Algorithms Used For Tackling Course Timetabling Computer Science Essay

Timetabling is an country of increasing involvement in the community of both research and pattern in recent decennaries. Typical instances in this country include educational timetabling, athletics timetabling, employee timetabling, conveyance timetabling and so on. In this survey, we consider an educational timetabling job. Educational timetabling jobs are classified into two classs: test timetabling and class timetabling. The later can be farther divided into two sub-categories: station enrollment-based class timetabling and curriculum-based class timetabling. The chief difference is that for station registration timetabling, struggles between classs are set harmonizing to the pupils en-rollment informations, whereas the curriculum-based class timetable is scheduled based on the course of study published by the university. Every twelvemonth or term in a university, each person section has to plan a new timetable for topics or lessons. The timetabling jobs are multi-dimensional assignment optimisation and constrained combinative optimisation job that consists of apportioning a set of talks in between module and pupils in a finite period of clip ( typically a hebdomad ) , in available schoolrooms, that satisfies a set of restraints. University Course Timetabling Problem ( UCTP ) is one of its types. Many of these jobs are tackled manually, which is a tough and time-consuming undertaking. The impact of bring forthing a timetable manually was when stipulations change ; so whole work becomes unserviceable ( low quality timetable ) , and has to be restarted from abrasion. In this paper, we have surveyed different types of algorithms used to undertake Course Timetabling Problem and tabulated their assorted parametric quantities along with virtues, demerits, issues to be addressed and so on. Largely, the bing timetabling algorithm does non see fittingness value and the maximal figure of free timeslots allocated. Therefore, there is a demand to implement a Course Timetabling algorithm that can heighten the optimality and fittingness.


Difficult Constraints, Soft Constraints, Fitness Function, Execution Time, Local Search, Genetic Algorithm, Particle Swarm Optimization, Tabu Search, Simulated Annealing.

1. Introduction

Timetabling is one of the common programming jobs, which we see, in daily life. It is a multi-dimensional assignment job in which set of events, resources, pupils, module, schoolrooms and timeslots are scheduled harmonizing to given restraints depends on the particular job. An Efficient solution of timetable job of specific sphere will non work good for some other sphere job depending upon the restraints specified. By and large, there are two types of restraints viz. difficult restraints and soft restraints. Difficult restraints are restraints, which are non to be violated at any cost. Soft restraints are restraints, which can be accepted with a punishment associated to their misdemeanor. A executable solution of timetabling job is one, which satisfies all the difficult restraints, and the quality of executable solution is measured by fulfilling soft restraints while fulfilling all difficult restraints as good.

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Many algorithms have been proposed to work out the timetabling job. In earlier yearss, graph-coloring method is used. It works good for little cases but as the figure of cases increased, it could non work expeditiously. Later stochastic algorithms like Genetic Algorithm, Stimulated Annealing Algorithm, Tabu Search Algorithm, etc. , were introduced. There are two types of algorithms used viz. local-area-based algorithms and population-based algorithms. Each type has its ain advantages and disadvantages.

Local-area-based algorithms dressed ore on development i.e. they search in one way without happening all the possible solutions. E.g. , Simulated Annealing, Very Large Neighborhood Search, Tabu Search, etc. These sorts of algorithms improve the quality of solution.

Population-based algorithm starts with figure of solutions and refines the solutions to acquire optimal solution. Therefore, this is called as global-area-based algorithms. It requires more clip and premature convergence. E.g. Evolutionary Algorithm, Particle Swarm Optimization, Ant-Colony Optimization, Artificial Immune System, Genetic Algorithm etc. Assorted combinations of local-area-based and global-area-based algorithms are reported to work out timetabling job.

The aim of this paper is to concentrate on assorted Course Timetabling algorithms. The remainder of the paper is organized as follows. Section II presents assorted bing Course Timetabling algorithms. Section III presents the comparing of the timetabling algorithms along with the tabular arraies. Section IV highlights the public presentation metrices of the algorithms and subdivision V concludes the paper with a sum-up of our parts.


In this chapter, we will reexamine most recent and important plants about the algorithms used for work outing Course Timetabling Problem. Algorithms are grouped as local-area-based and population-based or global-area-based. Some algorithms used both sorts to obtain better consequences. The Following Course Timetabling algorithms are presently prevailing in usage and these algorithms are summarized in Table1 and Table2.


Tuga M. et Al. [ 1 ] proposed an algorithm to turn to a executable solution for timetabling job. A executable solution is one that satisfies all difficult restraints. This method proposes the solution by loosen uping one of its difficult restraints and making a soft restraint to counterbalance.

