Let's take a real-life problem to get started. You're organising a
an international Python Programming event, and you have to schedule
conferences. There are 10 different conferences, you have 3 conference
rooms available during 2 days. Each conference is 4 hours long, so you
can organize at most 2 conferences per day in a given room.
Conferences 3, 4, 5 and 6 have to take place in room C, because
it's the only one with Internet access.
Some of the speakers are not available on both days, so
conferences 1, 5 and 10 have to take place on day 1, and conferences 2,
3 4 and 9 on day 2.
You have made a quick poll over the python mailing list, and it
turns out that people attending some of the conferences are likely to be
attending some other conferences too, so you want to make sure that such
conferences are not scheduled at the same time. A careful statistical
study has found 4 groups of potential attendees. The first group want to
attend conferences 1, 2, 3 and 10, the second conferences 2, 6, 8 and 9
the third group conferences 3, 5, 6 and 7, and the last group
conferences 1, 3, 7 and 8.
You've tried to put this on a whiteboard, but this quickly proved
to be tedious, so you thought about using the constraint solving
package.
1.2. Variables, Domains and Constraints
The first thing to find out in order to use the constraint package
is what the variables are, what their domains are and what the
constraints between variables are.
If we look at our problem, the variables are the conferences' room
and time slot, and for each conference, the domain is the cross product
of the set of available rooms with the set of available time slots. We
could say that the conferences which require Internet access have a
different domain, because they need to be in room C. This is perfectly
valid. However, we will model this as a constraint.
Variables are manipulated as names, stored in character
strings. Domains are instances of the fd.FiniteDomain class, which is
instantiated with a list of values. Domains are manipulated through a
dictionnary mapping a variable to its domain. Do not use the same domain
instance for several variables, because in the current implementation,
this is guaranteed to break. The code looks like this:
# import Repository class and fd module,
from logilab.constraint import *
variables = ('c01','c02','c03','c04','c05','c06','c07','c08','c09','c10')
values = [(room,slot)
for room in ('room A','room B','room C')
for slot in ('day 1 AM','day 1 PM','day 2 AM','day 2 PM')]
domains = {}
for v in variables:
domains[v]=fd.FiniteDomain(values)
Constraints, like domains are objects. So far the only class that
can be used is fd.Expression and fd.BinaryExpression. We use the
fd.make_expression factory function to build an instance of the right
class, depending on the number of variables that is passed. This
function takes a list of affected variables and a python expression that
evaluates to true if the constraint is satisfied.
We have several constraints on our variables. First some
conferences need to take place in room C:
constraints = []
for conf in ('c03','c04','c05','c06'):
constraints.append(fd.make_expression((conf,),
"%s[0] == 'room C'"%conf))
Availability of the speakers impose some more constraints:
for conf in ('c01','c05','c10'):
constraints.append(fd.make_expression((conf,),
"%s[1].startswith('day 1')"%conf))
for conf in ('c02','c03','c04','c09'):
constraints.append(fd.make_expression((conf,),
"%s[1].startswith('day 2')"%conf))
Then we want to say that some of the conferences should not be
scheduled at the same time:
groups = (('c01','c02','c03','c10'),
('c02','c06','c08','c09'),
('c03','c05','c06','c07'),
('c01','c03','c07','c08'))
for g in groups:
for conf1 in g:
for conf2 in g:
if conf2 > conf1:
constraints.append(fd.make_expression((conf1,conf2),
'%s[1] != %s[1]'%\
(conf1,conf2)))
Finally, no two conferences can be scheduled in the same room at
the same time:
for conf1 in variables:
for conf2 in variables:
if conf2 > conf1:
constraints.append(fd.make_expression((conf1,conf2),
'%s != %s'%(conf1,conf2)))
The code is available in the file conferences.py in the examples
directory of the distribution. It finds 64 possible schedules in a
couple of seconds on my machine.
