A GENETIC ALGORITHM FOR POLYTECHNIC TIME TABLING (EEPIS Timetabling Case Study)

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1 A GENETIC ALGORITHM FOR POLYTECHNIC TIME TABLING (EEPIS Timetabling Case Study) Son Kuswadi 1, Achmad Basuki 1,Mohammad NUH 1,2, Osami Saito 3 1 Electronic Engineering Polytechnic Institute of Surabaya 2 Graduate Program, Electrical Engineering Department Institut Teknologi Sepuluh Nopember Kampus ITS Keputih Sukolilo Surabaya 60111, Indonesia {sonk, basuki, nuh}@eepis-its.ac-id.net 3 Department of Mechanical and Electronic Engineering, Chiba University 1-33 Yayoi-cho Inage-ku CHIBA 263, Japan saito@cute.te.chiba-u.ac.jp Abstract Timetabling of polytechnic case study using genetic algorithm will be presented. The proposed modified GA operators reflect the distinctive aspects of the polytechnic education compared with university. The both hard and soft constraints almost same with the university case, except its capacity constraint because polytechnic uses packet system, instead of credit system as university did. The proposed algorithm is verified through several experiments using some mutation probability values. KEYWORDS: genetic algorithms, time-tabling, polytechnics 1. Introduction Timetabling problem is could be solved by Genetic Algorithm quite successfully [1]. This class of problem is concerning to the optimization process of University timetabling, including lecture and laboratory assignment, examination schedule, and seminar. Optimization process is done in such a way that some constraints or penalties such as clashes (i.e. two teachers teach in the same room in the same time) could be minimized. The first successful GA-based timetabling application was proposed by Colorni et.al. [3]. They built the schedule of the teacher in an Italian high school. It was shown that a GA was as good as Tabu Search, and better than simulated annealing, at finding teacher schedules satisfying a number of hard and soft constraints. However, a study conducted by Peter Roos et.al. suggest that simulated annealing and stochastic hill-climbing generally seems a good choice in time-tabling, better than GA. In certain cases, though, the combination of acceptable solution quality and the delivery of many usefully distinct solutions make the GA the better choice [9]. E. Burke et.al. propose a specialized recombinative operators (using so-called late and spread operator) to enhance the time-tabling optimization result [7], meanwhile B. Paechter et.al. suggest the use of local search to improve the solution [8]. At its simplest, time-tabling is the problem of scheduling a set of events (for example: exams, lectures, tutorials and lab works) to specific time slots such that no person nor resources is expected to be in more than one location at the same time and that there is enough space available in each location for the number of people expected to be there [7]. If there are m events and n timeslots, then the number of ways associating events with timeslots is n m. This paper present the timetabling problem solving for polytechnics, in this case EEPIS as the test bed. This problem slightly different with the university case as reported in [2] - [9], because in polytechnic a packet system is used, instead of the credit system as implemented in university. It means that in polytechnic timetabling problem, the capacity constraint is irrelevant because in every event, always certain fix number of students attend the class. Another distinctive point is for the lecture there are two possibility: 2 hours/week or 4 hours / week. For the first case, it should be assigned in successive timeslot. For the later case, should be separated into two different successive timeslots, 2 hours/week each. Also, because of the nature of the polytechnic education system, students should attend lot of laboratory works every week. Time assignment of lab work is 3 or 4 hours/week and it should be assigned into one successive timeslots.

2 Additional constraints that added to the problem statement was to let the lecturers to choose their appropriate timeslot in order to provide more flexible lecture or laboratory time assignment. This feature is needed because every lecturer may have a special request to teach or not teach in certain timeslot because of any acknowledged official reason. 2. Representations and Algorithm Representation. For the timetabling problem, a chromosome is a vector symbols consist of all possible events and stored in several genes. Each gene location, or locus, within the chromosome structure is the events for each class (Note that in the polytechnic as we mention earlier uses a packet system, not credit system, therefore the students in the class always same for each semester). For example, the gene of II EB class (it means a second year B class of electronic engineering department) will consist of events from Monday to Saturday, each consists of 10 study hours everyday. See Fig II TA CLASS M T W T F S 1 II EB CLASS 2 M T W T F S Course: Automatic Control Room: HH-103 Lecturer: Son Kuswadi Gene n Gene 2 Gene 1 Fig. 1 The genes and chromosome for polytechnic timetabling There are 15 classes in total at EEPIS, 6 days lecture in a week and 10 lecture hours a day. Therefore, for every chromosome will consists of 900 (15x6x10) genes. Initial population. The initial timetables are produced from the chromosomes in the following manner: the genes are generated randomly, meaning that the events are selected randomly and stored in the timeslots in the chromosome until one chromosome completely established. Even though the events are randomly generated, there is a set of rules to generate the genes: Theoretical subjects that are more than 3 hours/week should be divided into two timeslots, in order to avoid long-and-boring lecture hours. In one day should consists of both theoretical subject and practical/lab work, to balancing the occupation of classroom and labs; and also to avoid a mental saturation of students (event-spread constraints) The lab work timeslots should be determined first before the theoretical subjects to avoid incomplete chromosomes. The lab work usually need 3 until 4 hours and should not be in different timeslots, hence because the total genes in chromosome are fix (900 genes), it is possible that some lab works are not selected because the vacant timeslots are not available. Fitness function. A satisfactory solution in time-tabling simply to have fitness inversely proportional to the number of constraints violated in a time-table with each instance of a violated constraint weighted according to how important or not it is to satisfy it [5]. The weight of specific penalty is determined as follows: If there is clashes for the lecture (edge constraints), the weight a i is set to 1, and 2 for lab works (denoted by b i ) If the lecturer assigned in more than one place one timeslots, the c i weight is set to 1. If the lecturer request on timeslot is not fulfilled set the weight d i according the level of lecturer. For example for the EEPIS director and vice director d i is set to be 1, 0.5 for head of departments, 0.25 for ordinary lecturer. If the location of lab works is not in laboratory and the lecture is not in the classroom set the weight e i to 1. Therefore, the simple fitness function to be used is: f(k)=4500-(σa i +Σb i +Σc i +Σd i +Σe i ) (1) Where k is the chromosome number, and 4500 is the possible maximum fitness value (=900

