Abstract
This study presents an investigation of enhancing the capability of the Scatter Search (SS) metaheuristic in guiding the search effectively toward elite solutions. Generally, SS generates a population of random initial solutions and systematically selects a set of diverse and elite solutions as a reference set for guiding the search. The work focuses on three strategies that may have an impact on the performance of SS. These are: explicit solutions combination, dynamic memory update, and systematic search re-initialization. First, the original SS is applied. Second, we propose two versions of the SS (V1 and V2) with different strategies. In contrast to the original SS, SSV1 and SSV2 use the quality and diversity of solutions to create and update the memory, to perform solutions combinations, and to update the search. The differences between SSV1 and SSV2 is that SSV1 employs the hill climbing routine twice whilst SSV2 employs hill climbing and iterated local search method. In addition, SSV1 combines all pairs (of quality and diverse solutions) from the RefSet whilst SSV2 combines only one pair. Both SSV1 and SSV2 update the RefSet dynamically rather than static (as in the original SS), where, whenever a better quality or more diverse solution is found, the worst solution in RefSet is replaced by the new solution. SSV1 and SSV2 employ diversification generation method twice to re-initialize the search. The performance of the SS is tested on three benchmark post-enrolment course timetabling problems. The results had shown that SSV2 performs better than the original SS and SSV1 (in terms of solution’s quality and computational time). It clearly demonstrates the effectiveness of using dynamic memory update, systematic search re-initialization, and combining only one pair of elite solutions. Apart from that, SSV1 and SSV2 can produce good quality solutions (comparable with other approaches), and outperforms some approaches reported in the literature (on some instances with regards to the tested datasets). Moreover, the study shows that by combining (simple crossover) only one pair of elite solutions in each RefSet update, and updating the memory dynamically, the computational time is reduced.
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References
Abdullah S, Turabieh H (2008) Generating university course timetable using genetic algorithms and local search. In: Proceedings of the 3rd international conference on convergence and hybrid information technology (ICCIT 2008). IEEE Comput Soc, Los Alamitos, pp 254–260
Abdullah S, Burke EK, McCollum B (2007) A hybrid evolutionary approach to the university course timetabling problem. In: Proceedings of the IEEE congress on evolutionary computation (CEC 2007) pp 1764–1768. ISBN 1-4244-1340-0
Abdullah S, Turabieh H, McCollum B, McMullan P (2010a) A hybrid metaheuristic approach to the university course timetabling problem. J Heuristics. doi:10.1007/s10732-010-9154-y
Abdullah S, Shaker K, McCollum B, McMullan P (2010b) Dual sequence simulated annealing with round-robin approach for university course timetabling. In: Cowling P, Merz P (eds) EVOCOP 2010. LNCS, vol 6022. Springer, Heidelberg, pp 1–10
Al-Betar M, Khader A, Liao I (2010) A harmony search with multi-pitch adjusting rate for the university course timetabling. In: Geem, ZW (ed) Recent advances in harmony search algorithm. SCI, vol 270. Springer, Heidelberg, pp 147–161
Atsuta M, Nonobe K, Ibaraki T (2008) ITC2007 track 2: an approach using general CSP solver. http://www.cs.qub.ac.uk/itc2007 [20 December 2010]
Blum C, Roli A (2008) Hybrid metaheuristics: an introduction, studies in computational intelligence. In: Blum C, Aguilera MJB, Roli A, Samples M (eds) Hybrid metaheuristics: an emerging approach to optimization. SCI, vol 114. Springer, Berlin, pp 1–30
Burke EK, Bykov Y, Newall JP, Petrovic S (2003) A time-predefined approach to course timetabling. Yugosl J Oper Res 13(2):139–151
Burke EK, Curtois T, Qu R, Berghe GV (2010) A scatter search approach to the nurse rostering problem. J Oper Res Soc 6:1667–1679
Cambazard H, Hebrard E, O’Sullivan B, Papadopoulos A (2012) Local search and constraint programming for the post enrolment-based course timetabling problem. Ann Oper Res 194(1):111–135. Url:http://dx.doi.org/10.1007/s10479-010-0737-7
Campos V, Laguna M, Martí R (2005) Context-independent scatter search and tabu search for permutation problems. INFORMS J Comput 17(1):111–122. ISSN 0899-1499
Campos V, Corberan A, Mota E (2008) A scatter search algorithm for the split delivery vehicle routing problem. In: Fink A, Rothlauf F (eds) Advances in computational intelligence. SCI, vol 144. Springer, Berlin, pp 137–152
Ceschia S, Di Gaspero L, Schaerf A (2011) Simulated annealing approach to post-enrolment course timetabling problem. J Comput Oper Res. doi:10.1016/j.cor.2011.09.014
Chiarandini M, Birattari M, Socha K, Rossi-Doria O (2006) An effective hybrid algorithm for university course timetabling. J Sched 9(5):403–432
Chiarandini M, Fawcett C, Hoos HH (2008) A modular multiphase heuristic solver for post enrollment course timetabling. In: Proceedings of the 7th international conference on the practice and theory of automated timetabling (PATAT 2008)
Cotta C (2004) Scatter search and memetic approaches to the error correcting code problem. In: Gottlieb J, Raidl GR (eds) EvoCOP 2004. LNCS, vol 3004. Springer, Berlin, pp 51–61
