Pattern-Based Heuristic for the Cell Formation Problem in Group Technology
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.
KeywordsCell formation problem Group technology Heuristic
The authors would like to thank professor Mauricio Resende for the 35 GT instances provided on his web page (http://www2.research.att.com/~mgcr/data/cell-formation/). We are also grateful to professors R. Jonker and A. Volgenant for making available for us their very efficient program implementation of the Hungarian algorithm.
The authors are supported by The LATNA Laboratory, National Research University Higher School of Economics (NRU HSE), and Russian Federation government grant, ag. 11.G34.31.0057. Boris Goldengorin and Mikhail Batsyn are partially supported by NRU HSE Scientific Fund grant “Teachers–Students” #11-04-0008 “Calculus for tolerances in combinatorial optimization: theory and algorithms.”
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