Pattern-based heuristic for the cell formation problem in group technology

Abstract

In this chapter we introduce a new pattern-based approach within the linear assignment model with the purpose to design heuristics for a combinatorial optimization problem (COP). We assume that the COP has an additive (separable) objective function and the structure of a feasible (optimal) solution to the COP is predefined by a collection of cells (positions) in an input file. We define a pattern as a collection of positions in an instance problem represented by its input file (matrix). We illustrate the notion of pattern by means of some well-known problems in COP, among them are the linear ordering problem (LOP) and cell formation problem (CFP), just to mention a couple. The CFP is defined on a Boolean input matrix, the rows of which represent machines and columns - parts. The CFP consists in finding three optimal objects: a block-diagonal collection of rectangles, a row (machines) permutation, and a column (parts) permutation such that the grouping efficacy is maximized. The suggested heuristic combines two procedures: the pattern-based procedure to build an initial solution and an improvement procedure to obtain a final solution with high grouping efficacy for the CFP. Our computational experiments with the most popular set of 35 benchmark instances show that our heuristic outperforms all well-known heuristics and returns either the best known or improved solutions to the CFP. © Springer Science+Business Media New York 2013.