Abstract
A constrained self-adaptive harmony search algorithm (CSAHS) with 2-opt swapping (CSAHS-2opt) for driver scheduling problem of university shuttle bus (DSPUSB) was proposed in this study. In generating a schedule, there are some constraints that should be catered to obtain an optimum result. In DSPUSB, fairness of task distribution among drivers is one of the main issues that are very crucial and can affect the performance and quality of services. Therefore, to maximise the fairness, the violation of soft constraints for DSPUSB including shift and route should be minimised. CSAHS with 2-opt swapping was proposed focusing on minimising soft constraint violation. In standard harmony search (HS), the value of distance bandwidth (BW) parameter was static, while in this study the BW was dynamically changed and determined based on the current solution of each driver every week. Here, a set of distance BW value was formed based on shift constraint. In each iteration, the BW values were often changed and randomly chosen within the set, whereas the 2-opt swapping normally used in travelling salesman problem was applied for route constraint based on some rules. These improvements are capable of reducing the repetition task that leads to fairness issue. The result demonstrated that CSAHS-2opt gave better solutions compared with standard HS, improved HS and parameter-adaptive HS.
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References
Geem, Z.W.; Kim, J.H.; Loganathan, G.V.: A new heuristic optimization algorithm: harmony search. Simulation 76(2), 60–68 (2001)
Mitchell, M.: An Introduction to Genetic Algorithms (Complex Adaptive Systems), p. 221. MIT Press, Cambridge (1998)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning, p. 412. Addison-Wesley Longman Publ. Co. Inc., Boston (1989)
Holland, J.H.: Genetic algorithms and adaptation. Springer 16, 317–333 (1984)
Abdel-raouf, O.: A survey of harmony search algorithm. Int. J. Comput. Appl. 70(28), 17–26 (2013)
Geem, Z.W.; Tseng, C.L.; Park, Y.: Harmony Search for Generalized Orienteering Problem: Best Touring in China, Advances in Natural Computation. ICNC 2005. Lecture Notes in Computer Science, vol. 3612. Springer, Berlin, Heidelberg (2005)
Jasmi, M.I.; Rahman, A.F.N.A.; Abas, Z.A.; Shibghatullah, A.S.: Optimized coating design of energy saving glass using binary harmony search for better transmission signal. Int. J. Comput. Sci. Inf. Secur. 14(8), 436–443 (2016)
Forsati, R.; Mahdavi, M.; Kangavari, M.; Safarkhani, B.: Web page clustering using Harmony Search optimization. In: 2008 Canadian Conference on Electrical and Computer Engineering, Niagara Falls, ON, pp. 001601–001604 (2008)
Geem, Z.W.: Optimal cost design of water distribution networks using harmony search. Eng. Optim. 39(3), 259–277 (2007). https://doi.org/10.1080/03052150500467430
Chang, Y.; Li, Z.; Kou, Y.; Sun, Q.; Yang, H.; Zhao, Z.: A new approach to weapon-target assignment in cooperative air combat. Math. Prob. Eng. 2017, 17 (2017). Article ID 2936279
Wang, C.M.; Huang, Y.F.: Self-adaptive harmony search algorithm for optimization. Expert Syst. Appl. 37(4), 2826–2837 (2010)
Mahdavi, M.; Fesanghary, M.; Damangir, E.: An improved harmony search algorithm for solving optimization problems. Appl. Math. Comput. 188(2), 1567–1579 (2007)
Kumar, V.; Chhabra, J.K.; Kumar, D.: Parameter adaptive harmony search algorithm for unimodal and multimodal optimization problems. J. Comput. Sci. 5(2), 144–155 (2014)
Zhao, X.; Liu, Z.; Hao, J.; Li, R.; Zuo, X.: Semi-self-adaptive harmony search algorithm. Nat. Comput. 16(4), 619–636 (2017)
Shaffiei, Z.A.; Abas, Z.A.; Shibghatullah, A.S.; Fadzli, A.; Abdul, N.: An optimized intelligent automation for university shuttle bus driver scheduling using mutual swapping and harmony search. Int. J. Comput. Sci. Inf. Secur. 14(8), 875–884 (2016)
Al-Betar, M.A.; Khader, A.T.: A harmony search algorithm for university course timetabling. Ann. Oper. Res. 194(1), 3–31 (2012)
Brucker, P.; Qu, R.; Burke, E.: Personnel scheduling: models and complexity. Eur. J. Oper. Res. 210(3), 467–473 (2011)
Ramli, R.; Ibrahim, H.; Shung, L.T.: Innovative crossover and mutation in a genetic algorithm based approach to a campus bus driver scheduling problem with break consideration and embedded overtime. Appl. Math. Inf. Sci. 7(5), 1921–1928 (2013)
