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A tabu search algorithm for the cell formation problem with part machine sequencing

Papaioannou G., Wilson J. M.

Foundations of Computing and Decision Sciences

2012

Vol. 37, No. 2

97--127

This paper presents extensions of the IP model where part-machine assignment and cell formation are addressed simultaneously and part machine utilisation is considered. More specifically, an integration of inter-cell movements of parts and machine set-up costs within the objective function, and also a combination of machine set-up costs associated with parts revisiting a cell when the part machine operation sequence is taken into account are examined and an enhanced model is formulated. Based upon this model’s requirements, an initial three stage approach is proposed and a tabu search iterative procedure is designed to produce a solution. The initial approach consists of the allocation of machines to cells, the allocation of parts to machines in cells and the evaluation of the objective function’s value. Special care has been taken when allocating parts to machine cells as part machine operation sequence is preserved making the system more complex but more realistic. The proposed tabu search algorithm integrates short term memory and an overall iterative searching strategy where two move types, single and exchange, are considered. Computational experiments verified both the algorithm’s robustness where promising solutions in reasonably short computational effort are produced and also the algorithm’s effectiveness for large scale data sets.

Optics in Croke-Kleiner spaces

Ancel F. D., Wilson J. M.

Bulletin of the Polish Academy of Sciences. Mathematics

2010

Vol. 58, no 2

147-165

We explore the interior geometry of the CAT(O) spaces {Xα : 0 < α ≤ π/2}, constructed by Croke and Kleiner [Topology 39 (2000)]. In particular, we describe a diffraction effect experienced by the family of geodesic rays that emanate from a basepoint and pass through a certain singular point called a triple point, and we describe the shadow this family casts on the boundary. This diffraction effect is codified in the Transformation Rules stated in Section 3 of this paper. The Transformation Rules have various applications. The earliest of these, described in Section 4, establishes a topological invariant of the boundaries of all the Xα's for which α lies in the interval [π/2(n + 1), π/2n), where n is a positive integer. Since the invariant changes when n changes, it provides a partition of the topological types of the boundaries of Croke-Kleiner spaces into a countable infinity of distinct classes. This countably infinite partition extends the original result of Croke and Kleiner which partitioned the topological types of the Croke-Kleiner boundaries into two distinct classes. After this countably infinite partition was proved, a finer partition of the topological types of the Croke-Kleiner boundaries into uncountably many distinct classes was established by the second author [J. Group Theory 8 (2005)], together with other applications of the Transformation Rules.