Title: Computer simulation-based optimisation: hybrid branch and bound and orthogonal array-based enumeration algorithm

Authors: Mohamed H. Gadallah

Addresses: Department of Operations Research, Institute of Statistical Studies and Research (ISSR), Cairo University, Giza, Cairo 12613, Egypt

Abstract: We propose a new modified algorithm for the branch and bound method. This algorithm is based on integration of orthogonal arrays and enumeration-based techniques. Several observations are given supplemented with simple model solutions to verify our assumptions. The modified algorithm is valid for higher dimensional problems. The algorithm employs several 2-levels orthogonal arrays and the complexity of solutions are always of the order 2ⁿ. For low to medium size problems, full factorial orthogonal arrays are employed. For higher size problems, the user uses fractional orthogonal arrays and the complexity of solutions are always of the order 2^n−k, k ≤ n. Fractional arrays result in incumbent solutions and the number of function evaluations is always low. This conclusion is rare as the number of continuous solutions resulting from relaxations is always tractable with standard arrays. Numerical results show that the proposed hybrid algorithm is able to save 20–96% of the original computations.

Keywords: branch and bound algorithms; approximation; hybrid techniques; simulation; optimisation; orthogonal arrays; enumeration algorithms.

DOI: 10.1504/IJMOR.2010.034341

International Journal of Mathematics in Operational Research, 2010 Vol.2 No.5, pp.554 - 590

Published online: 01 Aug 2010 *

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