Abstract. The construction of course timetables for academic institutions is a very difficult problem with a lot of constraints that have to be respected and a huge search space to be explored, even if the size of the problem input is not significantly large, due to the exponential number of the possible feasible timetables. On the other hand, the problem itself does not have a widely approved definition, since different variations of it are faced by different departments. However, there exists a set of entities and constraints among them which are common to every possible instantiation of the timetabling problem. In this paper, we present a model of this common core in terms of Ilog Solver, a constraint programming object-oriented C++ library, and we show the way this model may be extended to cover the needs of a specific academic unit.

Abstract-Constraint Programming constitutes a prominent paradigm for solving time-consuming Constraint Satisfaction Problems (CSPs). In this work, at first we model a generic course scheduling problem as a CSP, that complies with the International Timetabling Competition (ITC) standards. Constraint Programming allowed us to search for a solution via several state-of-the-art methodologies and compare them. For the stochastic search methods, we propose new hybrid semi-random heuristics. Second, we chose to maintain bounds consistency during search to prune 'no-good' branches of the search tree. We theoretically define new lightweight consistency types, namely k-bounds-consistency, in order to speed up the overall search procedure. Eventually, we process real world data and show the efficiency of our proposal: While plain backtracking produces poor results, constraint propagation dramatically boosts the solutions quality, and can be 'finetuned' in our adjustable schema to make it even faster.

The Airline Crew Assignment Problem (ACA) consists of assigning lines of work to a set of crew members such that a set of activities is partitioned and the costs for that assignment are minimized. Especially for European airline companies, complex constraints defining the feasibility of a line of work have to be respected. We developed two different algorithms to tackle the large scale optimization problem of Airline Crew Assignment. The first is an application of the Constraint Programming (CP) based Column Generation Framework. The second approach performs a CP based heuristic tree search. We present how both algorithms can be coupled to overcome their inherent weaknesses by integrating methods from Constraint Programming and Operations Research. Numerical results show the superiority of the hybrid algorithm in comparison to CP based tree search and column generation alone.

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