Bus Driver Scheduling and Rostering: Maximise Fairness using Enhanced Harmony Search Algorithm with Varieties of Step Functions and Fret Spacing Formula

  • Authors

    • N. F. Mansor
    • Z. Abal Abas
    • A. S. Shibghatullah
    • A. F.N. Abdul Rahman
    https://doi.org/10.14419/ijet.v7i3.28.24682
  • meta-heuristics, fairness, harmony search, scheduling, rostering,
  • This research proposes an adjustment of harmony search algorithm as a strategy to achieve a superior performance by manipulate three key operators in harmony search known as the Harmony Memory Consideration Rate (HMCR), Pitch Adjustment Rate (PAR) and Bandwidth (BW) that lead harmony search to accomplish a balancing between local exploitation and global exploration. The first contribution is having HMCR parameter using step function, while the second is applying the fret spacing concept on guitars toward BW parameter. There are three proposed models on the alteration of HMCR parameters based on the use of the fundamental step function; the constant interval of step function, dynamic increase and decrease interval functions. From an observation result, our proposed technique is superior adopted by using a second model that contrast to parameter adaptive harmony search (PAHS).  In brief, this proposed technique magnificently to construct a fairer roster among drivers.

     

     

  • References

    1. [1] M. Dorigo and T. Stützle, Ant Colony Optimization. Cambridge: MIT Press, 2004.

      [2] D. T. Pham, A. Ghanbarzadeh, E. Koc, S. Otri, S. Rahim, and M. Zaidi, “The bees algorithm–A novel tool for complex optimisation,†Proc. 2nd Int. Virtual Conf. Intell. Prod. Mach. Syst., pp. 454–459, 2006.

      [3] A. Aderhold et al., “A New Metaheuristic Bat-Inspired Algorithm,†Nat. Inspired Coop. Strateg. Optim. (NICSO 2010), vol. 284, no. Nicso 2013, pp. 283–294, 2010.

      [4] E. Bonabeau, M. Dorigo, and G. Theraulaz, Swarm Intelligence: From Natural to Artificial Systems. Santa Fe Institute Studies on the Sciences of Complexity OUP, USA, 1999.

      [5] Geem et al, “A New Heuristic Optimization Algorithm: Harmony Search,†Simulation, vol. 76, no. 2, pp. 60–68, 2001.

      [6] D. Weyland, “A critical analysis of the harmony search algorithm -- How not to solve sudoku,†Oper. Res. Perspect., vol. 2, pp. 97–105, 2015.

      [7] S. Sivasubramani and K. S. Swarup, “Multi-objective harmony search algorithm for optimal power flow problem,†Int. J. Electr. Power Energy Syst., vol. 33, no. 3, pp. 745–752, 2011.

      [8] K. Z. Gao, P. N. Suganthan, Q. K. Pan, and M. F. Tasgetiren, “An effective discrete harmony search algorithm for flexible job shop scheduling problem with fuzzy processing time.,†Int. J. Prod. Res., vol. 53, no. 19, p. 5896, 2015.

      [9] Z. W. Geem, “Optimal cost design of water distribution networks using harmony search,†Eng. Optim., vol. 38, no. 3, pp. 259–277, 2006.

      [10] A. Kaveh and S. Talatahari, “Particle swarm optimizer, ant colony strategy and harmony search scheme hybridized for optimization of truss structures,†Comput. Struct., vol. 87, no. 5–6, pp. 267–283, 2009.

      [11] Z. Geem, C. Tseng, and Y. Park, “Harmony search for generalized orienteering problem: best touring in China,†Adv. Nat. Comput., 2005.

      [12] Z. Geem, “Harmony search algorithm for solving sudoku,†… Based Intell. Inf. Eng. Syst., 2007.

      [13] M. P. Saka, “Optimum Design of Steel Sway Frames to BS5950 using Harmony Search Algorithm,†J. Constr. Steel Res., vol. 65, no. 1, pp. 36–43, 2009.

      [14] N. F. Mansor, Z. A. Abas, A. Fadzli, N. Abdul, A. S. Shibghatullah, and S. Sidek, “A New HMCR Parameter of Harmony Search for Better Exploration,†vol. 382, pp. 181–195, 2016.

      [15] P. Yadav, R. Kumar, S. K. Panda, and C. S. Chang, “An Intelligent Tuned Harmony Search algorithm for optimisation,†Inf. Sci. (Ny)., vol. 196, pp. 47–72, 2012.

      [16] M. Fesanghary, M. Mahdavi, M. Minary-Jolandan, and Y. Alizadeh, “Hybridizing harmony search algorithm with sequential quadratic programming for engineering optimization problems,†Comput. Methods Appl. Mech. Eng., vol. 197, no. 33–40, pp. 3080–3091, 2008.

      [17] A. H. Khazali and M. Kalantar, “Optimal Reactive Power Dispatch based on Harmony Search Algorithm,†Int. J. Electr. Power Energy Syst., vol. 33, no. 3, pp. 684–692, 2011.

