Table 3 - uploaded by Sara Ceschia
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Minimum and maximum values of the features for the families of instances (#I: number of instances): courses (C), total lectures (Le), rooms (R), periods (Pe), curricula (Cu), room occupation (RO), average number of conflicts (Co), average teachers availability (Av), room suitability (RS), average daily lectures per curriculum (DL).
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The problem about p-median on the minimum is considered in the integer statement. As known, this problem is NP-difficult. For solving the problem, the algorithms of ant colony and simulated annealing are suggested. The computer simulation results are analyzed.
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... A feasible schedule must satisfy a set of hard constraints and must also take into account a set of soft constraints. From ITC-2007, many researchers have developed advanced models and methods to solve CB-CTT (see, e.g., [3,4,8,16,17,19,[22][23][24]31]). The survey by [5] is devoted to review the main works on the topic, with focus on mathematical models, lower bounds, and exact and heuristic algorithms. ...
This paper deals with curriculum-based course timetabling. In particular, we describe the results of a real application at the University of Rome “Tor Vergata.” In this regard, we developed a multi-objective mixed-integer model which attempts to optimize (i) the flow produced by the students enrolled in the lectures, (ii) soft conflicts produced by the possible overlap among compulsory and non-compulsory courses, and (iii) the number of lecture hours per curriculum within the weekdays. The model has been implemented and solved by means of a commercial solver and experiments show that the model is able to provide satisfactory solutions as compared with the real scenario under consideration.
... There are two types of methods in metaheuristic such as local search-based methods and population-based methods [18]. Local search-based methods used in solving CBCTT include simulated annealing (SA) [19,20], great deluge (GD) [21] and tabu search (TS) [22] require only one initial timetable in order to proceed with the improvement process. In the other hand, population-based methods used in solving CBCTT include ant colony optimization (ACO) [23], artificial bee colony (ABC) [15,24], genetic algorithm (GA) [25,26] and harmony search algorithm (HSA) [27,28] require population of initial timetable in its improvement process. ...
The construction of population of initial timetable is an essential stage in population-based metaheuristic approach for solving curriculum-based university course timetabling problem because it may impact the quality of the final timetable. This paper presents population of initial timetable construction approach in curriculum based course timetabling problem by using the graph heuristics to determine the sequential order of courses/lectures to be assigned in the timetable. The graph heuristics were implemented as single and combination of two heuristics. The courses in curriculum-based university course timetabling problem that was organized based on the heuristics setting will be repeatedly assigned to valid empty slots while fulfilling all the hard constraints. If a course is unable to be assigned to whichever slots because of no more valid empty slots, it will be inserted into the unscheduled courses/lectures list. The unscheduled courses/lectures list will be assigned later to the timetable using several procedures executed in a sequence. The approaches were tested on the ITC2007 instances and the results were analyzed with some statistical tests to determine the best setting of heuristics in the construction approach. The result shows that the construction approach with combination of largest degree followed by saturation degree heuristic, generate the maximum number of population of initial timetables. The result from this study can be used in the improvement stage of metaheuristic algorithm that uses population-based approach.
... One of the prevalent issues in the CB-CTT is low convergence exhibited by metaheuristic algorithms such as Artificial Bee Colony algorithm (Agahian, Pehlivan, and Dehkharghani, 2014), Ant Colony Optimization (Thepphakorn, Pongcharoen, and Hicks, 2014) and Simulated Annealing (Bellio, et. al., 2013) to name a few. In this work, we attempt to solve Track 3 of the International Timetabling Competition 2007, a curriculum-based course timetabling (CB-CTT) problem by introducing four pre-processor matrices to assist in a higher probability of convergence. The problem essentially deals with the scheduling of a set of lectures to various ...
