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Incorporating of constraint-based reasoning into particle swarm optimization for university timetabling problem
Abstract
Timetabling problems are often difficult and time-consuming task. It involves a set of timeslots, classrooms, subjects, students and lecturers. The complexity problem is the constraints that exist within the resources. Thus, a technique that can handle constraints is needed to optimize the problem. Various approaches have been reported in the literature on solving university timetabling problem. This paper focuses on developing a hybrid algorithm consisting of a particle swarm optimization and constraint-based reasoning in solving university timetabling problem in generating a feasible and near-optimal solution. The proposed algorithm is tested using real data from the Faculty of Computer Science and Information System, Universiti Teknologi Malaysia. The result is compared against standard particle swarm optimization and hybrid particle swarm optimization-local search. It shows that the proposed method has outperformed others
... Masalah tersebut secara umum memiliki karakteristik yang tidak jauh berbeda dengan perguruan tinggi lainya, dimana jadwal kuliah selalu berkaitan dengan timeslot, ruangan, mata kuliah, mahasiswa, dosen dan constraint, dimana setiap tahun ajaran terdiri dari dua semester yaitu ganjil dan genap (Irene et al., 2009). ...
... Untuk menyusun penjadwalan kuliah pada perguruan tinggi Politeknik Negeri Bengkalis ada dua constraints yang harus diperhatikan yaitu : a. Hard constraints 1. Dosen tidak boleh mengajar lebih dari satu matakuliah dalam timeslot yang sama (Irene et al., 2009). 2. Satu group kelas mahasiswa tidak boleh ditugas lebih dari satu matakuliah dalam timeslot yang sama (Irene et al., 2009). ...
... Untuk menyusun penjadwalan kuliah pada perguruan tinggi Politeknik Negeri Bengkalis ada dua constraints yang harus diperhatikan yaitu : a. Hard constraints 1. Dosen tidak boleh mengajar lebih dari satu matakuliah dalam timeslot yang sama (Irene et al., 2009). 2. Satu group kelas mahasiswa tidak boleh ditugas lebih dari satu matakuliah dalam timeslot yang sama (Irene et al., 2009). 3. Satu ruangan tidak boleh ditugaskan lebih dari satu matakuliah untuk timeslot yang sama (Irene et al., 2009). ...
Course timetabling management information system is a system focusing on data management resource and constraints in optimizing the use of available resources and avoid clashing in the process of making class timetabling, so that the resulting information will be effective. Results of such information may assist the college in planning the use of space, and to develop programs of study. Data resource and constraints are implemented using timetabling information system with PSO algorithm. The results of the data analysis using the PSO algorithm by combining six hard constraint and two soft constraints cannot produce an optimal solution, because there are still clashing lecturer-timeslot (soft1), but without combining both soft constraints can produce maximum solutions in the use of the room, where the solution with the best fitness value (0.333), c1(2,0), c2(2,0), w(0,2), and maximum of 10 iterations of the desired solution. The final results are timetabling management information system for resource utilization that generates class timetable information and use of the room. Keywords : Management information system; PSO algorithm; Resource; Constraints; Course timetabling; Higher education
... This research is referred to the heuristics approach 11 in timetabling problem, where generating initial timetables should be implemented in order to solve the hard constrains. The research can be proved satisfying even with Swarm Particle Optimization to solve the hard constraint in short period of time 6,7 . ...
This paper presents the implementation of Constraint Programming in UCTP with special requirement based on the requirement given by Academic Service Divison of UMSLIC, with various forms of constraint which needed to be satisfied in order to obtain a feasible solution for the real-world course timetabling problem obtained from the Universiti Malaysia Sabah Labuan International Campus (UMSLIC), Malaysia. The problem domains in UMSLIC have several constraints that need to be satisfied. Solutions are feasible if all the hard constraints are satisfied. This research does not take into account the soft constraints involved in the domains. The Constraint Programming approach algorithm is tested over three real world datasets: testing dataset; semester 2 session 2014/2015 dataset; semester 1 session 2015/2016 dataset. The result shows that the algorithm studied in this research is able to produce feasible solution within short period of time without violating any hard constraints, which is applicable towards the UCTP in UMSLIC.
