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Complete University Modular Timetabling Using Constraint Logic Programming.
Abstract
In preparation for the changeover to a new modular degree structure, at the University of Leeds, a new modular timetable for the 1993–94 academic session had to be constructed from scratch. This paper describes our experience in constructing a large scale modular timetable using Constraint Logic Programming techniques.
... Genetic grouping is also an effective way to find a feasible solution for the problem [10]. Mathematics methods like logic programing is another manner for solving this problem [11,12]. Hybrid harmony search [13] and artificial bee colony [14,15] are two new methods which obtained prominent results. ...
scheduling courses in university is an important matter in all academic institutes across the world. Scheduling courses, students, and class rooms without any crash is the main aim of university course time tabling problem. This problem is categorized as a NP-hard problem. The proposed algorithm is firstly based on a genetic grouping approach to generate feasible solutions. In the second step, an effective neighborhood structure which is embedded in an artificial bee colony is used to overcome the problem's conflicts. Experimental results showed that proposed algorithm can obtain comparative results with the best known results of previous articles. The proposed algorithm has been performed on a standard and well known dataset named Socha. The results revealed the efficiency of proposed method. The suggested approach could find the best results on large scale instances of Socha dataset. Results on medium size of the dataset has been improved approaches in four cases out of five instances of dataset.
... The CTTP has been studied intensively, from early solution approaches based on logic programming [2,5,14] to metaheuristic schemes such as Tabu-list [16], Genetic Algorithms [28], Ant Colony [17], PSO [12], Variable Neighborhood Search [3] and Bee Algorithms [20]. In the same way, a great number of surveys of metaheuristics solution schemes that have been used to solve the CTTP problem are available [7,8,15,18]. ...
The course timetabling problem is one of the most difficult combinatorial problems, it requires the assignment of a fixed number of subjects into a number of time slots minimizing the number of student conflicts. This article presents a comparison between state-of-the-art hyper-heuristics and a newly proposed iterated variable neighborhood descent algorithm when solving the course timetabling problem. Our formulation can be seen as an adaptive iterated local search algorithm that combines several move operators in the improvement stage. Our improvement stage not only uses several neighborhoods, but it also incorporates state-of-the-art reinforcement learning mechanisms to adaptively select them on the fly. Our approach substitutes the adaptive improvement stage by a variable neighborhood descent (VND) algorithm. VND is an ingredient of the more general variable neighborhood search (VNS), a powerful metaheuristic that systematically exploits the idea of neighborhood change. This leads to a more effective search process according course timetabling benchmark results.
... Let us consider a basic timetabling problem which is often solved via the constraint programming approach [8,7,6,10] to demonstrate where possible directions of solution for our problem may lead. The timetabling problem is represented by given sets of of course offerings, each consisting of several courses. ...
Classical notions of disjunctive and cumulative scheduling are studied from the point of view of soft constraint satisfaction. Soft disjunctive scheduling is introduced as an instance of soft CSP and preferences included in this problem are applied to generate a lower bound based on existing discrete capacity resource. Timetabling problems at Purdue University and Faculty of Informatics at Masaryk University considering individual course requirements of students demonstrate practical problems which are solved via proposed methods. Implementation of general preference constraint solver is discussed and first computational results for timetabling problem are presented.
... Formally, [7]. Many approaches have been proposed for solving variants of educational timetabling problems, ranging from early approaches based on graph heuris- tics [26], linear programming [27] and logic programming [28, 29] to metaheuristics including tabu search [30], genetic algorithms [31, 32], ant colony optimization [33, 34], variable neighborhood search [35], simulated annealing [36], among others. Various CSP solvers have also been proposed to solve timetabling problems [37, 38]. ...
Hyper-heuristics are (meta-)heuristics that operate at a higher level to choose or generate a set of low-level (meta-)heuristics in an attempt of solve difficult optimization problems. Iterated local search (ILS) is a well-known approach for discrete optimization, combining perturbation and hill-climbing within an iterative framework. In this study, we introduce an ILS approach, strengthened by a hyper-heuristic which generates heuristics based on a fixed number of add and delete operations. The performance of the proposed hyper-heuristic is tested across two different problem domains using real world benchmark of course timetabling instances from the second International Timetabling Competition Tracks 2 and 3. The results show that mixing add and delete operations within an ILS framework yields an effective hyper-heuristic approach.