Ramli, M.R.; Hussin, B.; Ibrahim, N.K.: Utilizing particle swarm optimisation techniques in solving unfair nurse scheduling problem. Int. Rev. Comput. Software (IRECOS) 8(August), 2205–2212 (2013)
Lenstra, J.; Kan, A.R.: Complexity of vehicle routing and scheduling problems. Networks 11(2), 221–227 (1981)
Li, J.: A Self-adjusting algorithm for driver scheduling. J. Heuristics 11(4), 351–367 (2005)
Rohani, M.M.; Wijeyesekera, D.C.; Karim, A.T.A.: Bus operation, quality service and the role of bus provider and driver. Procedia Eng. 53, 167–178 (2013)
Abas, Z.; Shaffiei, Z.; Rahman, A.F.N.A.; Samad, A.: Using harmony search for optimising university shuttle bus driver scheduling for better operational management. Int. Conf. Innov. Trends Multidiscip. Acad. Res. ” (ITMAR- 2014) 1, 614–621 (2014)
Hadwan, M.; Ayob, M.; Sabar, N.R.; Qu, R.: A harmony search algorithm for nurse rostering problems. Inf. Sci. (NY) 233, 126–140 (2013). https://doi.org/10.1016/j.ins.2012.12.025
Yang, X.S.: Harmony search as a metaheuristic algorithm. Stud. Comput. Intell. 191, 1–14 (2009)
Lee, K.S.; Geem, Z.W.: A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Comput. Methods Appl. Mech. Eng. 194(36–38), 3902–3933 (2005)
Moon, Y.Y.; Geem, Z.W.; Han, G.T.: Vanishing point detection for self-driving car using harmony search algorithm. Swarm Evol. Comput. 2018(41), 111–119 (2017). https://doi.org/10.1016/j.swevo.2018.02.007
Del Ser, J.; Bilbao, M.N.; Perfecto, C.; Salcedo-Sanz, S.: A harmony search approach for the selective pick-up and delivery problem with delayed drop-off. In: Harmony Search Algorithm: Proceedings of the 2nd International Conference on Harmony Search Algorithm (ICHSA2015) (2016). https://doi.org/10.1007/978-3-662-47926-1_26
Alwani, Z.; Abas, Z.A.; Nizam, A.F.; Rahman, A.: Optimization in driver ’ s scheduling for university. In: International Symposium on Research and Innovation for Sustainable. 2014 (ISoRIS ’14) 15–16 Oct. 2014, Malacca, Malaysia (2014)
Marti, R.; Reinelt, G.: Heuristic method. In: The Linear Ordering Problem, Exact and Heuristic Methods in Combinatorial Optimization, pp. 17–40. Springer, Berlin, Heidelberg (2011). https://doi.org/10.1007/978-3-642-16729-4
Grosche, T.: Computational Intelligence in Integrated Airline Scheduling. Springer, Berlin (2009)
Widmer, M.; Hertz, A.; Costa, D.: Metaheuristics and scheduling. In: Production Scheduling, pp. 33–68. Wiley (2010). https://doi.org/10.1002/9780470611050
Kuang, E.: A 2-opt-based Heuristic for the Hierarchical Traveling Salesman Problem (2012). http://honors.cs.umd.edu/reports/kuang.pdf
Lin, S.: Computer solutions of the traveling salesman problem. Bell Syst. Tech. J. 44(10), 2245–2269 (1965)
Ma, Z.; Liu, L.; Sukhatme, G.S.: An Adaptive k -opt method for solving traveling salesman problem. In: 2016 IEEE 55th Conference on Decision and Control (Cdc), pp. 6537–6543 (2016)
Osogami, T.; Imai, H.: Classification of various neighborhood operations for the nurse scheduling problem. Lect. Notes Comput. Sci. 1969, 72–83 (2000)
Englert, M.; Röglin, H.; Vöcking, B.: Worst case and probabilistic analysis of the 2-opt algorithm for the TSP. Algorithmica 68(1), 190–264 (2014)
Mansor, N.F.; Abas, Z.A.; Rahman, A.F.N.A; Shibghatullah, A.S.; Sidek, S.: A New HMCR parameter of harmony search for better exploration. In: Kim, H.J., Geem, W.Z. (eds.) Harmony Search Algorithm: Proceedings of the 2nd International Conference on Harmony Search Algorithm (ICHSA2015). pp. 181–195. Springer, Berlin, Heidelberg (2016). https://doi.org/10.1007/978-3-662-47926-1_18
Zamli, K.Z.; Din, F.; Kendall, G.; Ahmed, B.S.: An experimental study of hyper-heuristic selection and acceptance mechanism for combinatorial t-way test suite generation. Inf. Sci. (NY) 399, 121–153 (2017). https://doi.org/10.1016/j.ins.2017.03.007
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This study was funded by MyBrain15 MyPhD and Grant TRGS/1/2016/FKP-AMC/01/D00005 under Ministry of Higher Education (MoHE), Malaysia.
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Shaffiei, Z.A., Abas, Z.A., Yunos, N.M. et al. Constrained Self-Adaptive Harmony Search Algorithm with 2-opt Swapping for Driver Scheduling Problem of University Shuttle Bus. Arab J Sci Eng 44, 3681–3698 (2019). https://doi.org/10.1007/s13369-018-3628-x
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DOI: https://doi.org/10.1007/s13369-018-3628-x