A computational study of hybrid approaches of metaheuristic algorithms for the cell formation problem Luong Thuan Thanh 1 , Jacques A Ferland 2 * , Bouazza Elbenani 3 , Nguyen Dinh Thuc 4 and Van Hien Nguyen 1,5 1 Institute for Computational Science and Technology at Ho Chi Minh City (ICST), Vietnam; 2 Department of Computer Science and Operations Research, University of Montreal, Montreal, Canada; 3 Research Laboratory of Informatics, Mohammed V University-Agdal, Morocco; 4 University of Science, VNU-HCM, Vietnam; and 5 University of Namur, Namur, Belgium In this paper we solve the 0–1 cell formation problem where the number of cells is fixed a priori and where the objective is to maximize the overall efficiency of a production system by grouping together machines providing service to similar parts into a subsystem (denoted cell). Three different methods are introduced and compared numerically. The first local search method is an implementation of simulated annealing (SA) where the definition of the neighbourhood is specific to the application and requires using a diversification and intensification strategies. The second local search method is an adaptive simulated annealing method where the neighbourhood is selected randomly at each iteration. The procedure is adaptive in the sense that the probability of selecting a neighbourhood is updated during the process. The third method is a hybrid method (HM) of a population-based method and a local search method. To improve the solution obtained with HM, we apply a SA method afterward. The best variants are very efficient to solve the 35 benchmark problems commonly used in the literature. Journal of the Operational Research Society advance online publication, 1 July 2015; doi:10.1057/jors.2015.46 Keywords: metaheuristics; evolutionary computation; fractional programming; simulated annealing; genetic algo- rithm; combinatorial optimization 1. Introduction Group Technology is an approach often used in manufacturing and engineering management taking advantage of similarities in production design and processes. In this context, Cellular Manufacturing refers to maximize the overall efficiency of a production system by grouping together machines providing service to similar parts into a subsystem (denoted cell). The corresponding problem is formulated as a (Machine-Part) Cell Formation Problem (CFP). As a consequence, the interactions of the machines and the parts within a cell are maximized, and those between machines and parts of other cells are reduced as much as possible. In fact this research project was motivated by our interest in designing computer chip architecture. The cell formation problem seems appropriate to complete the decom- position of the processors and the data units into a fixed number of cells. Thus this leads us to study the cell formation problem where the the number of cells is fixed a priori. The purpose of this study is to develop algorithmic procedures that are efficient and effective for obtaining machine-part groupings. Researchers have proposed many performance measures to evaluate the quality of the cell formation solution (see, for example, Sarker, 2001 and Sarker and Khan, 2001) for reviews on performance measures specified in different functions to evaluate the impact of the interactions of the machines and parts within a cell and those between machines and parts of other cells. It is important for the cell formation solution to minimize the total number of exceptional elements (1’s outside cells) and of voids (0’s inside cells) in order to minimize intercell movement and maximize machine utilization. The most widely used are: grouping efficiency suggested by Chandrasekharan and Rajagopalan (1989); grouping efficacy suggested by Kumar and Chandrasekharan (1990); group capability index proposed by Hsu (1990). In this paper we have chosen to use the Kumar-Chandrasekharan grouping efficacy objective func- tion in all the computational experiments because it has been used as a benchmark measure for most algorithmic studies in the literature (see Brown and Sumichrast, 2001; Dimopoulos and Mort, 2001; Farahani and Hosseini, 2011; James et al, 2007; Joines et al, 1996; Manimaran et al, 2011; Saraç and Ozcelik, 2012; Sarker and Mondal, 1999; Srinivasan et al, 1990; Vannelli and Kumar, 1986; Lin et al, 2010; see also Gonçalves and Resende, 2004 for more information on the grouping efficacy measure). *Correspondence: Jacques A. Ferland, DIRO, Université de Montréal, Pavillon André-Aisenstadt, 2920 chemin de la Tour, Montréal H3C 3J7, Canada. E-mail: ferland@iro.umontreal.ca Journal of the Operational Research Society (2015) 1–17 © 2015 Operational Research Society Ltd. All rights reserved. 0160-5682/15 www.palgrave-journals.com/jors/