Structure based partial solution search for the examination timetabling problem.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.The aim of this work is to present a new approach, namely, Structure Based Partial Solution Search (SBPSS) to solve the Examination Timetabling Problem. The success of the Developmental Approach in this problem domain suggested that the strategy of searching the spaces of partial timetables whilst constructing them is promising and worth pursuing. This work adopts a similar strategy. Multiple timetables are incrementally constructed at the same time. The quality of the partial timetables is improved upon by searching their partial solution spaces at every iteration during construction. Another key finding from the literature survey revealed that although timetables may exhibit the same behaviour in terms of their objective values, their structures or exam schedules may be different. The challenge with this finding is to decide on which regions to pursue because some regions may not be worth investigating due to the difficulty in searching them. These problematic areas may have solutions that are not amenable to change which makes it difficult to improve them. Another reason is that the neighbourhoods of solutions in these areas may be less connected than others which may restrict the ability of the search to move to a better solution in that neighbourhood. By moving to these problematic areas of the search space the search may stagnate and waste expensive computational resources. One way to overcome this challenge is to use both structure and behaviour in the search and not only behaviour alone to guide the search. A search that is guided by structure is able to find new regions by considering the structural components of the candidate solutions which indicate which part of the search space the same candidates occupy. Another benefit to making use of a structure-based search is that it has no objective value bias because it is not guided by only the objective value. This statement is consistent with the literature survey where it is suggested that in order to achieve good performance the search should not be guided by only the objective value. The proposed method has been tested on three popular benchmark sets for examination timetabling, namely, the Carter benchmark set; the benchmark set from the International Timetabling competition in 2007 and the Yeditepe benchmark set. The SBPSS found the best solutions for two of the Carter problem instances. The SBPSS found the best solutions for four of the competition problem instances. Lastly, the SBPSS improved on the best results for all the Yeditepe problem instances

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

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

Genetic algorithms with guided and local search strategies for university course timetabling

This article is posted here with permission from the IEEE - Copyright @ 2011 IEEEThe university course timetabling problem (UCTP) is a combinatorial optimization problem, in which a set of events has to be scheduled into time slots and located into suitable rooms. The design of course timetables for academic institutions is a very difficult task because it is an NP-hard problem. This paper investigates genetic algorithms (GAs) with a guided search strategy and local search (LS) techniques for the UCTP. The guided search strategy is used to create offspring into the population based on a data structure that stores information extracted from good individuals of previous generations. The LS techniques use their exploitive search ability to improve the search efficiency of the proposed GAs and the quality of individuals. The proposed GAs are tested on two sets of benchmark problems in comparison with a set of state-of-the-art methods from the literature. The experimental results show that the proposed GAs are able to produce promising results for the UCTP.This work was supported by the Engineering and Physical Sciences Research Council of U.K. under Grant EP/E060722/1

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

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

Solving Examination Timetabling Problem using Partial Exam Assignment with Great Deluge Algorithm

Constructing a quality solution for the examination timetable problem is a difficult task. This paper presents a partial exam assignment approach with great deluge algorithm as the improvement mechanism in order to generate good quality timetable. In this approach, exams are ordered based on graph heuristics and only selected exams (partial exams) are scheduled first and then improved using great deluge algorithm. The entire process continues until all of the exams have been scheduled. We implement the proposed technique on the Toronto benchmark datasets. Experimental results indicate that in all problem instances, this proposed method outperforms traditional great deluge algorithm and when comparing with the state-of-the-art approaches, our approach produces competitive solution for all instances, with some cases outperform other reported result