A well-planned arrangement of manufacturing departments on a two-dimensional planar region considerably increases the efficiency of its production systems, which is termed facility layout problem (FLP). Conventional layout design approach often designs intercell layout (determining exact location of each department on shop floor area) and flow path layout design of material handling system (MHS) step by step in a sequential manner. This results in suboptimal solutions for FLP. In this paper, an integrated approach is adopted to design the intercell layout and the flow path layout of MHS simultaneously. The quality of the final layout is evaluated by minimizing total material handling cost. Sequence pair (SP) representation is used for layout encoding. The translation from SP to layout is efficiently made by longest common subsequence (LCS) methodology. An elitist strategy genetic algorithm using simulated annealing (E-GASAA) as a local search mechanism is developed and tested with four test problem instances available in the literature. Elitist strategy is incorporated to enhance convergence characteristic of the proposed algorithm. It is found that the proposed E-GASAA is able to produce best solutions consistently for the test problem instance of different sizes within acceptable computational effort. In addition to that, we tried to reduce the computational load with the help of adopted LCS computation methodology and achieved a good improvement.