      [18] M. Shabani, S. Abolghasem Mirroshandel, and H. Asheri, “Selective Refining Harmony Search: A new optimization algorithm,†Expert Syst. Appl., vol. 81, pp. 423–443, 2017.

      [19] S. Kang and J. Chae, “Harmony Search for the Layout Design of an Unequal Area Facility,†Expert Syst. Appl., vol. 79, pp. 269–281, 2017.

      [20] B. Alatas, “Chaotic harmony search algorithms,†Appl. Math. Comput., vol. 216, no. 9, pp. 2687–2699, 2010.

      [21] C. A. Glass and R. A. Knight, “The nurse rostering problem: A critical appraisal of the problem structure,†Eur. J. Oper. Res., vol. 202, no. 2, pp. 379–389, 2010.

      [22] M. Y. Cheng, D. Prayogo, Y. W. Wu, and M. M. Lukito, “A Hybrid Harmony Search Algorithm for Discrete Sizing Optimization of Truss Structure,†Autom. Constr., vol. 69, pp. 21–33, 2016.

      [23] C.-M. Wang and Y.-F. Huang, “Self-adaptive harmony search algorithm for optimization,†Expert Syst. Appl., vol. 37, no. 4, pp. 2826–2837, 2010.

      [24] Z. W. Geem, “Harmony search applications in industry,†Studies in Fuzziness and Soft Computing, vol. 226. pp. 117–134, 2008.

      [25] M. Mahdavi, M. Fesanghary, and E. Damangir, “An improved harmony search algorithm for solving optimization problems,†Appl. Math. Comput., vol. 188, no. 2, pp. 1567–1579, 2007.

      [26] B. Alatas, “Chaotic harmony search algorithms,†Appl. Math. Comput., vol. 216, no. 9, pp. 2687–2699, Jul. 2010.

      [27] [F. Zhao, Y. Liu, C. Zhang, and J. Wang, “A self-adaptive harmony PSO search algorithm and its performance analysis,†Expert Syst. Appl., vol. 42, no. 21, pp. 7436–7455, 2015.

      [28] M. Shivaie, M. G. Kazemi, and M. T. Ameli, “A modified harmony search algorithm for solving load-frequency control of non-linear interconnected hydrothermal power systems,†Sustain. Energy Technol. Assessments, vol. 10, pp. 53–62, 2015.

      [29] B. Zeng and Y. Dong, “An Improved Harmony Search Based Energy-Efficient Routing Algorithm for Wireless Sensor Networks,†Appl. Soft Comput., vol. 41, pp. 135–147, 2015.

      [30] M. G. H. Omran and M. Mahdavi, “Global-best harmony search,†Appl. Math. Comput., vol. 198, no. 2, pp. 643–656, 2008.

      [31] N. A. El-Sherbeny, “Vehicle routing with time windows: An overview of exact, heuristic and metaheuristic methods,†J. King Saud Univ. - Sci., vol. 22, no. 3, pp. 123–131, 2010.

      [32] B. Yu, Z. Z. Yang, and B. Z. Yao, “A hybrid algorithm for vehicle routing problem with time windows,†Expert Syst. Appl., vol. 38, no. 1, pp. 435–441, 2011.

      [33] M. I. Jasmi, A. F. N. A. Rahman, Z. Abal Abas, and A. S. Shibghatullah, “Optimized Coating Design of Energy Saving Glass Using Binary Harmony Search for Better Transmission Signal,†Int. J. Comput. Sci. Inf. Secur., vol. 14, no. 8, pp. 436–443, 2016.

      [34] N. F. Mansor, Z. Abal Abas, A. S. Abdul Rahman, Ahmad Fadzli Nizam Shibghatullah, and S. Safiah, “An analysis of the parameter modifications in varieties of harmony search algorithm,†Int. Rev. Comput. Softw., vol. 9, no. 10, pp. 1736–1749, 2014.

      [35] N. Mansor, Z. Abas, A. Abdul Rahman, A. Shibghatullah, and S. Sidek, “An Optimization Solution using a Harmony Search Algorithm,†in International Symposium on Research in Innovation and Sustainability 2014, 2014, vol. 2014, pp. 1745–1749.

      [36] Z. A. Shaffiei, Z. A. Abas, A. F. Nizam, and A. Rahman, “Optimization in Driver’s Scheduling for University Shuttle Bus using Harmony Search,†vol. 2014, pp. 15–16, 2014.

      [37] Z. Abal Abas, Z. Shaffiei, A. F. N. A. Rahman, and A. Samad, “Using Harmony Search for Optimising University Shuttle Bus Driver Scheduling for Better Operational Management,†in ITMAR 2014, 2014, vol. 1, pp. 614–621.

      [38] N. F. Mansor, Z. A. Abas, A. F. N. A. Rahman, A. S. Shibghatullah, and S. Sidek, “A New HMCR Parameter of Harmony Search for Better Exploration,†in Harmony Search Algorithm: Proceedings of the 2nd International Conference on Harmony Search Algorithm, H. J. Kim and W. Z. Geem, Eds. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016, pp. 181–195.

