I'm a lab practises tutor at the university, based on last year student comments, we wanted, my boss and I, to address them. My boss chose to go with writing a C script and I pick python (python-constraint) to try to resolve our problem.
Assign each student to 4 roles, in 4 practices in 4 different sessions.
Here is the template that I feel with students, where each team is composed of 4 students, positions [0, 1, 2 or 3] are roles assigned to them. Each available position is numbering from 1 to 128
[# Semester
[ # Session
[ # Practice/Team
1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[13, 14, 15, 16],
[17, 18, 19, 20],
[21, 22, 23, 24]],
[[25, 26, 27, 28],
[29, 30, 31, 32],
[33, 34, 35, 36],
[37, 38, 39, 40],
[41, 42, 43, 44],
[45, 46, 47, 48]],
[[49, 50, 51, 52],
[53, 54, 55, 56],
[57, 58, 59, 60],
[61, 62, 63, 64],
[65, 66, 67, 68],
[69, 70, 71, 72]],
[[73, 74, 75, 76],
[77, 78, 79, 80],
[81, 82, 83, 84],
[85, 86, 87, 88],
[89, 90, 91, 92],
[93, 94, 95, 96]],
[[97, 98, 99, 100],
[101, 102, 103, 104],
[105, 106, 107, 108],
[109, 110, 111, 112]],
[[113, 114, 115, 116],
[117, 118, 119, 120],
[121, 122, 123, 124],
[125, 126, 127, 128]]]
In other words :
This is a session :
[[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[13, 14, 15, 16],
[17, 18, 19, 20],
[21, 22, 23, 24]],
Those team do the same practice:
[
[1, 2, 3, 4],
[25, 26, 27, 28],
[49, 50, 51, 52],
[73, 74, 75, 76],
[97, 98, 99, 100],
[113, 114, 115, 116]
]
Those position do the same role :
[
1,
5,
9,
13,
17,
21,
25,
...
]
Using python-constraint I was able to validate the first three constraints :
Valid solution : False
- sessions : [True, True, True, True, True, True]
- practices : [True, True, True, True, True, True]
- roles : [True, True, True, True]
- teams : [False, False, True, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, False, False, False, False, False]
For each condition I use AllDifferentConstraint. For example, for one session I do:
problem.addConstraint(AllDifferentConstraint(), [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24])
I'm not able to find a way to constraint team, my last attempt on the entire semester was this :
def team_constraint(self, *semester):
students = defaultdict(list)
# get back each teams based on the format [# Semester [ #Session [# Practice/Team ...
teams = [list(semester[i:i+4]) for i in range(0, len(semester), 4)]
# Update Students dict with all mate they work with
for team in teams:
for student in team:
students[student] += [s for s in team if s != student]
# Compute for each student if they meet someone more than once
dupli = []
for student, mate in students.items():
dupli.append(len(mate) - len(set(mate)))
# Loosly constraint, if a student meet somone 0 or one time it's find
if max(dupli) >= 2:
print("Mate encounter more than one time", dupli, min(dupli) ,max(dupli))
return False
pprint(students)
return True
def person_works_with_different():
# over all the sessions, each person works with each other person no more than once.
# 'works with' means in 'same session team'
for p in all_people:
buddy_constraint = []
for s in all_sessions:
for g in all_teams:
p_list = [pv[k] for k in filter(lambda i: i[P] == p and i[S] == s and i[G] == g, pv)]
for o in all_people:
if o != p: # other is not person
o_list = [self.pv[k] for k in filter(lambda i: i[self.P] == o and i[self.S] == s and i[self.G] == g, self.pv)]
tmp = model.NewBoolVar('')
buddy_constraint.append(tmp)
model.Add(sum(o_list) == sum(p_list)).OnlyEnforceIf(tmp)
# tmp is set only if o and p are in the same session/team
# The number of times a student gets to take part is the number of roles.
# The size of the group controlled by the number of roles
model.Add(sum(buddy_constraint) = all_roles * (all_roles - 1))
Added Edit
I had another look at your problem yesterday - (admittedly not long, as I have a lot of work on at the moment), and...
First of all, I see that your 'team' entity, is pretty much what I called an 'action' entity, and in retrospect I think 'team' (or 'group') was a better word for it.
If you are still finding the constraints hard, I suggest you break them out, and work on them individually - particularly the team/person/session constraints, followed by the role/task constraints.
/Added Edit
team: a gathering of 4 persons during a session
person (32): a participant of a team
session (6): time: eg, 8am -10am
role (4): what responsibility a person has in an action
task (6): type of action
A person does:
0..1 action per session-group
1 role per action
1 task per action
0..1 of each task
1 of each role in an action
4 persons in an action
A person meets each other person 0..1 times
An action requires exactly 4 people
I had a similar problem recently, and in the end turned to OR-tools. https://developers.google.com/optimization/cp/cp_solver
Particularly, have a look at the nurse scheduling problem: https://developers.google.com/optimization/scheduling/employee_scheduling#nurse_scheduling
Anyhow, the problem is not too complex, so maybe using a solver would be overkill for you.
Likewise, for this sort of problem it may be better to use a tuple-keyed dict to hold your variables, rather than nested lists:
{ Team, Session, Person: BoolVar }
The main reason is that you can then apply constraints via filters, which is much easier than having to do nested list manipulations, for instance, to apply a constraint across persons/teams, you can do (where person is index 2 and team is index 0):
for p in all_persons:
for t in all_teams:
stuff = [b_vars[k] for k in filter(lambda i: i[2] == p and i[0] == t, b_vars)]
model.Add(sum(stuff) == 4) # persons per team == 4