On Solving Manufacturing Cell Formation via Bicluster Editing

This work investigates the Bicluster Graph Editing Problem (BGEP) and how it can be applied to solve the Manufacturing Cell Formation Problem (MCFP). We develop an exact method for the BGEP with a new separation algorithm. We also describe a new preprocessing procedure for the BGEP derived from theoretical results on vertex distances in the input graph. Computational experiments performed on randomly generated instances with various levels of difficulty show that our separation algorithm accelerates the convergence speed, and our preprocessing procedure is effective for low density instances. Another contribution of this work is to take advantage of the fact that the BGEP and the MCFP share the same solution space. This leads to the proposal of two new exact approaches for the MCFP that are based on mathematical formulations for the BGEP. Both approaches use the grouping efficacy measure as the objective function. Up to the authors’ knowledge, these are the first exact methods that employ such a measure to optimally solve instances of the MCFP. The first approach is based on a new ILP formulation for the MCFP, and the second consists of iteratively running several calls to a parameterized version of the BGEP. Computational experiments performed on instances of the MCFP found in the literature show that our exact methods for the MCFP are able to prove several previously unknown optima.

[1]  M. Chandrasekharan,et al.  MODROC: an extension of rank order clustering for group technology , 1986 .

[2]  Panos M. Pardalos,et al.  Cell Formation in Industrial Engineering: Theory, Algorithms and Experiments , 2013 .

[3]  Gilles Bisson,et al.  Chi-Sim: A New Similarity Measure for the Co-clustering Task , 2008, 2008 Seventh International Conference on Machine Learning and Applications.

[4]  G. Srinivasan,et al.  GRAFICS—a nonhierarchical clustering algorithm for group technology , 1991 .

[5]  Werner Dinkelbach.  On Nonlinear Fractional Programming , 1967 .

[6]  Basilis Boutsinas,et al.  Production , Manufacturing and Logistics Machine-part cell formation using biclustering , 2013 .

[7]  Tai-Hsi Wu,et al.  A water flow-like algorithm for manufacturing cell formation problems , 2010, Eur. J. Oper. Res..

[8]  John A. Hartigan,et al.  Clustering Algorithms , 1975 .

[9]  Panos M. Pardalos,et al.  Exact model for the cell formation problem , 2014, Optim. Lett..

[10]  Béla Bollobás,et al.  Random Graphs , 1985 .

[11]  Jayme Luiz Szwarcfiter,et al.  Applying Modular Decomposition to Parameterized Bicluster Editing , 2006, IWPEC.

[12]  Yong Zhang,et al.  Improved Algorithms for Bicluster Editing , 2008, TAMC.

[13]  J. Miltenburg,et al.  A comparative evaluation of nine well-known algorithms for solving the cell formation problem in group technology , 1991 .

[14]  Mauricio G. C. Resende,et al.  An evolutionary algorithm for manufacturing cell formation , 2004, Comput. Ind. Eng..

[15]  Luiz Satoru Ochi,et al.  A numerical comparison between simulated annealing and evolutionary approaches to the cell formation problem , 2010, Expert Syst. Appl..

[16]  Richard Bellman,et al.  Dynamic Programming Treatment of the Travelling Salesman Problem , 1962, JACM.

[17]  Tai-Hsi Wu,et al.  A hybrid heuristic algorithm adopting both Boltzmann function and mutation operator for manufacturing cell formation problems , 2009 .

[18]  B. Sarker,et al.  A comparison of existing grouping efficiency measures and a new weighted grouping efficiency measure , 2001 .

[19]  Jim Euchner.  Design , 2014, Catalysis from A to Z.

[20]  G. Nemhauser,et al.  Integer Programming , 2020 .

[21]  Luiz Satoru Ochi,et al.  Hybrid Metaheuristic for Bicluster Editing Problem , 2012, Electron. Notes Discret. Math..

[22]  M. Chandrasekharan,et al.  Grouping efficacy: a quantitative criterion for goodness of block diagonal forms of binary matrices in group technology , 1990 .

[23]  Tai-Hsi Wu,et al.  A simulated annealing algorithm for manufacturing cell formation problems , 2008, Expert Syst. Appl..

[24]  S. P. Mitrofanov.  SCIENTIFIC PRINCIPLES OF GROUP TECHNOLOGY , 1961 .

[25]  Jacques A. Ferland,et al.  Genetic algorithm and large neighbourhood search to solve the cell formation problem , 2012, Expert Syst. Appl..

[26]  Amir Hussain,et al.  A new biclustering technique based on crossing minimization , 2006, Neurocomputing.

[27]  A. Sen Gupta,et al.  On clique generation using Boolean equations , 1979, Proceedings of the IEEE.

[28]  I. Stancu-Minasian.  Nonlinear Fractional Programming , 1997 .

[29]  Beverly Sackler,et al.  The Bicluster Graph Editing Problem , 2004 .

[30]  Francis Sourd,et al.  Biclique completion problems for multicast network design , 2007, Discret. Optim..

[31]  F. Glover.  IMPROVED LINEAR INTEGER PROGRAMMING FORMULATIONS OF NONLINEAR INTEGER PROBLEMS , 1975 .

[32]  David Bennett,et al.  Production Flow Analysis , 2015 .

[33]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[34]  Mingyuan Chen,et al.  A COMPREHENSIVE MATHEMATICAL MODEL FOR THE DESIGN OF CELLULAR MANUFACTURING SYSTEMS , 2006 .

[35]  M. Chandrasekharan,et al.  ZODIAC—an algorithm for concurrent formation of part-families and machine-cells , 1987 .

[36]  John L. Burbidge,et al.  Production flow analysis , 1963 .

[37]  George M. Church,et al.  Biclustering of Expression Data , 2000, ISMB.