This paper describes the effects of pre-processors on the solution quality of the university course timetabling problem. The University Course Timetabling Problem (UCTP) is regarded as both an NP-hard and NP-complete combinatorial optimization problem and is a difficult task since many constraints are needed to be satisfied in order to obtain a feasible solution. The constraints, in this case, are related to the characteristics and regulations of the particular institution. This paper describes the effects of pre-processors which consist of four matrices on the solution quality of the university course timetabling problem as they play a critical role and have significant impact on the solution. In order to evaluate the effects of the pre-processor matrices, the fitness score which is obtained without the pre-processor matrices are tabulated and compared against the fitness score that is obtained with the pre-processor matrices. Seven neighborhood structures are implemented and the experiment is conducted using the datasets obtained from Track 3 of the ITC-2007. The result indicates that there is a significant difference in terms of the fitness score between the solutions obtained without the pre-processors and with the pre-processors, with the latter showing promising results.
... More speci cally, we show two di erent solution methods, namely a neighborhood search by Simulated Annealing (SA), and a Large Neighborhood Search (LNS) based on a novel CP model for CB-CTT. The chapter is based on the results described in two papers, [5] and [104], which I respectively co-authored and authored, and have been presented to the 6th Multidisciplinary International Conference on Scheduling: Theory and Applications (MISTA'13), and to the Doctoral Program of CP'13. Moreover, a follow-up of [5] has been recently submitted to a relevant journal of the eld. ...
... The chapter is based on the results described in two papers, [5] and [104], which I respectively co-authored and authored, and have been presented to the 6th Multidisciplinary International Conference on Scheduling: Theory and Applications (MISTA'13), and to the Doctoral Program of CP'13. Moreover, a follow-up of [5] has been recently submitted to a relevant journal of the eld. ...
... This can be done by using techniques that allow to generate representative sets of points, while keeping the number of generated setups low. q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q One such parameter is the Hammersley point set [52], which we employed for the rst time in [5]. Two properties, in particular, make this point generation strategy particularly suitable for parameter tuning. ...
Combinatorial optimization problems arise, in many forms, in various aspects of everyday life. Nowadays, a lot of services are driven by optimization algorithms, enabling us to make the best use of the available resources while guaranteeing a level of service. Examples of such services are public transportation, goods delivery, university time-tabling, and patient scheduling. The fields of meta-heuristics, artificial intelligence, and operations research, have been tackling many of these problems for years without much interaction. However, in the last few years, such communities have started looking at each other's advancements, in order to develop optimization techniques that are faster, more robust, and easier to maintain. This effort gave birth to the fertile field of hybrid meta-heuristics. In this thesis, we analyze some of the most common hybrid meta-heuristics approaches, and show how these can be used to solve hard real-world combinatorial optimization problems, and what are the major advantages of using such techniques. This thesis is based on results obtained by working together with many local and international researchers, and published in a number of peer-reviewed papers.
... I would like to mention our experience with the latter one, which has been very positive. In fact, as reported in Bellio et al. (2014), a tuning procedure that uses only generated instances and no real ones, has been able to obtain comparable or better results with those tuned (maybe overtuned) on the competition instances. ...
... The generated instances can be used to tune an algorithm, to avoid overtuning phenomena on the set of benchmark instances. In Bellio et al. (2014), for example, a simulated annealing algorithm is tuned on the generated instances and 1 Contributed by Moritz Mühlenthaler. ...
... In Bellio et al. (2014) (see also Bellio et al. 2013), a simulated annealing algorithm is proposed. Two neighborhoods are considered, i.e., the move of a lecture from a time period/room to another time period and/or another room (possibly to one that is empty in that time period), and the swap of time periods and rooms of two lectures of distinct courses. ...
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.
Automated timetabling is a challenging area in the timetabling and scheduling theory and practice, intensively addressed in research papers in the last two decades. There are three main classes of problems, which are usually studied: school timetabling, course timetabling and examination timetabling. In this report, we address a case study of the Curriculum-Based Course Timetabling (CB-CTT) problem, arising at Engineering Department of Sannio University. In general, the problem consists of finding a feasible weekly assignment of course lectures to rooms and time periods while respecting a wide range of constraints, which have to be either strictly satisfied (hard constraints) or satisfied as much as possible (soft constraints). The case study here addressed here has many special requirements due to local organizational rules. We were able to model the complex requirements by an Integer Programming formulation. The solution approach consists of using an MIP solver, integrated with two local branching heuristics tailored for the problem. The effectiveness of the proposed approach is illustrated by the computational results on two real instances.
