The facility layout problem (FLP) is the determination of the most efficient physical arrangement of a number of interacting facilities on the factory floor of a manufacturing system in order to meet one or more objectives. Facilities usually represent the largest and most expensive assets of the organization and are of crucial importance to the organization (Nordin, Zainuddin, Salim, & Ponnusamy, 2009). Tompkins et al. (1996) estimate that between 20% and 50% of operating cost can be attributed to facility planning and material handling., and such costs can be reduced considerably by an effective layout design. Several heuristic approaches have been proposed in the literature in the recent years to find (sub-) optimal solutions to the FLP, including simulated annealing algorithms, tabu search methods, neural networks and genetic algorithms (GAs). According to Sirinaovakul and Thajchayapong (1994), a frequent drawback of such algorithms is that they do not explore enough possibilities while generating their solutions thus being extremely sensitive to the initial solution. Heragu and Alfa (1992) sited these algorithms as local optimization algorithms which, once hit an unattractive region, had no way of backing out and exploring other regions. Glover and Greenberg (1989) noted that reliable heuristic algorithms are not sensitive to their initial solutions and that an exhaustive search of the solution space can be achieved by parallel processing. This should avoid the search procedure to be trapped into inferior solution regions. A GA is a stochastic search technique based on the concept of the survival of the best, emulating the mechanisms of the Darwinian evolution, thus achieving a sub-optimal solution via recursive operations of crossover and mutation (Holland, 1975 and Michalewicz, 1992). Most of the studies conducted in FLPs have focused on a single objective, either quantitative or qualitative goodness of the layout (Tuzkaya & Ertay, 2004). In contrast, practical FLPs involve several conflicting objectives. Therefore, both quantitative and qualitative objectives must be considered simultaneously before arriving at any conclusion. A layout that is optimal with respect to a given criterion might be a poor candidate when another criterion is paramount. In general, minimization of the total material handling (MH) cost is often used as the optimization criterion in FLPs. The closeness rating, hazardous movement, safety, and the like are also important criteria in FLPs. In fact, these qualitative factors have significant influence on the final layout and should give consideration. Consequently, the FLP falls into the category of multi-objective optimization problem (MOOP). Multi-objective optimization is a technique to treat several objectives simultaneously without converting them into one. The objective of MOOPs is to find a set of Pareto-optimal solutions, which are the superior solutions when considering all the objectives. In MOOPs, the absolute optimal solution is absent and the designer must select a solution that offers the most profitable trade-off between the objectives as an alternative. Thus, instead of offering a single solution, it is more realistic and appropriate to generate a number of ‘‘good’’ layouts that meet several criteria laid down by the facility designer and let decision makers choose between them based on the current requirement. Presumably, the most comprehensive way to take all these features into consideration in the selection process is to personally involve the decision maker(s) in the selection process, which is the procedure adopted in the Interactive Genetic Algorithms (Brintup, Takagi, Tiwari, & Ramsden, 2006) which have been recently applied to FLP (Hernandez, Morera, & Azofra, 2011). Such procedure, however, may expose the decision maker to a time consuming activity, and may result unpractical in many contexts, where a structured and transparent decision making is required. In such cases a fully automated procedure is preferred to select at least a set of best solution candidates, thus allowing the decision maker to evaluate a limited number of alternatives. For such purpose the different objectives are frequently combined into a single one by means of some aggregation procedures such as in the weighted sum method. The drawbacks of these methodologies are well documented in the multi-objective decision theory, as well as the benefits of a “true” multi-objective exploration of the solution space, resulting from a Pareto based approach. Pareto approaches (Goldberg, 1989) involve the evolution of the Pareto front constituted by the fitness of a generic individual corresponding to each optimality criterion considered. It has been recognized the GAs belonging to this class generally outperform the non-Pareto Based approaches (Tamaki et al., 1996 and Zitzler and Thiele, 1999). The methodology here proposed refers to the class of Pareto-based and is developed according to the framework of non-dominated sorting GA (NSGA) proposed by Srinivas and Deb (1995). More specifically, in this paper we propose a novel Multi Objective Genetic Algorithm (MOGA) to solve the facility layout problem considering four separate objectives based on an advanced encoding structure in order to ensure an efficient exploration of the search space. The objectives considered are commonly employed in the literature (Aiello et al., 2012, Harmonosky and Tothero, 1992, Meller and Gau, 1996 and Srinivas and Deb, 1995), namely the minimization of the total Material Handling Cost the distance and the closeness requirements among the departments, and the desired aspect ratio. Additionally, the presence of feasibility constraints, required to ensure the practicability of the solution determined, may significantly hamper the convergence of the algorithm, which consequently requires a solid and efficient structure. In particular, it is well known that the very basic and most crucial component of a GA is related to the solution representation (i.e. the chromosome encoding scheme), as it significantly affects the overall performance of the algorithm and the quality of the solutions obtained (Datta, Amaral, & Figueira, 2011). In order to be implemented in a genetic algorithm, a layout representation scheme must be encoded into a string form, suitable for being employed within the common genetic operators such as mutation and crossover. The simplifications introduced in the layout representation in order to cope with these requirements, and to ensure that a chromosome can be easily decoded to a unique layout scheme, generally restrict the flexibility of the representation, thus limiting the feasible search space. The two general mechanisms reported in the literature for constructing such layouts are the flexible bay structure (FBS) developed by Goetschalckx (1992), and the more recent slicing tree structure (Arapoglu et al., 2001 and Moghaddam and Shayan, 1998). The slicing structure results from dividing an initial rectangle either in horizontal or vertical direction completely from one side to the other (guillotine cut) and recursively going on with the newly generated rectangles (Scholz, Jaehn, & Junker 2010). The Multi Objective Genetic Algorithm (MOGA) here proposed is hence based on a slicing tree encoding in order to ensure an efficient convergence towards the Pareto frontier, outperforming the current referenced approaches. Finally, the best block layout is determined by employing the well known multi-criteria decision-making procedure Electre. The remainder of this paper is organized as follows. Section 2 describes the genetic algorithm implemented in this study for the facility layout problem and in particular the ranking procedure adopted. To show performance of the suggested algorithm, comparative experiments are done in Section 3. In Section 4 the best solution is determined by means the Electre method and Section 5 concludes the paper with a short summary of the results obtained.