Di Gaspero L, Schaerf A (2006) Neighborhood portfolio approach for local search applied to timetabling problems. J Math Model Algorithms 5(1):65–89
Dowsland KA, Thompson JM (2008) An improved ant colony optimisation heuristic for graph colouring. Discrete Appl Math 156:313–324
Eiben AE, Smith JE (2003) Introduction to evolutionary computing, 1st edn. Springer, Berlin. Corrected 2nd printing, 2007. ISBN 978-3-540-40184-1
Engin O, Kahraman Y, Yilmaz MK (2009) A scatter search method for multiobjective fuzzy permutation flow shop scheduling problem: a real world application. In: Chakraborty UK (ed) Comput intel in flow shop and job shop sched. SCI, vol 230. Springer, Berlin, pp 169–189
Even S, Itai A, Shamir A (1976) On the complexity of timetable and multi commodity flow problem. SIAM J Comput 5:691–703
Glover F (1977) Heuristics for integer programming using surrogate constraints. Decis Sci 8:156–166
Glover F (1997) A template for scatter search and path relinking. In: Hao JK, Lutton E, Ronald E, Schoenauer M, Snyers D (eds.) LNCS, vol 1363, pp 13–54
Glover F, Laguna M, Martí R (2002) Scatter search. In: Ghosh A, Tsutsui S (eds) Theory and applications of evolutionary computation: recent trends. Springer, Berlin, pp 519–529
Glover F, Laguna M, Martí R (2004) Scatter search and path relinking: foundations and advanced designs. In: Onwubolu G, Babu BV (eds) New optimization techniques in engineering. Springer, Berlin
Greistorfer P (2000) On the algorithmic design in heuristic search. In: European conference on operational research (EURO XVII), Budapest, Ungarn, pp 16–19
Greistorfer P, VoßS (2005) Controlled pool maintenance in combinatorial optimization. In: Rego C, Alidaee B (eds) Conference on adaptive memory and evolution: tabu search and scatter search, University of Mississippi. Kluwer Academic, Dordrecht, pp 387–424. Chap 18
Jat SN, Yang S (2010) A hybrid genetic algorithm and tabu search approach for post enrolment course timetabling. J Sched. doi:10.1007/s10951-010-0202-0
Kostuch P (2005) The university course timetabling problem with a 3-phase approach. In: Burke EK, Trick M (eds) The practice and theory of automated timetabling V (PATAT 2004). LNCS, vol 3616. Springer, Berlin, pp 109–125
Laguna M, Marti R (2003) Scatter search: methodology and implementations in C. Kluwer Academic, Boston
Laguna M (2009) Scatter search and path relinking. In: Ehrgott M et al. (eds) EMO 2009. LNCS, vol 5467. Springer, Berlin, p 1
Landa-Silva D, Obit JH (2008) Great deluge with nonlinear decay rate for solving course timetabling problems. In: Proceedings of the 2008 IEEE conference on intelligent systems (IS 2008). IEEE Press, New York, pp 8.11–8.18
Lewis R (2008) A survey of metaheuristic-based techniques for university timetabling problems. OR Spektrum 30:167–190
Lewis R (2010) A time-dependent metaheuristic algorithm for post enrolment-based course timetabling. J Ann Oper Res. doi:10.1007/s10479-010-0696-z
Lewis R, Paechter B, McCollum B (2007a) Post enrolment based course timetabling: a description of the problem model used for track two of the second international timetabling competition. In: Cardiff working papers in accounting and finance A2007-3, Cardiff Business School, Cardiff University, Wales. ISSN 1750-6658
Lewis R, Paechter B, Rossi-Doria O (2007b) Metaheuristics for university course timetabling. In: Dahal K, Chen Tan K, Cowling P (eds) Evolutionary scheduling. Studies in computational intelligence, vol 49. Springer, Berlin, pp 237–272
Maenhout B, Vanhoucke M (2006) New computational results for the nurse scheduling problem: a scatter search algorithm. In: Gottlieb J, Raidl GR (eds) EvoCOP 2006. LNCS, vol 3906. Springer, Berlin, pp 159–170
Mansour N, Isahakian V, Ghalayini I (2009) Scatter search technique for exam timetabling. Applied intelligence. Springer, Berlin
Martí R, Laguna M, Campos V (2004) Scatter search vs. genetic algorithms: an experimental evaluation with permutation problems. In: Rego C, Alidaee B (eds) Metaheuristic optimization via adaptive memory and evolution: tabu search and scatter search. Kluwer Academic, Dordrecht, pp 263–282. Chap 12
Marti R, Laguna M, Glover F (2006) Principles of scatter search. Eur J Oper Res 169:359–372
Mayer A, Nothegger C, Chwatal A, Raidl G (2008) Solving the post enrolment course timetabling problem by ant colony optimization. In: Proceedings of the 7th international conference on the practice and theory of automated timetabling (PATAT 2008)
Metaheuristics Network (2001). The official website: http://www.idsia.ch/Files/ttcomp2002/. Accessed in 20 June 2011
Moscato PA, Cotta C (2007) Memetic algorithms. In: Handbook of approximation algorithms and metaheuristics. Taylor & Francis, Boca Raton, pp 27-1–27-12
Müller T (2008) ITC2007 solver description: a hybrid approach. In: Proceedings of the 7th international conference on the practise and theory of automated timetabling (PATAT 2008)
Petrovic S, Burke EK (2004) University timetabling. In: Leung J (ed) Handbook of scheduling: algorithms, models and performance analysis. CRC Press, Boca Raton. Chap 45
Qu R, Burke EK, McCollum B, Merlot LTG, Lee SY (2009) A survey of search methodologies and automated system development for examination timetabling. J Sched 12:55–89
Resende MGC, Ribeiro CC, Glover F, Marti R (2010) Scatter search and path-relinking: fundamentals, advances, and applications. In: Gendreau M, Potvin J-Y (eds) Handbook of metaheuristics, 2nd edn. Springer, Berlin.
