Int. J. Industrial and Systems Engineering, Vol. 7, No. 3, 2011 341 Copyright © 2011 Inderscience Enterprises Ltd. A bi-tour ant colony optimisation framework for vertical partitions Chun-Hung Cheng* Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, NT, Hong Kong SAR, PR China E-mail: chcheng@se.cuhk.edu.hk *Corresponding author Angappa Gunasekaran Department of Decision and Information Sciences, University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA E-mail: agunasekaran@umassd.edu Kwan-Ho Woo XML Asia Ltd., Room 1601, 16/F., Jubilee Centre, 18 Fenwick Street, Wan Chai, Hong Kong SAR, PR China E-mail: khwoo@se.cuhk.edu.hk Abstract: Clustering refers to a process of grouping together similar objects while separating out the dissimilar objects. In this work, we consider block clustering in vertical partitioning. Block clustering is a specific clustering method, which clusters the sets of objects and their associated attributes (descriptors) together, simultaneously, in a solution matrix. For this specific problem we propose using a bi-tour ant colony optimisation. To show the quality of the new proposed approach, we conduct an extensive computational study and show that our method is performed better than some traditional clustering methods, such as genetic algorithms and average linkage clustering. Keywords: block clustering; ACO; ant colony optimisation; vertical partitioning. Reference to this paper should be made as follows: Cheng, C-H., Gunasekaran, A. and Woo, K-H. (2011) ‘A bi-tour ant colony optimisation framework for vertical partitions’, Int. J. Industrial and Systems Engineering, Vol. 7, No. 3, pp.341–356. Biographical notes: Chun-Hung Cheng obtained BSSc from The Chinese University of Hong Kong, MSc in Computer Science and PhD in Management Science from the University of Iowa. Currently, he is an Associate Professor at the Chinese University of Hong Kong (CUHK). His research interests lie in computer and information technology, and logistics and operations management. His work has produced over 65 articles in reputed journals and is