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Summary University timetabling problems can be classifi ed into two main categories: course and examination timetabling. We discuss the problem statements and constraints for each of them and provide an overview of some recent research advances that have been made by the authors and members of their research team. We particularly concentrate upon:...
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... example, the nodes of level 1, 2, and 3 store elements a 11 , a 21 a 22 a 12 a 31 a 32 a 33 a 23 a 13 of the adjacency matrix, respectively. For example, the 3-course problem given in Figure 3, which requires 6 permutations of courses to be stored will lead to the decision tree presented in Figure 4. ... ...
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Citations
... The timetabling problem, which is a type of scheduling problem, is assigning a specified number of events, such as courses, exams, and meetings, to a limited number of periods in a way to satisfy constraints [2]. In educational institutions, frequently encountered timetabling problems occur with the scheduling of courses and exams [3], [4]. Systemic imperatives, preferences of educational institutions, students, instructors, and limited resources such as classrooms, equipment, and instructors add to the challenges of the educational timetabling problem. ...
In this study, faculty-level university course timetabling problem with double major and minor program constraints where classrooms are shared with several faculties is taken into account. This is the first study considering all these constraints together. A goal programming model is proposed to solve the considered problem. Since it is not possible to find a feasible solution for large-size problems with the proposed model in a time limit, a simulated annealing algorithm is developed. The performance of the proposed solution methods is tested by using randomly generated test problems. In addition, a case study is performed at the engineering faculty of a private university. Computational results show the success of the proposed simulated annealing algorithm to solve large-sized problems. An 83% improvement was achieved with the proposed algorithm for the real-life problem.
... We can find in the literature a great number of excellent contributions to examination scheduling problems (de Werra 1985;Carter 1986;Burke et al. 1997;Schaerf 1999;Petrovic and Burke 2004). More recently, a very interesting technical report was published, giving a general overview on recent approaches to this problem . ...
... More recently, a very interesting technical report was published, giving a general overview on recent approaches to this problem . To present the state of the art of some of the most successful contributions in the literature, we adopted a classification of the methods proposed by and later completed by Petrovic and Burke (2004). ...
In this paper, we present an application of Tabu Search (TS) to the examination timetabling problem. One of the drawbacks
of this meta-heuristic is related to the need of tuning some parameter (like tabu tenure) whose value affects the performance
of the algorithm. The importance of developing an automatic procedure is clear considering that most of the users of timetabling
software, like academic staff, do not have the expertise to conduct such tuning. The goal of this paper is to present a method
to automatically manage the memory in the TS using a Decision Expert System. More precisely a Fuzzy Inference Rule Based System
(FIRBS) is implemented to handle the tabu tenure based on two concepts, “Frequency” and “Inactivity”. These concepts are related
respectively with the number of times a move is introduced in the tabu list and the last time (in number of iterations) the
move was attempted and prevented by the tabu status. Computational results show that the implemented FIRBS handles well the
tuning of the tabu status duration improving, as well, the performance of Tabu Search.
... Timetabling has attracted a significant level of research interest since the 1960's. The general timetabling problem comes in many different guises such as sports timetabling [14], transportation timetabling [23] and educational timetabling [4,27,[30][31][32]34]. Educational timetabling problems are probably the most widely studied. ...
Numerous papers based on various search methods across a wide variety of applications have appeared in the literature over
recent years. Most of these methods apply the following same approach to address the problems at hand: at each iteration of
the search, they first apply their search methods to generate new solutions, then they calculate the objective values (or
costs) by taking some constraints into account, and finally they use some strategies to determine the acceptance or rejection
of these solutions based upon the calculated objective values. However, the premise of this paper is that calculating the
exact objective value of every resulting solution is not a must, particularly for highly constrained problems where such a
calculation is costly and the feasible regions are small and disconnected. Furthermore, we believe that for newly-generated
solutions, evaluating the quality purely by their objective values is sometimes not the most efficient approach. In many combinatorial
problems, there are poor-cost solutions where possibly just one component is misplaced and all others work well. Although
these poor-cost solutions can be the intermediate states towards the search of a high quality solution, any cost-oriented
criteria for solution acceptance would deem them as inferior and consequently probably suggest a rejection. To address the
above issues, we propose a pattern recognition-based framework with the target of designing more intelligent and more flexible
search systems. The role of pattern recognition is to classify the quality of resulting solutions, based on the solution structure
rather than the solution cost. Hence, the general contributions of this work are in the line of “insights” and recommendations.
