Decomposition, Reformulation, and Diving in University Course Timetabling

In many real-life optimisation problems, there are multiple interacting components in a solution. For example, different components might specify assignments to different kinds of resource. Often, each component is associated with different sets of soft constraints, and so with different measures of soft constraint violation. The goal is then to minimise a linear combination of such measures. This paper studies an approach to such problems, which can be thought of as multiphase exploitation of multiple objective-/value-restricted submodels. In this approach, only one computationally difficult component of a problem and the associated subset of objectives is considered at first. This produces partial solutions, which define interesting neighbourhoods in the search space of the complete problem. Often, it is possible to pick the initial component so that variable aggregation can be performed at the first stage, and the neighbourhoods to be explored next are guaranteed to contain feasible solutions. Using integer programming, it is then easy to implement heuristics producing solutions with bounds on their quality. Our study is performed on a university course timetabling problem used in the 2007 International Timetabling Competition, also known as the Udine Course Timetabling Problem. In the proposed heuristic, an objective-restricted neighbourhood generator produces assignments of periods to events, with decreasing numbers of violations of two period-related soft constraints. Those are relaxed into assignments of events to days, which define neighbourhoods that are easier to search with respect to all four soft constraints. Integer programming formulations for all subproblems are given and evaluated using ILOG CPLEX 11. The wider applicability of this approach is analysed and discussed.Comment: 45 pages, 7 figures. Improved typesetting of figures and table

A stochastic local search algorithm with adaptive acceptance for high-school timetabling

Automating high school timetabling is a challenging task. This problem is a well known hard computational problem which has been of interest to practitioners as well as researchers. High schools need to timetable their regular activities once per year, or even more frequently. The exact solvers might fail to find a solution for a given instance of the problem. A selection hyper-heuristic can be defined as an easy-to-implement, easy-to-maintain and effective 'heuristic to choose heuristics' to solve such computationally hard problems. This paper describes the approach of the team hyper-heuristic search strategies and timetabling (HySST) to high school timetabling which competed in all three rounds of the third international timetabling competition. HySST generated the best new solutions for three given instances in Round 1 and gained the second place in Rounds 2 and 3. It achieved this by using a fairly standard stochastic search method but significantly enhanced by a selection hyper-heuristic with an adaptive acceptance mechanism. © 2014 Springer Science+Business Media New York

Solving Challenging Real-World Scheduling Problems

This work contains a series of studies on the optimization of three real-world scheduling problems, school timetabling, sports scheduling and staff scheduling. These challenging problems are solved to customer satisfaction using the proposed PEAST algorithm. The customer satisfaction refers to the fact that implementations of the algorithm are in industry use. The PEAST algorithm is a product of long-term research and development. The first version of it was introduced in 1998. This thesis is a result of a five-year development of the algorithm. One of the most valuable characteristics of the algorithm has proven to be the ability to solve a wide range of scheduling problems. It is likely that it can be tuned to tackle also a range of other combinatorial problems. The algorithm uses features from numerous different metaheuristics which is the main reason for its success. In addition, the implementation of the algorithm is fast enough for real-world use.Siirretty Doriast

High quality timetables for Italian schools

This work introduces a complex variant of the timetabling problem, which is motivated by the case of Italian schools. The new requirements enforce to (i) provide teachers with the same idle times, (ii) avoid consecutive days with heavy workload, (iii) limit multiple daily lessons for each class, (iv) introduce shorter time units to differentiate entry and exit times. We present an integer programming model for this problem, which is denoted by Italian High School Timetabling Problem (IHSTP). However, requirements (i), (ii), (iii) and (iv) cannot be expressed according to the current XHSTT standard. Since the IHSTP model is very hard to solve by an off-the-shelf solver, we present a two-step optimization method: the first step optimally assigns teachers to lesson times and the second step assigns classes to teachers. An extensive experimentation is performed on the model by realistic and real instances from Italian schools, as well as benchmark instances from the literature. Finally, the experiments show that the method is effective in solving both this new problem and the simplified problem without the new requirements

Solving an application of university course timetabling problem by using genetic algorithm

Generating timetables for academic institutions is a complex problem. This is due to many constraints involved whether they are vital or desirable, which are known as hard and soft constraints. The problem becomes more complicated and difficult to solve as the number of courses increase. Moreover, generating manual timetables is challenging and time-consuming, particularly to meet lecturers’ preferences. Thus, it is crucial to establish an automated course timetable system. Many efforts have been made using various computational heuristic methods to acquire the best solutions. Among the approaches, genetic algorithm (GA), constructed based on Darwin's theory of evolution, becomes the renowned approach to solve various types of timetabling problems. Therefore, this study produces the best timetable using GA to solve clashed courses, optimize room utilization and maximize lecturers’ preferences. Data of 41 course sections from 17 courses offered in semester A172 were taken from Decision Science Department, School of Quantitative Sciences (SQS). The phases in GA involves a number of main operators which are population initialization, crossover and mutation. The best parameter setting for GA was determined through combination of different mutation rate, population and iteration. The simulation results of GA show that this method is able to produce the best fitness value that satisfied all hard and soft constraints. There are no clashes either between lecturers or lecture rooms, and lecturers’ preferences were satisfied. The system can help SQS or any other academic schools or institutions to easily develop course timetabling in the coming semesters