... Over the past years, a wide variety of techniques have been proposed in solving course timetabling and its variants. Several techniques have been developed such as genetic Algorithm [7], Constraints Based Reasoning [8], Harmony Search Algorithm [9]- [10], Local Search and so forth. Particle Swarm Optimization has become an interesting approach for solving timetabling problems. ...
It is time consuming for lecturers to manually compile, run and verify students' programming assignments. Moreover, they also need to define test cases for different programming exercises in order to assess students' code. This paper presents a swarm inspired automatic test case generation for Online Programming Assessment or Judge (UOJ) system. The UOJ is built with the purpose to assist lecturers in evaluating codes submitted from students and generate test cases for every programming problem automatically. It also helps students to practice and enhance their programming skills. In this study, the mechanism of automatic test case generation was explored using Particle Swarm Optimization (PSO) algorithm and new fitness function is proposed to determine the optimal solution for each problem. Experiments were set up to benchmark between manual and automatic PSO test case generation results to evaluate the efficiency of the proposed method. The preliminary results are satisfactory for automatic test case generation using swarm inspired PSO algorithm in C++ programming assignments.
A multi-dimensional assignment problem in which Students, Faculty and Subjects together as events are scheduled to suitable timeslots and available classrooms, is termed to be University Course Timetabling Problem (UCTP). Previous literature studies reveal that getting the best fitness function value with generating an optimized timetable is not considered to a great extent. This paper proposes a novel method of solving the UCTP through various Hybrid Search Optimization algorithms combined with Particle Swarm Optimization (PSO). This approach is implemented for the real time data taken from the Faculty of Computer Science and Engineering of a typical Indian University. Our experimentation clearly confirms by giving promising results that, getting a near or sub optimal solution is highly feasible through various hybrid algorithms.
Constraint satisfaction optimization problem is a kind of optimization problem involving cost minimization as well as complex constraints. Local search and constraint programming respectively have been used for solving such problems. In this paper, I propose a method to integrate local search and constraint programming to improve search performance. Basically, local search is used to solve the given problem. However, it is very difficult to find a feasible neighbor satisfying all the constraints when we use only local search. Therefore, I introduced constraint programming as a tool for neighbor generation. Through the experimental results using weighted N-Queens problems, I confirmed that the proposed method can significantly improve search performance.
University Course Timetabling Problem (UCTP) belongs to Constraint Satisfaction Problems (CSPs), which are the set of objects whose state must satisfy a number of constraints. The constraints, in this case, are related to characteristics and regulations of a particular university. Certainly, these will vary from one university to the other. A number of approaches have provided feasible and optimal solutions for UCTP. However, their solutions are still based certain university's constraints. Our approach has given another way to occupy various constraints for various universities. Dynamic Constraint Matching (DCM) consists of constraints logical formulation, collision matrix generation, and validation using the collision matrix. Our experiment, using 93 subjects offered in Faculty of Information Technology Tarumanagara University, has shown that all constraints, taken from the characteristics and regulations of the Faculty, can be formulated successfully. When DCM were integrated with Vertex Graph Coloring (VGC) as one of the guaranteed optimal solutions for UCTP, the approach results a course schedule that does not contain any hard or soft constraints violations. The processing time can be said fast, which is less than 1 minutes.
