In constraint programming, combinatorial problems are specified
declaratively in terms of constraints. Constraints are relations over
problem variables that define the space of solutions by specifying
restrictions on the values that variables may take simultaneously. To
solve problems stated in terms of constraints, the constraint
programmer typically combines chronological backtracking with
constraint propagation that identifies infeasible value combinations
and prunes the search space.
In recent years, constraint programming has emerged as a key
technology for combinatorial optimization in industrial
applications. In this success, global constraints have been playing a
vital role. Global constraints are carefully designed abstractions
that, in a concise and natural way, allow to model problems that arise
in different fields of application. For example, the alldiff
constraint allows to state that variables must take pairwise distinct
values; it has numerous applications in timetabling and scheduling.
In school timetabling, we are required to schedule a given set of
meetings between students and teachers s.t. the resulting timetables
are feasible and acceptable to all people involved. Since schools
differ in their educational policies, the school-timetabling problem
occurs in several variations. Nevertheless, a set of entities and
constraints among them exist that are common to these variations. This
common core still gives rise to NP-complete combinatorial problems.
In the first place, this thesis proposes to model the common core of
school-timetabling problems by means of global constraints. The
presentation continues with a series of operational enhancements to
the resulting problem solver which are grounded on the "track
parallelization problem" (TPP). A TPP is specified by a set of task
sets which are called "tracks". The problem of solving a TPP
consists in scheduling the tasks s.t. the tracks are processed in
parallel. We show how to infer TPPs in school timetabling and we
investigate two ways of TPP propagation: On the one hand, we utilize
TPPs to down-size our models. On the other hand, we propagate TPPs to
prune the search space. To this end, we introduce the TPP
constraint along with a suitable constraint solver for modeling and
solving TPPs in a finite-domain constraint programming framework.
To investigate our problem solvers' behavior, we performed a
large-scale empirical study. When designing the experiment, the top
priority was to obtain results that are both reliable from a
statistical point of view and practically relevant. To this end, the
sample sizes have been chosen accordingly - for each school, our
problem set contains 1000 problems - and the problems have been
generated from detailed models of ten representative schools. Our
timetabling engine essentially embeds network-flow techniques and
value sweep pruning into chronological backtracking.