Feasible solution is constructed for relaxed restraint job by utilizing graph-based method. In graph-based method, events are considered as nodes and there is an border between two nodes if and merely those events are assigned at the timeslot.

Simulated Annealing based attack is used for minimising soft restraints. Fake Annealing is a stochastic hunt method used in local hunt i.e. in each measure, it moves either to better vicinity solution if it finds or to a worse solution.

To better variegation, kempe concatenation vicinity is introduced. Apart from simple and swap vicinity, kempe concatenation vicinity operates over two selected timeslots. For this, bipartite graph is used in which each node consists of an event and a resource for one of its timeslot and an border exists if and merely if the two resources are used by conflicting events within those timeslots.

A kempe concatenation vicinity is formed by taking one resource randomly from timeslot t1 and corresponding event will trip a concatenation which forms connected sub graph. New Timetable can be obtained by transfering events in this concatenation to the events present in the brace timeslot.


Z.Lu et Al. [ 28 ] and Khang Nguyen et Al. [ 2 ] proposed an adaptative taboo hunt algorithm which follows a general model consists of 3 stages viz. low-level formatting, intensification and variegation.

In low-level formatting stage, executable initial timetable is obtained utilizing fast greedy heuristics. In fast greedy heuristics, at each measure, one talk is inserted into timetable at each clip. In each measure, two operations, one is choice of unassigned talk and second is to find a period-room for this talk.

Intensification and variegation stages are used to minimise figure of soft restraints while keeping difficult restraints satisfaction. Intensification uses taboo hunt, which explores the hunt infinite by replacing the current solution with non-recently visited adjacent solution even if the later is worse than current solution. Tabu list is maintained to avoid cycling and the hunt to travel farther by hive awaying already visited solutions.

This attack introduces other important characteristics like original dual kempe ironss neighborhood construction, a penalty-guided disturbance operator, and an adaptative hunt mechanism. In Original dual kempe concatenation vicinity, two kempe ironss are allowed to trade their talk and period and therefore bring forthing new solution. In variegation, original dual kempe concatenation vicinity is used.

When the best solution can non be improved utilizing Tabu hunt, a disturbance operator is used. It is guided by disturbance strength. If disturbance strength is strong, re-start will be at random. Otherwise, hunt will get down from the merely visited local optimum and hunt infinite is little. All the talks are arranged in non-increasing punishment values harmonizing to the soft restraints. Highly penalized talks are foremost assigned to a random choice of a given figure of neighborhood moves.


Salwani Abdullah T Al. [ 3 ] proposed a really big vicinity hunt to fulfill every bit much as possible soft restraints while keeping difficult restraints satisfaction. It proposes 11 vicinity moves to bring forth as many solutions as possible so that it will fulfill soft restraints.


Halvard Arntzen et Al. [ 4 ] proposed a local hunt heuristic algorithm, which uses a simple adaptative memory hunt to better the quality of an initial solution. The hunt is guided by taboo hunt mechanisms based on recentness and frequence of certain properties of old moves.


Majid Joudaki et Al. [ 5 ] proposed a intercrossed method, which is based on combination of improved Memetic and Simulated Annealing Algorithms utilizing Simulated Annealing Algorithm as the local hunt modus operandi additions working ability of Memetic Algorithm. In add-on, modifying Crossover operator of Memetic Algorithm and making initial population by a heuristic-based method improves this algorithm.

In order to better produced chromosomes and diminishing the figure of misdemeanor of the restraints, a new operator is designed and added to Memetic Algorithm, called betterment operator.

2.6 A MAX-MIN ANT-COLONY Optimization

Krzysztof Socha et Al. [ 6 ] presented a Max-Min Ant-Colony optimisation uses separate local hunt modus operandi. In add-on, it proposes appropriate building graph and pheromone matrix representation. Construction graph is given by E – Thymine, where Tocopherol is events and T is timeslots. We can besides make up one’s mind whether move along list of timeslots and choose events to be placed or travel along lists of events and take suited timeslots. Pheromone matrix is a matrix of values ? : E – T i? R ? 0, where Tocopherol is events and T is timeslots. These values are initialized to a parametric quantity ?0 and finally updated by local and planetary regulations. At the terminal of the iterative hunt, event-timeslot assignment is converted into candidate solution ( timetable ) . This can be improved by local hunt.


