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Timetabling can be considered to be a certain type of scheduling problem. In 1996, Wren described timetabling as the problem of placing certain resources, subject to constraints, into a limited number of time slots and places with the aim being to satisfy a set of stated objectives to the highest possible extent (Wren, 1996). This general represent...
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... Timetabling problems are eminently relevant in practice. Petrovic and Burke (2004) state that these problems can be found in various fields, including nurse rostering, timetabling of public transport systems, timetabling of sport events and educational timetabling. Schaerf (1999) subdivides educational timetabling into school timetabling, examination timetabling and course timetabling and generally defines the problem as scheduling lectures that involve teachers and students in a prefixed period of time, while taking different constraints into account. ...
In curriculum-based course timetabling, lectures have to be assigned to periods and rooms, while avoiding overlaps between courses of the same curriculum. Taking into account the inherent complexity of the problem, a metaheuristic solution approach is proposed, more precisely an adaptive large neighborhood search, which is based on repetitively destroying and subsequently repairing relatively large parts of the solution. Several problem-specific operators are introduced. The proposed algorithm proves to be very effective for the curriculum-based course timetabling problem. In particular, it outperforms the best algorithms of the international timetabling competition in 2007 and finds five new best known solutions for benchmark instances of the competition.
... En la literatura existen investigaciones similares, las cuales tratan de manera independiente, o la construcción de equipos [2,3,4] o la planificación docente [5,6,7]. Sin embargo, hasta donde se conoce, no existen investigaciones que se planteen resolver ambos problemas al mismo tiempo, como es el caso del presente trabajo. ...
In Cuba, university professors are often evaluated during the development of a class. Scheduling such evaluations along the academic semester is a common task of the head of the department, who must satisfy several criteria at the same time. Examples of these criteria are the presence of at least one tribunal member of the same academic unit, the presence of at least one tribunal member with equal docent category, availability and the utilization level of the tribunal members, among others. However, scheduling professor evaluations can become a complex task if several professors and evaluations are considered. Aiming at solving this problem, in the present work we propose a computational approach based on 1) modelling this task as a multi-objective optimization problem and 2) solving this problem by adapting a variant of a very well-known evolutionary algorithm, NSGA-II. The results of the performed computational experiments show that our proposal contributes to obtaining useful quality solutions.
... By gathering information from a document in the system, the quality of each of the relevant procedures, the data collected will be used to display information in tables, graphs and flow charts to show in each step to make more understand (Schaef, 1999) (Burke, 2002). b) Select a sample in a study using the method of group selection (Cluster Sampling) those were divided into 3 groups of 12 systems based on the relationship of each group and selected the 3 systems to study (Wang, 2006) (Petrovic, 2004 (Ming-Hsien, 2008). The data collected has made the process of successful end of each process, and then have collected the fault information from all qualifying issues that were significant. ...
This study aim to resolve the software testing processes by create reliance of a system. With traditional testing processes, there are many issues of unacceptable defects found after the end of testing processes. To solve this problem, we applied quality management according to Six Sigmas quality improvements. From the principles of DMAIC, they found the most of mistakes came from runtime error, logical error and syntax error at 3.83%, 2.83% and 5.50%, respectively. This research consists of five stages of problem identification, the root cause analysis to find out the problems, drawn tree and fishbone diagrams help to analyze and solve problems. The quality improvement concepts were implement by using experiment designed techniques which controlled by standard software testing in the final step to ensure that the problems will not occur again. The results show that using quality management with the principles of DMAIC integration can reduce defects referring to Run Time error from 3.83%, 2.83%, 5.50% to 2.67%, 1.33%, 3.83%. This benefit will improve the confidence level, and raise the good image of the company.
... Some of the most important methods used are sequential methods, cluster methods, constraint-based methods and generalized search methods. The hybrid evolutionary algorithms, metaheuristics, multi-criteria approaches, case based reasoning techniques, hyper-heuristics and adaptive approaches to solve them are described in (Petrovic & Burke, 2004). One approach (Abdullah & Turabieh, 2008; Wijaya & Manurung, 2009) converted it to a graph in which the nodes correspond to lectures and the edges between the nodes correspond to the constraints and used graph coloring algorithms. ...
... In which, from this study point of view, if the course-room assignments were also considered in the dissimilarity measurements, it might be very restrictive and hence, a few number of diverse solutions will have the possibility to update the Ref- Set. The reason behind the selection of the course-timeslot pair regardless the room, was due to the timeslot permutations which had a larger impact on the quality of the timetable significantly more than the room (Petrovic and Burke 2004) (actually, in these datasets, no soft constraint was associated with room assignment, i.e. it did not affect the quality of solution but the course must be assigned to a room). By contrast, SSV2 had failed to produce a good quality results (for the comp22, inTable 6) compared to others. ...