Two real-world cases of the assignment problem, i.e. the hospital personnel scheduling and educational timetabling, are used
as the case studies. For each case, we apply neural networks as the tool for pattern recognition. In addition, we present
our theoretical and experimental results in terms of runtime speedup.
KeywordsNeural networks–Assignment problem–Personnel scheduling–Exam timetabling–Search method
... Carter (1986) categorized these approaches into four types: sequential methods, cluster methods, constraint-based methods and generalized search. Petrovic and Burke (2004) added the following categories: hybrid evolutionary algorithms, meta-heuristics, multi-criteria approaches, case based reasoning techniques, hyper-heuristics and adaptive approaches. ...
... The following papers represent a comprehensive list of surveys and overviews on educational timetabling (which include issues related to university course timetabling) i.e. Bardadym (1996), Burke and Petrovic (2002), Burke et al. (1996), Carter (1986, Petrovic and Burke (2004), Schaerf (1999), de Werra (1985 and McCollum (2007) that discussed issues of bridging the gap between theory and practice in university timetabling. ...
This paper describes the development of a novel metaheuristic that combines an electromagnetic-like mechanism (EM) and the
great deluge algorithm (GD) for the University course timetabling problem. This well-known timetabling problem assigns lectures
to specific numbers of timeslots and rooms maximizing the overall quality of the timetable while taking various constraints
into account. EM is a population-based stochastic global optimization algorithm that is based on the theory of physics, simulating
attraction and repulsion of sample points in moving toward optimality. GD is a local search procedure that allows worse solutions
to be accepted based on some given upper boundary or ‘level’. In this paper, the dynamic force calculated from the attraction-repulsion
mechanism is used as a decreasing rate to update the ‘level’ within the search process. The proposed method has been applied
to a range of benchmark university course timetabling test problems from the literature. Moreover, the viability of the method
has been tested by comparing its results with other reported results from the literature, demonstrating that the method is
able to produce improved solutions to those currently published. We believe this is due to the combination of both approaches
and the ability of the resultant algorithm to converge all solutions at every search process.
... The course timetabling problems mainly comprise of assigning a set of courses, students and lecturers to a specific and fixed number of timeslots and rooms in a week, while satisfying some constraints[18]. In this paper, we tested our approach on benchmark post-enrolment course timetabling instances introduced by Socha[19]considering only student assignments. ...
... Where the matching between two solutions in a population of timetables is concerned only with counting the number of courses that occupies the same resources (timeslots) in both solutions. The reason behind the selection of the course-timeslot pair regardless the room, is due to that the timeslot permutations are affecting the quality of the timetable significantly more than the room do[18]. The results obtained by our SS algorithm indicting a good performance of the SS behaviour over Socha's instances. ...
Scatter Search (SS) is an evolutionary population-based metaheuristic that has been successfully applied to hard combinatorial optimization problems. In contrast to the genetic algorithm, it reduces the population of solutions size into a promising set of solutions in terms of quality and diversity to maintain a balance between diversification and intensification of the search. Also it avoids using random sampling mechanisms such as crossover and mutation in generating new solutions. Instead, it performs a crossover in the form of structured solution combinations based on two good quality and diverse solutions. In this study, we propose a SS approach for solving the course timetabling problem. The approach focuses on two main methods employed within it; the reference set update and solution combination methods. Both methods provide a deterministic search process by maintaining diversity of the population. This is achieved by manipulating a dynamic population size and performing a probabilistic selection procedure in order to generate a promising reference set (elite solutions). It is also interesting to incorporate an Iterated Local Search routine into the SS method to increase the exploitation of generated good quality solutions effectively to escape from local optima and to decrease the computational time. Experimental results showed that our SS approach produces good quality solutions, and outperforms some results reported in the literature (regarding Socha's instances) including population-based algorithms.
