Bee Parameter Determination via Weighted Centriod Modified Simplex and Constrained Response Surface Optimisation Methods

Various intelligences and inspirations have been adopted into the iterative searching process called as meta-heuristics. They intelligently perform the exploration and exploitation in the solution domain space aiming to efficiently seek near optimal solutions. In this work, the bee algorithm, inspired by the natural foraging behaviour of honey bees, was adapted to find the near optimal solutions of the transportation management system, dynamic multi-zone dispatching. This problem prepares for an uncertainty and changing customers- demand. In striving to remain competitive, transportation system should therefore be flexible in order to cope with the changes of customers- demand in terms of in-bound and outbound goods and technological innovations. To remain higher service level but lower cost management via the minimal imbalance scenario, the rearrangement penalty of the area, in each zone, including time periods are also included. However, the performance of the algorithm depends on the appropriate parameters- setting and need to be determined and analysed before its implementation. BEE parameters are determined through the linear constrained response surface optimisation or LCRSOM and weighted centroid modified simplex methods or WCMSM. Experimental results were analysed in terms of best solutions found so far, mean and standard deviation on the imbalance values including the convergence of the solutions obtained. It was found that the results obtained from the LCRSOM were better than those using the WCMSM. However, the average execution time of experimental run using the LCRSOM was longer than those using the WCMSM. Finally a recommendation of proper level settings of BEE parameters for some selected problem sizes is given as a guideline for future applications.

Authors:

• P. Luangpaiboon

Keywords:

• Meta-heuristic
• Bee Algorithm
• Dynamic Multi-Zone Dispatching
• Linear Constrained Response SurfaceOptimisation Method
• Weighted Centroid Modified Simplex Method

References:

[1] R.W. Holl, and V.C. Sabnani, "Control of vehicle dispatching on a
cyclic route serving trucking terminals," Transportation Research, Part
A, vol. 36, pp. 257-276, 2002.
[2] G.D. Taylor and T.S. Meinert, "Improving the quality of operation in
truckload trucking," IIE Transaction, vol. 32, no. 6, pp. 551-562, 2000.
[3] G.D. Taylor, T.S. Meinert, R.C. Killian, and G.L. Whicker,
"Development and analysis of alternative dispatching methods in
truckload trucking," Transportation Research, Part E, vol. 35, pp. 191-
205, 1999.
[4] G.D. Taylor, G.L. Whicker and J.S. Usher, "Multi-zone dispatching in
truckload trucking," Transportation Research, Part E, vol. 37, pp. 375-
390, 2001.
[5] K.S. Lee and Z.W. Geem, "A new meta-heuristic algorithm for
continuous engineering optimisation: harmony search theory and
practice," Comput. Methods Appl. Mech. Engrg., vol. 194, pp. 3902-
3933, 2004.
[6] P. Muller and D.R. Insua, "Issues in bayesian analysis of neural network
models," Neural Computation, vol. 10, pp. 571-592, 1995.
[7] M. Dorigo, V. Maniezzo and A. Colorni, "Ant system: optimisation by a
colony of cooperating agents," IEEE Transactions on Systems, Man, and
Cybernetics Part B, vol. 26, numéro 1, pp. 29-41, 1996.
[8] E. Emad, H. Tarek and G. Donald, "Comparison among five
evolutionary-based optimisation algorithms," Advanced Engineering
Informatics, vol. 19, pp. 43-53, 2005.
[9] J.Y. Jeon, J.H. Kim and K. Koh, "Experimental evolutionary
programming-based high-precision control," IEEE Control Sys. Tech.,
vol. 17, pp. 66-74, 1997.
[10] R. Storn, "System design by constraint adaptation and differential
evolution," IEEE Trans. on Evolutionary Computation, vol. 3, no. 1, pp.
22-34, 1999.
[11] M. Clerc and J. Kennedy, "The particle swarm-explosion, stability, and
convergence in a multidimensional complex space," IEEE Transactions
on Evolutionary Computation, vol. 6, pp.58-73, 2002.
[12] A. Lokketangen, K. Jornsten and S. Storoy, "Tabu search within a pivot
and complement framework," International Transactions in Operations
Research, vol. 1, no. 3, pp. 305-316, 1994.
[13] V. Granville, M. Krivanek and J.P. Rasson, "Simulated annealing: a
proof of convergence", Pattern Analysis and Machine Intelligence,
IEEE Transactions, vol. 16, issue 6, pp. 652 - 656, 1994.
[14] H. Zang, S. Zhang and K. Hapeshi, "A review of nature-inspired
algorithms", Journal of Bionic Engineering, vol. 7 (Suppl.), S232-S237,
2010.
[15] D.T. Pham, A.J. Soroka, A. Ghanbarzadeh, E. Koç, S. Otri and M.
Packianather, "Optimising nNeural networks for identification of wood
defects using the bees algorithm," in Proc. 2006 IEEE International
Conference on Industrial Informatics, Singapore, 2006.
[16] D.T. Pham, E. Koç, J.Y. Lee and J. Phrueksanant, "Using the bees
algorithm to schedule jobs for a machine," in Proc. Eighth International
Conference on Laser Metrology, CMM and Machine Tool Performance,
LAMDAMAP, Euspen, UK, Cardiff, 2007, pp. 430-439.
[17] D.T. Pham, S. Otri, A.A. Afify, M. Mahmuddin and H. Al-Jabbouli,
"Data clustering using the bees algorithm," in Proc. 40th CIRP Int.
Manufacturing Systems Seminar, Liverpool, 2007.
[18] L. Ozbakir, A. Baykasoglu and P. Tapkan, "Bee algorithm for
generalised assignment problem," Applied Mathematics and
Computation, vol. 215, pp. 3782-3795, 2010.