The DAO Objective Function

The Objective Function, $f$, embodies all the contraints used to match students and dorm room beds. The domain is all the students in their beds.

The details of the two types of errors: Room-student and student-consensus, are as follows:

1. ROOM-STUDENT RELATED CONSTRAINTS: For each student:
NAME	DESCRIPTION	SCORE
Bed	not in a bed	1 * ERR_NOBED
Gender $^{\ref{hardsex}}$	male in a female room, or female in a male room	1 * ERR_WRONG_SEX
Smoke	non-smoker in a smoking room, or smoker in a non-smoking room;	1 * ERR_WRONG_SMOKE
	objector in a smoking room, or objector in a smoking-either room	* SMOKE_OBJ_WEIGHT
Dorm Prefs$^{\ref{fndp}}$	specific room/bed, building, or better bed request not granted	$w$ * ERR_SPECIFIC_ROOM$^{\ref{fnw}}$
	Special Living Option (SLO)	$w$ * ERR_SPECIAL_LIVING$^{\ref{fnw}}$
	$1^{st}$ Hall choice not granted	$w$ * ERR_DORM_CHOICE1$^{\ref{fnw}}$
	$2^{nd}$ Hall choice not granted	$w$ * ERR_DORM_CHOICE2$^{\ref{fnw}}$
	$3^{rd}$ Hall choice not granted	$w$ * ERR_DORM_CHOICE3$^{\ref{fnw}}$
	Room-type not granted	$w$ * ERR_ROOM_PREF$^{\ref{fnw}}$
Underage	the dorm has age restrictions $^{\ref{fndini}}$ and the student's age is less than UNDER_THIS_AGE, or missing uses MIN_AGE_DEFAULT	# years under age * ERR_UNDERAGE
New Resident	the dorm has new restrictions $^{\ref{fndini}}$ and the student has been a resident NEW_RESIDENCY_SEMESTERS	(NEW_RESIDENCY_SEMESTERS - student$[ncs] + 1)$ * ERR_NEW_RESIDENT $^{\ref{fnncs}}$
Un-requested SLO	the dorm has special living options but the student did not request a slo $^{\ref{fndvns}}$, or dorm has special living options different than the student's requested slo $^{\ref{fndvns}}$	1 * ERR_UNREQUESTED_SLO
Better Bed	student is not in a better bed $^{\ref{fndini2}}$	student$[ncs]$ * ERR_BETTER_BED $^{\ref{fnncs}}$
Different Hall	student is not in the first hall, as initialized by ASSIGN.LST $^{\ref{fninitpl}}$	1 * ERR_DIFFERENT_HALL
Different Bed	student is in the same first hall, but a different bed, as initialized by ASSIGN.LST $^{\ref{fninitpl}}$	1 * ERR_DIFFERENT_BED
Worse Hall	student is not in the first hall or better hall according to their prefs, as initialized by ASSIGN.LST $^{\ref{fninitpl}}$	1 * ERR_WORSE_HALL

2. STUDENT-CONSENSUS CONSTRAINTS: For each room:
NAME	DESCRIPTION	SCORE
Gender $^{\ref{fneither}}$+	not completely one gender	# students * $\min[gender]$ * ERR_MIXED_SEX
Smoke $^{\ref{fneither}}$+	not completely smokers or non-smokers (smokers penalized);	# smokers * ERR_MIXED_SMOKE
	if any smoke objector is present	* SMOKE_OBJ_WEIGHT
Music	for each student's objection clashing with another student's preference (both penalized)	2 * # clashes * ERR_MIXED_MUSIC
Study Late	not completely late studiers, or not, lateness specifiers suffer	# late studiers * $\min[late yes/no]$ * ERR_MIXED_STUDY_LATE
Age Difference	for each student in the room with a dob, $\max[\Delta age]$ between everyone unacceptable	each student's $\max[\Delta age]$ $>$ ACCEPT_AGE_DIFF * ERR_AGE_DIFF
Group $^{\ref{fneither}}$+	for each student in the room without requested roommates$^{\ref{fnbf}}$	$w$ * # requested mates not present * ERR_GROUP_INCOMPLETE$^{\ref{fnw}}$
Suite	each adjoining room's Group, Gender, and Smoke constraints are re-evaluated upon a move for the intermediate global grade calculations
Partial Fill $^{\ref{fnpf}}$	room is partially filled or empty, not including blocks	$\min[emptybeds,filledbeds]$ * # students * ERR_PARTIAL_FILL
Triple Fill	double room is packed with three students	# students * ERR_TRIPLE_FILL
First Timer	room has first time residents and overriding renewals	# first-time students * (old$[ncs] -$firsts$[ncs]) *$ ERR_MIXED_FIRSTTIMER $^{\ref{fnncs}}$

NOTES:

1. Gender became a `hard constraint' in DAO version v0.93, guaranteeing the randomly-chosen bed will always be the appropriate gender, without requiring a large constraint value to ensure it.

2. Each student is allowed three hall choices, one special living option, one specific room request, and a room type.

3. Where $ncs$ is the number of consecutive semesters of dorm residency.

4. Where $w$ is the weight based on the seniority (the number of concurrent semesters residing in the dorms) times SENIORITY_WEIGHT, plus any lottery benefit, $l$.
   
   $$w = \mbox{(senior * {\small SENIORITY\_WEIGHT})} + l$$
   
   
   Lottery benefit is based on the LOTTERY_BENEFIT: The tenths of a semester's seniority weight the first lottery number is worth. The last lottery number is worth no extra priority. The Lottery number in the middle is worth half as much as the first, the rest are distributed evenly in between. Lottery numbers are tracked separately for new and returning students. To maintain distinct seniority levels, the LOTTERY_BENEFIT should be less than one full semester's weight (9 at most). The lower this benefit, the better the overall assignments will be since first-come order is just random noise to good matches.

5. The DORMS.INI configuration file designates the dorms with new resident and underage restrictions.

6. For non-smokers, the DVNS special living option is a big exception because it refers to the entire non-smoking building of DeVargas (version v1.00).

7. The DORMS.INI configuration file designates the dorms with better beds and the beds that are better.

8. The ASSIGN.LST input file contains students' current assignments in HMS.

9. Applies to rooms where the specific designation is either (not including virtuals). The + indicates the constraint applies across adjoining suites.

10. A bestfriend is the first roommate requested when a double room is also requested. A bestfriend must be present in the same room, an adjoining room is not sufficient.

11. Minimizes the number of partially filled rooms and reduces the consolidation process. This error compensates for the smaller music, age or other penalties, but if too large, can disregard hall choices.

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