      [39] A. S. Shibghatullah, Z. Abal Abas, and A. F. N. A. Rahman, “Enhanced Harmony Search Algorithm for Better Decision Tree Classification,†in ITMAR 2014, 2014, vol. 1, pp. 602–607.

      [40] K. Das, A. Chatterjee, and A. Rakshit, “Harmony search algorithm and Lyapunov theory based hybrid adaptive fuzzy controller for temperature control of air heater system with transport-delay,†vol. 25, pp. 40–50, 2014.

      [41] M. M. Bhaskar and S. Maheswarapu, “A Hybrid Harmony Search Algorithm Approach for Optimal Power Flow,†Telkomnika, vol. 9, no. 2, pp. 211–216, 2011.

      [42] M. A. Awadallah, “Hybrid harmony search algorithm for global optimization,†2013 World Congr. Nat. Biol. Inspired Comput., pp. 69–75, 2013.

      [43] V. Kumar, J. K. Chhabra, and D. Kumar, “Parameter adaptive harmony search algorithm for unimodal and multimodal optimization problems,†J. Comput. Sci., vol. 5, no. 2, pp. 144–155, 2014.

      [44] X. Chang-ming and Y. Lin, “Research on adjustment strategy of PAR in harmony search algorithm,†Int. Conf. Autom. Control Artif. Intell., pp. 1705–1708, 2012.

      [45] N. F. Mansor et al., “An Optimization Solution Using a Harmony Search Algorithm,†Sci. Int. Lahore, vol. 2014, pp. 1745–1749, 2014.

      [46] Z. Abal Abas, S. Salleh, and Z. Manan, “Extended Advancing Front Technique for the Initial Triangular Mesh Construction on a Single Coil for Radiative Heat Transfer,†Arab. J. Sci. Eng., vol. 38, no. 9, pp. 2245–2262, 2013.

      [47] S. F. Abdullah, A. F. N. A. Rahman, and Z. Abal Abas, “Classification of Gender by Using Fingerprint Ridge Density in Northen Part of Malaysia,†ARPN J. Eng. Appl. Sci., vol. 10, no. 22, pp. 10722–10726, 2015.

      [48] Z. A. Abas and S. Salleh, “An insight into the science of unstructured meshes in computer numerical simulation,†Appl. Math. Sci., vol. 8, no. 171, pp. 8493–8516, 2014.

      [49] A. S. H. Basari, Z. A. Abas, and Shaharuddin Salleh, “Seven Cases Unstructured Triangulation Technique for Simplified Version of Conceptual Model of Ethylene Furnace for Radiative Heat Transfer Approximation,†Int. J. Comput. Appl., vol. 44, 2012.

      [50] M. R. Ramli, Z. Abal Abas, F. Arif, and M. I. Desa, “An Analysis Review Approaches Used In Health Human Resources Planning,†Int. J. Comput. Sci. Inf. Secur., vol. 14, no. August 2016, pp. 908–935, 2016.

      [51] S. Alias, Z. Abal Abas, A. S. Shibghatullah, and A. F. N. Abdul Rahman, “A brief review of surface meshing in medical images for biomedical computing and visualization,†Sci.Int., vol. 26, no. 5, 2014.

      [52] Z. Abal Abas, S. Salleh, A. F. N. Rahman, H. Basiron, A. S. Hasan Basari, and N. Hassim, “Improvement of Element Creation Procedure for Generating Initial Triangular Unstructured Mesh for Radiative Heat Transfer Modelling,†Int. Rev. Model. Simulations, vol. 6, no. 5, pp. 1649–1656, 2013.

      [53] Z. Abal Abas, L. Ee-theng, A. Fadzli, N. Abdul, and Z. Z. Abidin, “Enhanced scheduling traffic light model using Discrete Event Simulation for improved signal timing analysis,†ARPN J. Eng. Appl. Sci., vol. 10, no. 18, pp. 8135–8140, 2015.

      [54] Z. A. Abas et al., “The Implementation of Personal Monitoring System using Histogram of Gradient, Haar Classifier and Eigenfaces for Human Detection and Recognition,†ARPN J. Eng. Appl. Sci., vol. 10, no. 19, pp. 8799–8806, 2015.

      [55] O. Hasançebi, S. Çarbaş, E. Doǧan, F. Erdal, and M. P. Saka, “Performance evaluation of metaheuristic search techniques in the optimum design of real size pin jointed structures,†Comput. Struct., vol. 87, no. 5–6, pp. 284–302, 2009.

  • Downloads

  • How to Cite

    F. Mansor, N., Abal Abas, Z., S. Shibghatullah, A., & F.N. Abdul Rahman, A. (2018). Bus Driver Scheduling and Rostering: Maximise Fairness using Enhanced Harmony Search Algorithm with Varieties of Step Functions and Fret Spacing Formula. International Journal of Engineering & Technology, 7(3.28), 136-143. https://doi.org/10.14419/ijet.v7i3.28.24682