Sastry et Al. [ 29 ] and Salwani Abdullah et Al. [ 7 ] proposed an evolutionary algorithm which comprises of three phases: Choice, Reproduction and replacing. In the choice phase, the fittest persons have a higher opportunity than the less tantrum of being chosen as parents for the following coevals. The quality of the solution is measured in footings of a punishment value which represents the grade to which assorted soft restraints are satisfied.

Recombination and mutant operators applied to take parents execute reproduction. Recombination combines parts of each of two parents to make new single while mutant makes little change to make new single. Finally, in Replacement persons of original population is replaced by the freshly created 1s and cancel the worst 1s.


A. Colorni et Al. [ 30 ] and Branimir sigl et Al. [ 8 ] proposed a Familial algorithm ( GA ) in which the natural analogy is population genetic sciences. In GA, every possible solution is single and after the coevals of an initial set of executable solutions i.e. population, persons are indiscriminately mated leting recombination of familial stuff. The new population so obtained undergoes a procedure of natural choice where favors the endurance of the fittest persons. The fittingness of the persons is evaluated by fittingness map. Algorithm public presentation was significantly enhanced with alteration of basic familial operators, which restrain the creative activity of new struggles in the person.

Familial algorithm uses basic familial operators to bring forth new population of high fittingness. Reproduction operator produces new coevals in the increasing figure from the old coevals. Crossover indiscriminately selects two persons as parents and combines them to bring forth two new persons. Mutation selects two persons as parents and alters some parts of parents to make new coevals.

The Search is directed by fittingness map. The nonsubjective map is used to restrict the figure of persons with unfeasibilities. Filtering algorithm is used to filter impracticable solutions from executable solution. Genetic fix converts impracticable solution to executable solution by changing it every bit small as possible.


Sadaf Naseem Jat et Al. [ 9 ] proposed a familial algorithm with a guided hunt scheme and a local hunt technique. The guided hunt scheme is used to make offspring into the population based on a information construction that shops information extracted from old good persons. The local hunt technique is used to better the quality of persons. In GSGA, low-level formatting of the population by indiscriminately making each person via delegating a random clip slot for each event harmonizing to a unvarying distribution and using the fiting algorithm to apportion a room for the event is done. Then, a local hunt ( LS ) method is applied to each member of the initial population. The LS method uses three vicinity constructions to travel events to clip slots and so uses the fiting algorithm to apportion suites to events and clip slots.

After the low-level formatting of the population, a information construction ( MEM ) is constructed, which shops a list of room and clip slot braces ( R, T ) for all the events with nothing punishments ( no hard and soft misdemeanor at this event ) of selected persons from the population. After that, this MEM can be used to steer the coevals of offspring for the undermentioned coevalss.

The MEM information construction is reconstructed on a regular basis, e.g. , every n coevals. In each coevals of GSGA, one kid is foremost generated either by utilizing MEM or by using the crossing over operator. After that, a mutant operator followed by the LS method will better kid. Finally, the worst member in the population is replaced with the freshly generated child single. The loop continues until one expiration status is reached.


Legierski et Al. [ 31 ] and Ho Sheau Fen et Al. [ 10 ] proposed a method which deals with an effectivity of Constraint Programming ( CP ) for scheduling job peculiarly for timetabling. The chief advantage of the CP is declarativity, a straightforward statement of the restraints serves as a portion of the plan and it is compared with local hunt processs. The CP ‘s chief characteristics are constraint extension and distribution. The restraint programming linguistic communication Mozart-Oz allows to show complex restraints and create complicated, custom-tailored distribution scheme, which is needed for work outing timetabling job. Incorporation of the local hunt into restraint scheduling is needed as a method for optimisation.

This attack uses constraints-based concluding to seek for the best penchant value bsed on the pupil capacity for each talk.

It automatically removes from the sphere of variables all values that do non carry through restraints. Constraint extension does non take all values that are in struggle with all restraints and its public presentation is measured as a tradeoff between figure of removed values and executing clip. In the most instances constraint extension does non take to the solution ( as it is besides depicted in above-named illustration ) . Therefore, there is ever added to constraint extension a distribution connected with hunt.

Distribution is based on incorporation of an extra restraint, frequently it is a restraint stating about equality of one variable to one value ( one of the undertaking of the distribution is to take a proper variable and a value ) . When it is done a consistence is checked and there are three possibilities: a solution is found, variables spheres are narrowed, but there is no alone solution, so distribution is made with another variable, the extra restraint is inconsistent with other restraints, so the backtrack is made and from chosen variable sphere a chosen value is removed. This procedure is made in iterative manner and is called hunt. Search is responsible for halting after happening ; first solution or some figure of solution or all solution. Search forms a hunt tree, where each node is a province of variables.


