that any student in our pool can become roommates with any other student in the pool. There are 50 4-student suites. Thus we must assign 4 students to each room; we would prefer to do this in a way that optimizes student satisfaction. Rooms are considered interchangeable; we dont care which student or group of students is in which room as long as each room has exactly 4 students assigned to it.

We have given each student a questionnaire, covering student demographics (including things like year, major, etc) as well as several potential-roommate questionsDo you like getting up early, or are you a night owl? Is it important that your space be neat and tidy at all times? Do you like cranking the tunes, or would you rather have a quiet environment?--and assigned each possible pairing a compatibility score, ranging from 0 (disaster in the making) to 100 (will probably become close friends). Your task is to find an optimum or near-optimum assignment of roommates.

Your input file is a text file containing a 200x200 table. For each entry in the table at a particular row R and column C, Table[R][C] gives the compatibility of students # R and C. The table is symmetric, so Table[R][C] = Table[C][R]. Each student is assigned a score of 0 with themselves, as a place holder. Our compatibility measure is symmetric, but in general it need not be. Note that this measure codes a better fit as a higher score. How you address this in your program (changing the formula, recoding each score S as 100-S, whatever) is up to you as an implementation detail.

Start with an initial assignment of 200 students to 50 rooms using any convenient methodconsecutive assignment, random assignment, etc. Randomly select any 2 rooms and consider swapping two random students from those rooms. Note that you must compare total compatibility of the groupings that result; an exchange that works much better for 1 student at a cost of lower satisfaction for 2 others may or may not be worthwhile. Your overall suite roommate compatibility score is the RMS (root-mean-square) of the pairwise scores. That is, given students A, B, C, and D, find the scores for AB, AC, AD, BC, BD, and CD; square each score; then take the square root of the average squared value. Start with a value of T that seems generously high. Every 2000 accepted exchanges, or 20,000 attempted exchanges (whichever comes first), reduce T slightly (T = 0.95 T). Your stopping criterion is a full pass of 20,000 attempted exchanges with no exchanges accepted.

For each iteration (value of T), your program should print out how many exchanges were made and attempted, and the best, worst, and average compatibility score of your assignment. At the program conclusion, report the scores of the best, worst, and average match.

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