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 combinatorial optimization, including the Linear Ordering Problem, the Cell Formation Problem, just to mention a few. 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 rows (machines) permutation, and a columns (parts) permutation so 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.