... We have organized references in five major areas: machine learning and knowledge discovery (Table 6 .1); traditional combinatorial optimization (Table 6.2); planning, scheduling, and timetabling ( Data mining and Image analysis [37, 67, 68, 77, 211] knowledge discovery Fuzzy clustering [70] Feature selection [243, 286] Pattern recognition [94] Machine learning Decision trees [144] Inductive learning [69] Neural networks [64, 65, 103, 110, 159, 168, 195, 262] Binary and set problems Binary quadratic programming [173] Knapsack problem [87, 88, 105, 107, 222] Low autocorrelation sequences [91] MAX-SAT [18, 223] Set covering [125] Graph-based problems Crossdock optimization [2, 154] Graph coloring [38] Graph matching [12] Hamiltonian cycle [32] Maximum cut [270] Quadratic assignment [72, 255] Routing problems [19, 20, 56, 57, 74] [80, 145–147] [218, 259, 263] Spanning tree [79, 231] Steiner tree [131] TSP [21, 161, 163, 196, 271] Constrained optimization Golomb ruler [46, 48] Social golfer [47] Maximum density still life [89, 90] [49]) Manufacturing Assembly line [226, 257, 265] Flexible manufacturing [5, 31, 187, 258] Lot sizing [16] Multi-tool milling [13] Supply chain network [280] Planning Temporal planning [235] Scheduling Flowshop scheduling [82, 84, 152, 158, 160, 184, 209, 240, 241] Job-shop [27, 96–98, 224, 267, 268, 278] Parallel machine scheduling [184, 277] Project scheduling [29] Single machine scheduling [166, 184] Timetabling Driver scheduling [153] Examination timetabling [216] Rostering [3, 22, 206] Sport league [236] Train timetabling [239] University course [151, 215, 233] Phylogeny Phylogenetic inference [43, 93, 275] Consensus tree [217] Microarrays Biclustering [208] Feature selection [55, 284, 285] Gene ordering [169, 183] Sequence analysis Shortest common supersequence [42, 92] DNA sequencing [71] Protein science Sequence assignment [269] Structure comparison [140] Structure prediction [14, 40, 203, 234, 281] Systems biology Gene regulatory networks [200, 250] Cell models [232] Biomedicine Drug therapy design [194, 264] Electronics Analog circuit design [58, 170] Circuit partitioning [34] Electromagnetism [23, 104, 210] Filter design [254] VLSI design [7, 171, 256] Engineering Chemical kinetics [136, 137] Crystallography [212] Drive design [24, 25] Power systems [26] Structural optimization [129] System modeling [1, 260] Computer Science Code optimization [207] Information forensics [242] Information theory [41] Software engineering [6] Telecommunications Antenna design114115116117 Mobile networks [128, 225] P2P networks [174, 191, 192] Wavelength assignment [78] Wireless networks [113, 118, 130, 138] (Table 6.5). As mentioned before, we have tried to be illustrative rather than exhaustive , pointing out some selected references from these well-known application areas. ...
Memetic algorithms are optimization techniques based on the synergistic combination of ideas taken from different algorithmic
solvers, such as population-based search (as in evolutionary techniques) and local search (as in gradient-ascent techniques).
After providing some historical notes on the origins of memetic algorithms, this work shows the general structure of these
techniques, including some guidelines for their design. Some advanced topics such as multiobjective optimization, self-adaptation,
and hybridization with complete techniques (e.g., branch-and-bound) are subsequently addressed. This chapter finishes with
an overview of the numerous applications of these techniques and a sketch of the current development trends in this area.
... Timetabling has attracted a significant level of research interest since the 1960's. The general timetabling problem comes in many different guises such as nurse rostering [16,6], sports timetabling [20], transportation timetabling [25] and educational timetabling [13,14,37,29,32]. Educational timetabling problems are probably the most widely studied. ...
A hyper-heuristic often represents a heuristic search method that operates over a space of heuristic rules. It can be thought of as a high level search methodology to choose lower level heuristics. Nearly 200 papers on hyper-heuristics have recently appeared in the literature. A common theme in this body of literature is an attempt to solve the problems in hand in the following way: at each decision point, first employ the chosen heuristic(s) to generate a solution, then calculate the objective value of the solution by taking into account all the constraints involved. However, empirical studies from our previous research have revealed that, under many circumstances, there is no need to carry out this costly 2-stage determination and evaluation at all times. This is because many problems in the real world are highly constrained with the characteristic that the regions of feasible solutions are rather scattered and small. Motivated by this observation and with the aim of making the hyper-heuristic search more efficient and more effective, this paper investigates two fundamentally different data mining techniques, namely artificial neural networks and binary logistic regression. By learning from examples, these techniques are able to find global patterns hidden in large data sets and achieve the goal of appropriately classifying the data. With the trained classification rules or estimated parameters, the performance (i.e. the worth of acceptance or rejection) of a resulting solution during the hyper-heuristic search can be predicted without the need to undertake the computationally expensive 2-stage of determination and calculation. We evaluate our approaches on the solutions (i.e. the sequences of heuristic rules) generated by a graph-based hyper-heuristic proposed for exam timetabling problems. Time complexity analysis demonstrates that the neural network and the logistic regression method can speed up the search significantly. We believe that our work sheds light on the development of more advanced knowledge-based decision support systems.