Rossi-Doria O, Samples M, Birattari M, Chiarandini M, Dorigo M, Gambardella LM, Knowels J, Manfrin M, Mastrolilli M, Paechter B, Paquete L, Stultzle T (2003) A comparison of the performance of different metaheuristics on the timetabling problem. In: Burke EK, De Causmaecker P (eds) PATAT 2002. LNCS, vol 2740. Springer, Heidelberg, pp 329–354
Sabar NR, Ayob M (2009) Examination timetabling using scatter search hyper-heuristic. In: The 2nd data mining and optimization conference (DMO 2009), vol I, pp 127–131
Sabar R, Ayob M, Kendall G, Qu R (2011) A honey-bee mating optimization algorithm for educational timetabling problems. Eur J Oper Res. doi:10.1016/j.ejor.2011.08.006
Shaker K, Abdullah S (2010) Controlling multi algorithms using round robin for university course timetabling problem. In: Zhang Y et al. (eds) DTA/BSBT 2010. CCIS, vol 118. Springer, Heidelberg, pp 47–55
Socha K, Knowles J, Samples M (2002) A max-min ant system for the university course timetabling problem. In: Dorigo M, Di Caro GA, Sampels M (eds) Ant algorithms 2002. LNCS, vol 2463. Springer, Heidelberg, pp 1–13
Socha K (2003) The influence of run-time limits on choosing ant system parameters. In: Cantu-Paz E et al. (eds) GECCO 2003. LNCS, vol 2723. Springer, Berlin, pp 49–60
Socha K, Samples M, Manfrin M (2003) Ant algorithm for the university course timetabling problem with regard to the state-of-the-art. In: Proceedings of the 3rd European workshop on evolutionary computation in combinatorial optimisation, Essex, UK. LNCS, vol 2611. Springer, Berlin, pp 334–345
Talbi EG (2002) A taxonomy of hybrid metaheuristics. J Heuristics 8:541–564
Talbi EG (2009) Metaheuristics: from design to implementation. Wiley, New York
Turabieh H, Abdullah S (2009) Incorporating tabu search into memetic approach for enrolment-based course timetabling problems. In: The 2nd data mining and optimization conference (DMO 2009), pp 122–126
Turabieh H, Abdullah S, McCollum B (2009) Electromagnetism-like mechanism with force decay rate great deluge for the course timetabling problem. In: Wen P, Li Y, Polkowski L, Yao Y, Tsumoto S, Wang G (eds) RSKT 2009. LNCS, vol 5589. Springer, Heidelberg, pp 497–504
Turabieh H, Abdullah S, McCollum B, McMullan P (2010) Fish swarm intelligent algorithm for the course timetabling problem. In: Yu J et al. (eds) RSKT 2010. LNAI, vol 6401. Springer, Heidelberg, pp 588–595
Yang S, Jat SN (2011) Genetic algorithms with guided and local search strategies for university course timetabling. IEEE Trans Syst Man Cybern, Part C, Appl Rev 41(1):93–106
Acknowledgements
The authors wish to thank Ministry of Higher Education (Malaysia) for supporting this work under the Fundamental Research Grant Scheme (FRGS) no. (FRGS/1/2012/SG05/UKM/02/11).
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Jaradat, G., Ayob, M. & Ahmad, Z. On the performance of Scatter Search for post-enrolment course timetabling problems. J Comb Optim 27, 417–439 (2014). https://doi.org/10.1007/s10878-012-9521-8
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DOI: https://doi.org/10.1007/s10878-012-9521-8