Spyros Kazarlis et Al. [ 11 ] proposed a method based on Genetic Algorithms ( GAs ) , to work out university class timetabling jobs is presented. This method incorporates GAs utilizing an indirect representation based on event precedences, Micro-GAs and heuristic local hunt operators in order to undertake a existent universe timetabling job.


S.F.H Irene et Al. [ 12 ] proposed atom drove optimisation which is a computational method that optimizes a job by iteratively seeking to better campaigner solutions. Each solution is addressed here as atom. The campaigner solutions move around the hunt infinite and finds best place for each campaigner solution and overall best place harmonizing to fittingness map. The procedure is repeated when new places are discovered so that candidate solution can suit in new place, which is the best.


S.F.H Irene et Al. [ 13 ] presented a method which is a combination of atom drove optimisation and local hunt to efficaciously seek the solution infinite in work outing university class timetabling job. Three different types of dataset scope from little to big are used in formalizing the algorithm. The experiment consequences show that the combination of atom drove optimisation and local hunt is capable to bring forth executable timetable with less computational clip, comparable to other established algorithms.


S.F.H Irene et Al. [ 14 ] presented a method which focuses on developing a intercrossed algorithm consisting of a atom drove optimisation and constraint-based logical thinking in work outing university timetabling job in bring forthing a executable and near-optimal solution. The consequence is compared against standard atom drove optimisation and intercrossed atom drove optimization-local hunt.


Khang Nguyen et Al. [ 15 ] proposed a method which is concerned with the development of a new intercrossed metaheuristic attack for work outing a pratical university class timetabling job. It is a combination of Harmony Search ( HS ) algorithm and the Bees algorithm.


A.Araisa Mahiba et Al. [ 16 ] proposed a new method of Genetic algorithm with Search Bank Strategies viz. local, guided and taboo hunts. Local Search is used to increase the progeny or solutions. Guided Search is used to contract the solutions by utilizing events data Structure. Tabu Search is used to take the used solutions.


NguyenBa Phuc et Al. [ 17 ] presented a method, which combines the optimisation capablenesss of a familial algorithm with bees algorithm. The chief end is to happen the lower limit of optimisation jobs.


Meysam Shahvali Kohshori et Al. [ 18 ] presented a fuzzed familial algorithm ( GA ) with a local hunt for work outing university class timetabling job ( UCTP ) . The local hunt is applied to utilize its exploitative hunt ability to better the hunt efficiency of the proposed GA. Fuzzy logic is used to mensurate misdemeanor of soft restraints in fittingness map to cover with built-in unsteadily and vagueness involved in existent life informations.


Mohammed Azmi Al-Betar et Al. [ 19 ] proposed a memetic computer science technique that is designed for UCTP, called the loanblend harmoniousness hunt algorithm ( HHSA ) . In HHSA, the harmoniousness hunt algorithm ( HSA ) which is a metaheuristic population-based method, has been hybridized by: 1 ) hill mounting, to better local development ; and 2 ) a global-best construct of atom drove optimisation to better convergence.


Mohammed Azmi Al-Betar et Al. [ 20 ] proposed a MultiSwap Algorithm which contributes to major betterment in treating the room operations. This is achieved by uniting the MultiSwap algorithm with the graph colourising heuristic method to fulfill the difficult restraints and with the local search-based algorithms to minimise the misdemeanors of the soft restraints. The MultiSwap is incorporated with local hunt algorithm to minimise the misdemeanor of soft restraints.


Ehsan Alirezaei et Al. [ 21 ] proposed a intercrossed algorithm for work outing multinomial with fulfilling all job restraints. This attack has two consecutive stages with overall parallel execution ; it has a chief algorithm that employed prescheduling construction and overall high public presentation.


J-F. Cordeau et Al. [ 22 ] proposed a method which uses Iterated local hunt. Local hunt methods build a flight in constellation infinite, which leads from an initial solution to a local optimum, where local hunt Michigans ( no improving neighbours are available ) . If local optima present sub-optimal solutions, local hunt demands to be modified to go on the hunt beyond local optimality.

A simple alteration consists of repeating calls to the local hunt modus operandi, each clip get downing from a different initial constellation. This is called perennial local hunt, and implies that the cognition obtained during the old local hunt stages is non used. Learning implies that the old history, for illustration, the memory about the antecedently found local lower limit is mined to bring forth better and better get downing points for local hunt. Iterated Local Search is based on constructing a sequence of locally optimum solutions by:

unhinging the current local lower limit ;

Using local hunt after get downing from the modified solution.