... The university course timetabling problem mainly comprises assigning a set of courses, student and lecturers to a specific and fixed number of timeslots and rooms in a week while satisfying some constraints [1]. There are two types of constraints: the hard and soft ones. ...
The university course timetabling is a complex optimization problem which is difficult to solve for optimality. It involves assigning lectures to a fixed number of timeslots and rooms; while satisfying some constraints. The goal is to construct a feasible timetable and satisfy soft constraints as much as possible. In this study, we apply two hybrids ant colony systems, namely the simulated annealing with ant colony system (ACS-SA), and tabu search with ant colony system (ACS-TS) to solve the university course timetabling, a number of ants in the ACS construct a complete assignment of courses to timeslots. Based on a pre-ordered list of courses, the ants probabilistically choose the timeslot for the given course, guided by heuristic information and stigmergic information. We test both ACS algorithms over the Socha's benchmark course timetabling problem. We also compare our results with those obtained by other methodologies recent literature has illustrated. Experimental results showed that both ACS-SA and ACS-TS produces good quality solutions and outperforms previously applied Ant algorithms; they also outperform other methodologies tested on Socha's benchmark test instances, and approaches on some benchmark instances. We believe that these hybrid ACS algorithms are also valid for other types of combinational optimization problems.
... The university course timetabling problem involves assigning a set of courses, lecturers and students to a specific number of rooms and timeslots [1]. The goal is to produce high-quality timetables that satisfies all hard constraints and attempts to accommodate soft constraints as much as possible. ...
This work presents a Particle Collision Algorithm (PCA) to solve university course timetabling problems. The aim is to produce an effective algorithm for assigning a set of courses, lecturers and students to a specific number of rooms and timeslots, subject to a set of constraints. The structure of PCA resembles a simulated annealing structure. The basic difference is that PCA does not have cooling schedule and it does not rely on user-defined parameters. PCA differs from Simulated Annealing and other meta-heuristic approaches where, before accepting the trial solution (although we obtain good-quality solution). Therefore, PCA is capable of escaping from local optima. The Hybrid Multi-Neighbourhood Particle Collision Algorithm with Great Deluge using Composite Neighbourhood Structure (HPCA), which it is hybridize the Great Deluge acceptance criterion with PCA and enhances a PCA approach that was originally introduced by Sacco for policy optimization. HPCA differs from basic PCA in terms of applying multi-neighbourhood composite structures, which is divided into two stages, one in the solution construction phase and the other in the improvement phase. HPCA also differs from basic PCA in terms of accepting the worst solution in the scattering phase, which is hybrid the Great Deluge acceptance criterion with PCA. HPCA attempts to further enhance the trial solution by exploring different neighbourhood structures. Results tested on Socha benchmark datasets show that HPCA is able to produce significantly good quality solutions within a reasonable time and outperformed some other approaches in some instances.
... Carter (1986) divided these approaches into four broad categories: sequential methods, cluster methods, constraint-based methods and meta-heuristics. Petrovic and Burke (2004) added the following categories: multi criteria approaches, case based reasoning approaches and hyper-heuristics/self adaptive approaches. Socha et al. (2002) applied an ant based approach to the eleven datasets which are investigated here. ...
Combinations of population-based approaches with local search have provided very good results for a variety of scheduling
problems. This paper describes the development of a population-based algorithm called Electromagnetism-like mechanism with
force decay rate great deluge algorithm for university course timetabling. This problem is concerned with the assignment of
lectures to a specific numbers of timeslots and rooms. For a solution to be feasible, a number of hard constraints must be
satisfied. A penalty value which represents the degree to which various soft constraints are satisfied is measured which reflects
the quality of the solution. This approach is tested over established datasets and compared against state-of-the-art techniques
from the literature. The results obtained confirm that the approach is able to produce solutions to the course timetabling
problem which demonstrate some of the lowest penalty values in the literature on these benchmark problems.