Pengenalpastian bakteria lazimnya dilakukan dengan merujuk kepada Manual Bergey setelah beberapa siri ujian biokimia dijalankan. Kaedah ini memakan masa yang panjang, memerlukan pemerhatian dan kefahaman yang mendalam tentang alam bakteria. Sementelahan proses pengenalpastian yang rumit dan panjang, maka keputusan pengenalpastian sesuatu bakteria boleh menjadi kurang tepat. Justeru, tujuan utama kajian ini dijalankan adalah untuk membangunkan aturcara pengenalpastian bakteria dengan menggunakan sistem rangkaian neural. Untuk mencapai tujuan tersebut, terdapat beberapa kaedah kajian yang perlu dijalankan termasuklah mengumpul segala data maklumat bakteria yang terkandung dalam Manual Bergey dan melatih data tersebut dengan menggunakan sistem rangkaian neural dalam perisian program MATLAB Versi 7.0. Di samping itu, kajian ini juga bertujuan mengoptimumkan rangkaian neural yang dibentuk dengan mengambilkira faktor-faktor bilangan neuron pada lapisan tersembunyi, bilangan lapisan tersembunyi, fungsi pengaktifan, algoritma pembelajaran dan sebagainya. Ujikaji pengenalpastian bakteria menggunakan Microstation Biolog turut dijalankan yang mana ia merupakan salah satu percubaan ujian biokimia untuk mengesahkan kehadiran 3 spesies bakteria yang dikenalpasti tanpa melibatkan penggunaan aturcara pengenalpastian bakteria mahupun Manual Bergey. Skop kajian ini hanya meliputi spesies bakteria fakultatif anaerobik dari famili Peptococcaceae, salah satu daripada 3 famili dalam kumpulan Gram-Positif kokus. Pembinaan rangkaian neural dalam kajian ini melibatkan penggunaan multi-lapisan yang terdiri daripada lapisan masukan, tersembunyi dan keluaran. Setiap lapisan terdiri daripada sebilangan neuron yang akan bertindak menyelesaikan sesuatu permasalahan. Neuron dalam lapisan masukan mewakili ciri-ciri bakteria dan neuron dalam lapisan keluaran mewakili jawapan spesies bakteria yang ingin dikenalpasti. Manakala neuron dalam lapisan tersembunyi bertindak sebagai satu medium yang akan mengumpul data-data isyarat masukan, menghitung jumlah isyarat yang masuk dan kemudiannya mengeluarkan isyarat keluaran dengan data yang tepat untuk disalurkan kepada neuron dalam lapisan keluaran. Algoritma pembelajaran perambatan balik dan mod-sesekumpul telah diaplikasikan dalam kajian ini. Secara keseluruhan, hasil simulasi rangkaian neural telah berjaya memberi keputusan yang memiliki kejituan yang tinggi dengan ralat sebanyak kurang daripada 8% telah dicapai. Hasil simulasi juga membuktikan bahawa penggunaan 2 lapisan tersembunyi telah berjaya menghasilkan keputusan rangkaian neural dengan kejituan yang tinggi pada jumlah epochs yang rendah untuk saiz data latihan yang sangat besar. Manakala penggunaan 1 lapisan tersembunyi pula adalah memadai untuk saiz data yang kecil dan sederhana. Kesimpulannya, proses pengenalpastian bakteria menggunakan sistem rangkaian neural telah berjaya dibangunkan untuk mengenalpasti spesies bakteria dalam famili Peptococcaceae dengan cepat, mudah dan tepat.
Scheduling courses in university is an important matter in all academic institutes across the world. Scheduling courses, students, and class rooms without any crash is the main aim of university course time tabling problem. This problem is categorized as a NP-hard problem. The proposed algorithm is firstly based on a genetic grouping approach to generate feasible solutions. In the second step, an effective neighborhood structure which is embedded in an artificial bee colony is used to overcome the problem's conflicts. Experimental results showed that proposed algorithm can obtain comparative results with the best known results of previous articles. The proposed algorithm has been performed on a standard and well known dataset named Socha. The results revealed the efficiency of proposed method. The suggested approach could find the best results on large scale instances of Socha dataset. Results on medium size of the dataset has been improved approaches in four cases out of five instances of dataset.