The disturbance strength has to be sufficient to take the flight to a different attractive force basin taking to a different local optimum.


Legierski et Al. [ 23 ] proposed a system that selects a heuristic, from a aggregation of solutions, based on similarity of the job, its informations set, and nonsubjective maps. This attack works under the premise that similar jobs are solved most efficaciously by similar heuristic attacks. Case-based logical thinking is a problem-solving paradigm that in many respects is basically different from other major AI attacks.

Alternatively of trusting entirely on general cognition of a job sphere, or doing associations along generalized relationships between job forms and decisions, CBR is able to use the specific cognition of antecedently experienced, concrete job state of affairss ( instances ) . A new job is solved by happening a similar yesteryear instance, and recycling it in the new job state of affairs. A 2nd of import difference is that CBR besides is an attack to incremental, sustained acquisition, since a new experience is retained each clip a job has been solved, doing it instantly available for future jobs.


M. R. Malim et Al. [ 24 ] presented a method which uses three algorithms viz. clonal choice, immune web and negative choice.

Clonal choice algorithm uses three operators choice, cloning, and mutant. A timetable is indiscriminately selected to clone. Number of ringers will be equal to half of the population. Almost all the ringer will undergo mutant to bring forth new solution. Out of the new solutions, high affinity timetable will be used to replace old low affinity timetable. The procedure of cloning, mutant and choice will be repeated until the standards are met.

Immune Network Algorithm uses two operators viz. cloning and mutant. All timetables are selected to bring forth ringer. Each timetable will bring forth one ringer. All ringer will undergo mutant to bring forth executable solution. Timetable with high stimulation will be selected to bring forth new solution in the following coevals. The procedure of cloning and mutant will be repeated until the standards are met.

Negative Selection Algorithm uses operators viz. negative omission ( baning ) , cloning and mutant. In this, timetables in current population are determined by fittingness map. If the fittingness of the timetable is greater than or equal to the mean fittingness, it will be deleted from the current population. The staying timetables will undergo cloning and mutant. Again, mutated timetables will undergo fitness map. If the fittingness of the timetable is less than or equal to the mean fittingness, it will be added to the new population for the following coevals.


Der-Fang Shiau et Al. [ 25 ] proposed a method which focuses on the fresh meta-heuristic algorithm that is based on the rules of atom drove optimisation ( PSO ) . The algorithm includes some characteristics: planing an ‘absolute place value ‘ representation for the atom, leting teachers that they are willing to talk based on flexible penchants such as their preferable yearss and clip periods, the maximal figure of teaching-free clip periods and the lecture format ( back-to-back clip periods or separated into different clip periods ) and using a fix procedure for all impracticable timetables.

Furthermore, in the original PSO algorithm, particles search solutions in a uninterrupted solution infinite. Since the solution infinite of the class programming job is distinct, a local hunt mechanism is incorporated into the proposed PSO in order to research a better solution betterment.


Nguyen Tan Tran Minh Khang et Al. [ 26 ] presented the Bees Algorithm to work out a extremely constrained real-world university timetabling job. It is inspired by the scrounging behavior of Apis melliferas and performs a sort of vicinity hunt combined with random hunt to enable it to turn up the planetary optimum. A figure of parametric quantities controls the algorithm.


Patrick De Causmaecker et Al. [ 27 ] presented a attack in which the first phase reduces the figure of topics through the debut of new constructions that are called as ‘pillars ‘ . The following phase involves a metaheuristic hunt that attempts to work out the restraints one by one, alternatively of seeking to happen a solution for all the restraints at one time.


The timetabling job consists of scheduling a sequence of talks between instructors and pupils in a prefixed period of clip ( typically a hebdomad ) , fulfilling a set of restraints of assorted types. A big figure of discrepancies of the timetabling job have been proposed in the literature, which differ from each other based on the type of establishment involved ( university or school ) and the type of restraints. This job that has been traditionally considered in the operational research field, has late been tackled with techniques belonging to Artificial Intelligence ( e.g. , Genetic Algorithms, Tabu Search, and Constraint Satisfaction ) . In this paper, we have surveyed different types of algorithms used for undertaking Course Timetabling Problem. A comparative analysis has been made with the public presentation metrices which are tabulated with assorted parametric quantities along with virtues, demerits, issues to be addressed and so on. To a great extent, the bing timetabling algorithm does non see fittingness value, Instance type, Execution clip and the maximal figure of free timeslots allocated. Therefore, there is a demand to implement a Course Timetabling algorithm that can heighten the optimality and fittingness to acquire important public presentation sweetenings.