This study presents an investigation of enhancing the capability of the Scatter Search (SS) metaheuristic in guiding the search effectively toward elite solutions. Generally, SS generates a population of random initial solutions and systematically selects a set of diverse and elite solutions as a reference set for guiding the search. The work focuses on three strategies that may have an impact on the performance of SS. These are: explicit solutions combination, dynamic memory update, and systematic search re-initialization. First, the original SS is applied. Second, we propose two versions of the SS (V1 and V2) with different strategies. In contrast to the original SS, SSV1 and SSV2 use the quality and diversity of solutions to create and update the memory, to perform solutions combinations, and to update the search. The differences between SSV1 and SSV2 is that SSV1 employs the hill climbing routine twice whilst SSV2 employs hill climbing and iterated local search method. In addition, SSV1 combines all pairs (of quality and diverse solutions) from the RefSet whilst SSV2 combines only one pair. Both SSV1 and SSV2 update the RefSet dynamically rather than static (as in the original SS), where, whenever a better quality or more diverse solution is found, the worst solution in RefSet is replaced by the new solution. SSV1 and SSV2 employ diversification generation method twice to re-initialize the search. The performance of the SS is tested on three benchmark post-enrolment course timetabling problems. The results had shown that SSV2 performs better than the original SS and SSV1 (in terms of solution’s quality and computational time). It clearly demonstrates the effectiveness of using dynamic memory update, systematic search re-initialization, and combining only one pair of elite solutions. Apart from that, SSV1 and SSV2 can produce good quality solutions (comparable with other approaches), and outperforms some approaches reported in the literature (on some instances with regards to the tested datasets). Moreover, the study shows that by combining (simple crossover) only one pair of elite solutions in each RefSet update, and updating the memory dynamically, the computational time is reduced.
... In its survey, Carter (Carter, 1986) classified these approaches into four types: sequential methods, cluster methods, constraint-based methods and generalised search. Petrovic and Burke (Petrovic and Burke, 2004) later added more six categories: hybrid evolutionary algorithms, metaheuristics, multi-criteria approaches, case based reasoning techniques, hyperheuristics and adaptive approaches. A recent and detailed overview of the proposed methods to solve the ETTP can be found in (Qu et al., 2009). ...
Shuffled Frog-Leaping Algorithm (SFLA) is a recently proposed memetic metaheuristic algorithm for solving combinatorial optimisation problems. SFLA has both global and local search capabilities, and great convergence speed towards the global optimum. Compared to a genetic algorithm, the experimental results show an effective reduction of the number of evaluations required to find the global optimal solution. The Examination Timetabling Problem (ETTP) is a complex combinatorial optimisation problem faced by schools and universities every epoch. In this work, we apply the Shuffled Frog-Leaping Algorithm to solve the ETTP. The evolution step of the algorithm, specifically the local exploration in the submemeplex is adapted based on the standard SFLA. The algorithm was evaluated on the Toronto benchmark instances, and the preliminary experimental results obtained are comparable to those produced by state of art algorithms while requiring much less time.
This paper presents a new methodology for university exam timetabling problems, which draws upon earlier work on the Great Deluge metaheuristic. The new method introduces a "flexible" acceptance condition. Even a simple variant of this technique (with fixed flexibility) outperforms the original Great Deluge algorithm. Moreover, it enables a run-time adaptation of an acceptance condition for each particular move. We investigate the adaptive mechanism where the algorithm accepts the movement of exams in a way that is dependent upon the difficulty of assigning that exam. The overall motivation is to encourage the exploration of a wider region of the search space. We present an analysis of the results of our tests of this technique on two international collections of benchmark exam timetabling problems. We show that 9 of 16 solutions in the first collection and 11 of 12 solutions in the second collection produced by our technique have a higher level of quality than previously published methodologies.
The Teacher Assignment Problem is part of the University Timetabling Problem and involves assigning teachers to courses, taking their preferences into consideration. This is a complex problem, usually solved by means of heuristic algorithms. In this paper a Mixed Integer Linear Programing model is developed to balance teachers' teaching load (first optimization criterion), while maximizing teachers' preferences for courses according to their category (second optimization criterion). The model is used to solve the teachers-courses assignment in the Department of Management at the School of Industrial Engineering of Barcelona, in the Universitat Politècnica de Catalunya. Results are discussed regarding the importance given to the optimization criteria. Moreover, to test the model's performance a computational experiment is carried out using randomly generated instances based on real patterns. Results show that the model is proven to be suitable for many situations (number of teachers-courses and weight of the criteria), being useful for departments with similar requests. © 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS).
In 2007, the Second International Timetabling Competition (ITC-2007) has been organized and a formal definition of the Curriculum-Based Course Timetabling (CB-CTT) problem has been given, by taking into account several real-world constraints and objectives while keeping the problem general. CB-CTT consists of finding the best weekly assignment of university course lectures to rooms and time periods. A feasible schedule must satisfy a set of hard constraints and must also take into account a set of soft constraints, whose violation produces penalty terms to be minimized in the objective function. From ITC-2007, many researchers have developed advanced models and methods to solve CB-CTT. This survey is devoted to review the main works on the topic, with focus on mathematical models, lower bounds, and exact and heuristic algorithms. Besides giving an overview of these approaches, we highlight interesting extensions that could make the study of CB-CTT even more challenging and closer to reality.
The examination timetabling problem involves assigning exams to a specific or limited number of timeslots and rooms with the aim of satisfying all hard constraints (without compromise) and satisfying the soft constraints as far as possible. Most of the techniques reported in the literature have been applied to simplified examination benchmark data sets. In this paper, we bridge the gap between research and practice by investigating a problem taken from the real world. This paper introduces a modified and extended great deluge algorithm (GDA) for the examination timetabling problem that uses a single, easy to understand parameter. We investigate different initial solutions, which are used as a starting point for the GDA, as well as altering the number of iterations. In addition, we carry out statistical analyses to compare the results when using these different parameters. The proposed methodology is able to produce good quality solutions when compared with the solution currently produced by the host organisation, generated in our previous work and from the original GDA.