University course timetabling is a complex problem which must satisfy a list of constraints in order to allocate the right timeslots and venues for various courses. The challenge is to make the NP-hard problem user-friendly, highly interactive and faster run time complexity of algorithm. The objective of the paper is to propose Particle Swarm Optimization (PSO) timetabling model for Undergraduate Information and Communication Technology (ICT) courses. The PSO model satisfies hard constraints with minimal violation of soft constraints. Empirical results show that the rds: NP hard problem, timetabling, particle swarm optimization
In timetable scheduling problems, examination subjects must be slotted to certain times that satisfy several of constraints. They are NP-completeness problems, which usually lead to satisfactory but suboptimal solutions. As PSO has many successful applications in continuous optimization problems, the main contribution of this paper is to utilize PSO to solve the discrete problem of timetable scheduling. Experimental results confirm that PSO can be utilized to solve discrete problem as well
Presents a spreadsheet based system and the methods behind it as
motivated by the need for automated assistance for university exam and
course scheduling. The program is currently at the prototype stage with
the algorithms running quickly and efficiently giving often optimal
solutions to small test problems. Research is now directed toward
developing further algorithms and to further widen the scope of the
spreadsheet, possibly using probabilistic search techniques to optimize
several criteria relative to each other, criteria which may be chosen by
the scheduler
The particle swarm is an algorithm for finding optimal regions of
complex search spaces through the interaction of individuals in a
population of particles. This paper analyzes a particle's trajectory as
it moves in discrete time (the algebraic view), then progresses to the
view of it in continuous time (the analytical view). A five-dimensional
depiction is developed, which describes the system completely. These
analyses lead to a generalized model of the algorithm, containing a set
of coefficients to control the system's convergence tendencies. Some
results of the particle swarm optimizer, implementing modifications
derived from the analysis, suggest methods for altering the original
algorithm in ways that eliminate problems and increase the ability of
the particle swarm to find optima of some well-studied test functions
In this study, a solution to the school timetabling problem using parallel genetic algorithm with simulated annealing is presented. The hybridization of simulated annealing and parallel genetic algorithm is explained. Also, how these algorithms are run in parallel on a local network of workstations are discussed. Some comparative results among the different parallel models are exhibited. The implementation of the parallel algorithms are used to construct conflict-free and satisfying timetables for the Department of Mathematics of the University of the Philippines Diliman. The program output of this study can be easily modified to be used as a helpful and efficient guide to the decision-making process of the scheduler.
The paper deals with an effectiveness of Constraint Programming (CP) for scheduling problem particularly for timetabling. The main advantage of the CP is declarativity, a straightforward statement of the constraints serves as a part of the program and it is compared with local search procedures. The CP main features, constraint propagation and distribution, are briefly presented. The constraint programming language Mozart-Oz allows to express complex constraints and create complicated, custom-tailored distribution strategy, which is needed for solving timetabling problem. Incorporation of the local search into constraint programming is needed as a method for optimization. Results of implementation for real-world case are presented.
The particle swarm algorithm has shown ability to optimize in continuous problem spaces, although it can struggle in problem spaces containing multiple optima. A variant, called Waves of Swarm particles (WoSP), has been shown to be able to handle problem spaces containing multiple optima by sequentially exploring these optima. In this paper the WoSP algorithm is adapted to suit complex quantised problem spaces and applied to a highly constrained problem with many constraint-violating solutions but few constraint-satisfying solutions. The performance obtained is remarkably good and reflects the power of the WoSP algorithm that combines the search ability of particle swarm with that of evolution.
In university timetabling problems, course subjects must be assigned to a certain timeslots and rooms that satisfy preferred constraints. Timetabling problem is NP-completeness problem, which is a difficult problem with a lot of constraints to be solved and a huge search space needed to be explored if the problem size increases. As particle swarm optimization (PSO) has many successful applications in continuous optimization problems, the main contribution of this paper is to utilize PSO to solve the discrete problem of university course timetable (UCT). Experimental results confirm that PSO able to solve the timetabling problem with promising result.
College timetabling is a combinatoric and dynamic problem. In order to solve this problem, the approach must be efficient, flexible, portable, and adaptable. This paper describes a solution procedure based on a constraint-based reasoning technique implemented in an object-oriented approach. The problem is formulated as a constraint satisfaction model and it is then solved using the proposed algorithm. The algorithm is tested using real data from one of the colleges offering professional courses. The results show that a 18-weeks timetable for 1673 subject sections, 10 rooms, 21 lecturers can be solved in less than 33 minutes as compared to several weeks if it is to be solved manually. Since it is implemented using the object-oriented approach, the proposed system can also be modified and easily adapted to support changes.Scope and purposeTimetable planning is an activity of assigning subjects to time and space such that all constraints are satisfied. It can be categorized into several types and the most common types are academic (in universities, colleges, and schools), airline, and nurse timetablings. Constraint-based reasoning is a problem-solving technique that combines logic programming and constraint-solving technique based on an arc-consistency algorithm. It has been used to solve constraint satisfaction problems. The purpose of the paper is to present the modeling process of the college timetabling as a constraint satisfaction problem. The model is then solved using the constraint-based reasoning approach.