Course timetabling is an important and recurring administrative activity in most educational institutions. This chapter describes an automated configuration of a generic memetic algorithm to solving this problem. This algorithm shows competitive results on well-known instances compared against top participants of the most recent International ITC2007 Timetabling Competition. Importantly, our study illustrates a case where generic algorithms with increased autonomy and generality achieve competitive performance against human designed problemspecific algorithms.
The Course Timetabling problem is one of the most difficult combinatorial problems that arises with a University. The main objective of this problem is to obtain a timetable that minimises student conflicts between assigned activities. This is a discrete combinatorial problem that can be extremely difficult to solve for a human expert so computational heuristics are usually implemented in order to find good solutions within a reasonable time. With the advent of multi-core and hyperthreading technologies, parallel heuristics can speed up the solution process and with a proper parallel design these heuristics can improve the quality of solutions with the same number of Fitness evaluations than sequential algorithms. This paper explores the implementation of a parallel set of heuristic algorithms based on genetic algorithms, Scatter Search and discrete PSO for CTTP problem. Our experiments used as benchmark set instances from ITC2007 Track 2. Also the algorithms described in this paper make use of a layer of independence called methodology of design in order to be easily adaptable to new instances. Every parallel algorithm is compared against its sequential counterpart through speed-up metrics like Weak speed-up proposed by Alba et al.
Direct heuristic is widely used in scheduling applications, e.g., timeslot selection in school timetabling. Timeslot selection concerns which timeslot, among a number of applicable timeslots, be chosen for a yet-to-assign lesson. In this paper, we propose a timeslot selection heuristic based on the notion of timeslot contention among lessons. Due to the generality of the heuristic, it can be applied to other problem domains that involve disequality constraints such as examination timetabling problem. The new heuristic has been studied both analytically and empirically. Experimental results drawn from a set of real timetabling problem instances have shown that the new heuristic outperformed a variant of small-domain-first heuristic in terms of the timetable completion rate despite the similarity in both heuristics’ computational load.
The problem of constructing an automated system for use with timetabling is a par- ticularly well known one. Many programs exist for this task but perform well only in par- ticular isolated environments. We are currently developing a general system able to cope with the ever changing requirements of large educational institutions. In this paper, we present the methods and techniques behind such a system. We present graph colouring and room allocation algorithms and show how the two can be combined together to provide the basis of a flexible and widely applicable timetabling system. We also discuss, in some detail, how several common timetabling features can be handled within the system. We intend to overcome the problems of intractability by producing a spreadsheet type system that the user can guide in an informed and useful way. This gives the user control of the search and the possibility of bactracking where no reasonable solution is found, while still letting the heuristic algorithms do the hard work. Such an approach cannot guarantee an optimal solution but it can guarantee a solution the user is happy with. It is safe to assume that any user addressing a timetabling problem in an University environ- ment has some idea of the timetable required and is qualified to judge whether a solution is suitable or not.
Constraint logic programming (CLP) is a generalization of logic programming (LP) where unification, the basic operation of LP languages, is replaced by constraint handling in a constraint system. The resulting languages combine the advantages of LP (declarative semantics, nondeterminism, relational form) with the efficiency of constraint-solving algorithms. For some classes of combinatorial search problems, they shorten the development time significantly while preserving most of the efficiency of imperative languages.
This paper surveys this new class of programming languages from their underlying theory, to their constraint systems, and to their applications to combinatorial problems.
The construction of timetables involving three or more variables taking values from domains having thousands of values with several dozen constraints having different priorities is a problem common to many organizations. Various heuristics solutions have been proposed using results based on graph theory, mathematical programming and manual methods. We propose an approach based on logic progamming using the first order predicate calculus. An algorithm has been developed, implemented in WPROLOG, and thoroughly tested on an Amdahl 5880 under VM HPL.
A neural network which efficiently and nearly optimally solves combinatorial optimization problems was applied to the timetable problem. The network was tested on a real-world timetable problem. The results indicate that the Markovian neural network is an efficient and flexible tool for solving real-world combinatorial optimization problems such as construction of a timetable for high schools.
We consider a course scheduling problem in which the total number of time periods assigned to each topic has to be split into daily amounts of consecutive time periods called daily quantums. These daily quantums may be arbitrary but are bounded by given minimal and maximal values.In addition to the classical constraints of course scheduling problems, precedence and time windows requirements are taken into account. We describe a new method based on Tabu search techniques for finding a feasible course schedule.