Timetabling in constraint logic programming

In this paper we describe the timetabling problem and its solvability in a Constraint Logic Programming Language. A solution to the problem has been developed and implemented in ECLiPSe, since it deals with finite domains, it has well-defined interfaces between basic building blocks and supports good debugging facilities. The implemented timetable was based on the existing, currently used, timetables at the School of Informatics at out university. It integrates constraints concerning room and period availability

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

Operational Research in Education

Operational Research (OR) techniques have been applied, from the early stages of the discipline, to a wide variety of issues in education. At the government level, these include questions of what resources should be allocated to education as a whole and how these should be divided amongst the individual sectors of education and the institutions within the sectors. Another pertinent issue concerns the efficient operation of institutions, how to measure it, and whether resource allocation can be used to incentivise efficiency savings. Local governments, as well as being concerned with issues of resource allocation, may also need to make decisions regarding, for example, the creation and location of new institutions or closure of existing ones, as well as the day-to-day logistics of getting pupils to schools. Issues of concern for managers within schools and colleges include allocating the budgets, scheduling lessons and the assignment of students to courses. This survey provides an overview of the diverse problems faced by government, managers and consumers of education, and the OR techniques which have typically been applied in an effort to improve operations and provide solutions

Cyclic transfers in school timetabling

In this paper we propose a neighbourhood structure based\ud on sequential/cyclic moves and a Cyclic Transfer algorithm for the high school timetabling problem. This method enables execution of complex moves for improving an existing solution, while dealing with the challenge of exploring the neighbourhood efficiently. An improvement graph is used in which certain negative cycles correspond to the neighbours; these cycles are explored using a recursive method. We address the problem of applying large neighbourhood structure methods on problems where the cost function is not exactly the sum of independent cost functions, as it is in the set partitioning problem. For computational experiments we use four real world datasets for high school timetabling in the Netherlands and England. We present results of the cyclic transfer algorithm with different settings on these datasets. The costs decrease by 8% to 28% if we use the cyclic transfers for local optimization compared to our initial solutions. The quality of the best initial solutions are comparable to the solutions found in practice by timetablers

Cyclic transfers in school timetabling

In this paper we propose a neighbourhood structure based on sequential/cyclic moves and a cyclic transfer algorithm for the high school timetabling problem. This method enables execution of complex moves for improving an existing solution, while dealing with the challenge of exploring the neighbourhood efficiently. An improvement graph is used in which certain negative cycles correspond to the neighbours; these cycles are explored using a recursive method. We address the problem of applying large neighbourhood structure methods on problems where the cost function is not exactly the sum of independent cost functions, as it is in the set partitioning problem. For computational experiments we use four real world data sets for high school timetabling in the Netherlands and England.We present results of the cyclic transfer algorithm with different settings on these data sets. The costs decrease by 8–28% if we use the cyclic transfers for local optimization compared to our initial solutions. The quality of the best initial solutions are comparable to the solutions found in practice by timetablers

An XML format for benchmarks in High School Timetabling

The High School Timetabling Problem is amongst the most widely used timetabling problems. This problem has varying structures in different high schools even within the same country or educational system. Due to lack of standard benchmarks and data formats this problem has been studied less than other timetabling problems in the literature. In this paper we describe the High School Timetabling Problem in several countries in order to find a common set of constraints and objectives. Our main goal is to provide exchangeable benchmarks for this problem. To achieve this we propose a standard data format suitable for different countries and educational systems, defined by an XML schema. The schema and datasets are available online

Railway timetabling from an operations research

In this paper we describe Operations Research (OR) models andtechniques that can be used for determining (cyclic) railwaytimetables. We discuss the two aspects of railway timetabling: ($i$)the determination of arrival and departure times of the trains atthe stations and other relevant locations such as junctions andbridges, and ($ii$) the assignment of each train to an appropriateplatform and corresponding inbound and outbound routes in everystation. Moreover, we discuss robustness aspects of bothsubproblems.

Design, Engineering, and Experimental Analysis of a Simulated Annealing Approach to the Post-Enrolment Course Timetabling Problem

The post-enrolment course timetabling (PE-CTT) is one of the most studied timetabling problems, for which many instances and results are available. In this work we design a metaheuristic approach based on Simulated Annealing to solve the PE-CTT. We consider all the different variants of the problem that have been proposed in the literature and we perform a comprehensive experimental analysis on all the public instances available. The outcome is that our solver, properly engineered and tuned, performs very well on all cases, providing the new best known results on many instances and state-of-the-art values for the others

An efficient memetic, permutation-based evolutionary algorithm for real-world train timetabling

Train timetabling is a difficult and very tightly constrained combinatorial problem that deals with the construction of train schedules. We focus on the particular problem of local reconstruction of the schedule following a small perturbation, seeking minimisation of the total accumulated delay by adapting times of departure and arrival for each train and allocation of resources (tracks, routing nodes, etc.). We describe a permutation-based evolutionary algorithm that relies on a semi-greedy heuristic to gradually reconstruct the schedule by inserting trains one after the other following the permutation. This algorithm can be hybridised with ILOG commercial MIP programming tool CPLEX in a coarse-grained manner: the evolutionary part is used to quickly obtain a good but suboptimal solution and this intermediate solution is refined using CPLEX. Experimental results are presented on a large real-world case involving more than one million variables and 2 million constraints. Results are surprisingly good as the evolutionary algorithm, alone or hybridised, produces excellent solutions much faster than CPLEX alone