Timetable planning can be modelled as a constraint-satisfaction problem, and may be solved by various approaches, including genetic algorithms. An optimal solution for a timetable planning problem is difficult to find using genetic algorithms, due to the ambiguity in deciding the fitness function. Various approaches aimed at finding optimal solutions to constraint-satisfaction problems by genetic algorithms have been proposed, but most of these approaches are problem-dependent and hence are difficult to apply to real-world problems. In this paper, a hybrid algorithm consisting of a genetic algorithm and constraint-based reasoning is proposed to find a feasible and near-optimal solution. The proposed algorithm was tested by using real data for university timetable planning, and this approach can be applied to most constraint-satisfaction problems.
Hybridization of local search and constraint programming techniques for solving Constraint Satisfaction Problems is generally
restricted to some kind of master-slave combinations for specific classes of problems. In this paper we propose a theoretical
model based on K.R. Apt’s chaotic iterations for hybridization of local search and constraint propagation. Hybrid resolution
can be achieved as the computation of a fixpoint of some specific reduction functions. Our framework opens up new and finer
possibilities for hybridization/combination strategies. We also present some combinations of techniques such as tabu search,
node and bound consistencies. Some experimental results show the interest of our model to design such hybridization.
University Course Timetabling (UCT) is a complex problem and cannot be dealt with using only a few general principles. The complicated relationships between time periods, subjects and classrooms make it difficult to obtain feasible solution. Thus, finding feasible solution for UCT is a continually challenging problem. This paper presents a hybrid particle swarm optimization algorithm to solve University Course Timetabling Problem (UCTP). The proposed approach (hybrid particle swarm optimization with constraint-based reasoning) uses particle swarm optimization to find the position of room and timeslot using suitable objective function and the constraints-based reasoning has been used to search for the best preference value based on the student capacity for each lesson in a reasonable computing time. The proposed algorithm has been validated with other hybrid algorithms (hybrid particle swarm optimization with local search and hybrid genetic algorithm with constraint-based reasoning) using a real world data from Faculty of Science at Ibb University -- Yemen and results show that the proposed algorithm can provide more promising solution.
The university course timetabling problem is a combinatorial optimization problem concerning the scheduling of a number of subjects into a finite number of timeslots in order to satisfy a set of specified constraints. The timetable problem can be very hard to solve, especially when attempting to find a near-optimal solutions, with a large number of instances. This paper presents a combination of particle swarm optimization and local search to effectively search the solution space in solving university course timetabling problem. Three different types of dataset range from small to large are used in validating the algorithm. The experiment results show that the combination of particle swarm optimization and local search is capable to produce feasible timetable with less computational time, comparable to other established algorithms.
A huge variety of timetabling models have been described in the OR literature; they range from the weekly timetable of a school to the scheduling of courses or exams in a university. Graphs and networks have proven to be useful in the formulation and solution of such problems. Various models will be described with an emphasis on graph theoretical models.
A timetabling problem is usually defined as assigning a set of events to a number of rooms and timeslots such that they satisfy a number of constraints. Particle swarm optimization (PSO) is a stochastic, population-based computer problem-solving algorithm; it is a kind of swarm intelligence that is based on social-psychological principles and provides insights into social behavior, as well as contributing to engineering applications. This paper applies the particle swarm optimization algorithm to the classic timetabling problem. This is inspired by similar attempts belonging to the evolutionary paradigm in which the metaheuristic involved is tweaked to suit the grouping nature of problems such as timetabling, graph coloring or bin packing. In the case of evolutionary algorithms, this typically means substituting the "traditional operators" for newly defined ones that seek to evolve fit groups rather than fit items. We apply a similar idea to the PSO algorithm and compare the results. The results show that the number of unplaced events (error) is decreased in comparison with previous approaches.
A genetic algorithm for solving a timetable scheduling problem is described. The algorithm was tested on small and large instances of the problem. Algorithm performance was significantly enhanced with modification of basic genetic operators. Intelligent operators restrain the creation of new conflicts in the individual and improve the overall algorithm 's behavior.
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