3 genes x the maximum penalty for each genes, 5). Selection. A well-known roulette wheel approach was adopted to select the parents to be mated [13]. As such, more fit chromosomes more likely to be selected as parents. Crossover. As stated before, the lecture usually assigned for 2(two) successive timeslots, and the lab work either 3(three) or 4(four) If the selected genes are in the same successive timeslots either different or same subjects, exchange the genes. If one of the selected gene from the first parent is empty event but same amount of timeslot with one of second parent, put the other one selected gene of the second parent on it. To avoid the event or subject Fig. 2 Test result for mutation probability Fig. 3 Test result for mutation probability Fig. 4 Test result for 0.01 mutation probability Fig. 5 Test result for 0.04 mutation probability successive timeslots. It is different with university case especially in developed countries; the lecturer usually put into only one timeslot. As consequence, the crossover mechanism should consider the above requirement. Crossover used here is not one-cut-point method [10], which randomly selects one cut-point and exchanges the right parts of two parents to generate offspring but the exchange only happen on the selected genes of each parent in the same point location which it determined randomly. Note that the crossover mechanism of polytechnic time-tabling is different with the common GA problem because its requirement to place the certain lecture and lab work on successive timeslot as stated above. The proposed crossover mechanism is determined as follows: will be assigned twice in the first parent, select one of gene of the first parent, which contain the same subject with the selected gene of the second parent and put it on the same location of second parent. If the selected genes are in different successive timeslots, the gene exchange is discarded. Mutation. The mutation operator used here is the simple one; the randomly selected gene for mutation is moved to the empty timeslot. Another possibilities include VDM (Violation Directed Mutation) [5] and a method by replacing the gene with another one in the same chromosome, chosen at random [8]. 3. Experiments Experiments have been carried out under the following conditions:

4 Population size 100 Number of generation 200 Crossover probability 0.5 Mutation probability, varied between to 0.1 Population strategy A generation gap population was used, instead of steady state one as proposed by Paechter et.al. [8]. Software: Turbo Pascal and Microsoft Foxpro (used for comparison) 4. Results and Discussions The implementation of algorithm uses both Turbo Pascal and Microsoft Foxpro. As expected, Turbo Pascal need only 15 minutes for every run, meanwhile Microsoft Foxpro need 2 to 3 hours. Fig. 2 shows the run for mutation probability Hence, it seems that for the low mutation probability the optimization is trapped into the local optimum point. Fig. 3 shows the run for mutation probability As shown in the figure, the accepted optimum point was reached only several generations. The fitness value is 4495; it means only 5 points below the global optimum. After checked, the only soft constraints and requests that are not fulfilled and could be improved using a special algorithm and manual replacement as well. Another test result shows in Fig. 4 and 5 for 0.01 and 0.04 mutation probability respectively. It shows that for both mutation probabilities the optimization results were not good. Fig. 6 shows the experimental results of fitness values as a function of mutation probabilities for generic and elitist model. 5. Conclusions The application of genetic algorithm to the polytechnic time-tabling is proposed. Several modification of operator such as crossover and mutation is proposed. The experimental result suggests that the proposed method could produce the acceptable optimum efficiently. 6. Acknowledgements This work was supported in part by a grant from University Research for Graduate Education (URGE) Project (Graduate Team Research Grant, Batch IV, 1998/1999) and EEPIS Research Grant 1998/1999. Fig. 6 The experimental results of fitness values as a function of mutation probabilities for generic and elitist model References: [1].., The Hitch-Hiker s Guide to Evolutionary Computation, ftp://rtfm.mit.edu/pub/usenet/news. answers/ai_faq/genetic/ [2] Abramson, Abela, A parallel genetic algorithm for solving the school time tabling problem, Technical Report, Division of I.T., C.S.I.R.O, April 1991 [3] Colorni A., M. Dorigo and V. Maniezzo, Genetic algorithms and highly constrained problems: The Time-Table Case, Proceeding of The First International Workshop on Parallel Problem Solving from Nature, Dortmund, Germany, Lecture Note in Computer Science 496, Springer-Verlag, 1990, pp Also available from dorigo/conferences/ic.01-pssn1.ps.gz [4] Corne, D., Fang H.L., C. Mellish, Solving the modular exam scheduling problem with Genetic Algorithms, Proceeding of 6 th International Conference on Industrial and Engineering Applications of Artificial Intelligence & Expert System, 1993 [5] Corne D., Peter Ross, H.L., Fang, Fast practical evolutionary time-tabling, in T.C. Fogarty, Evolutionary Computing, AISB Workshop, Leed, UK, Selected Papers, Springer-Verlag, Berlin, 1994, pp [6] Paechter B., Optimising a presentation time table using Evolutionary Algorithms,, in T.C. Fogarty, Evolutionary Computing, AISB Workshop, Leed, UK, Selected Papers, Springer- Verlag, Berlin, 1994, pp [7] Burke E., D. Elliman and R. Weare, Specialised recombinative operators for time-tabling problems, in, in T.C. Fogarty, Evolutionary Computing,

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