Constraint-Based Facility Layout Problem (CBFLP) is an important problem for industrial engineernot only for setting up the new facility layouts but also improving the currently used facility layouts.Those constraints, limitations of department arrangement in facility layout, emerge from users oroperators requirement which response to maximize their usage or satisfaction. The constraints offacility layout from users in this research can be classified to many ways such as users can specifyshape of total area to non-rectangular area, users can fix position of some department in any total area,users can define shape of some department for install specific shape machine or department, users canspecify minimum area of some department, users can determine minimum aspect ratio of department.These constraints are related only with physical arrangement.The solving approach for these constraints is more complicated. In practically, the plant designer mustconsider any other information together with above constraints. The information can be classified to 3objective functions. Firstly, the objective function is to minimize cost of material flow. Cost ofmaterial flow in such plant layout depend on frequency of flow from department i to department j,unit cost of flow from department i to department j and distance from department i to department j.Secondly, the objective function is to minimize aisle relationship. Aisle relationship of facility layoutindicates to the utilization of intersection served area so that it should be minimize. Thirdly, forqualitative data, the objective is to minimize total closeness desirability by moving as closely aspossible the departments with high preference of reducing distance between departments. Moreover,material flow in such facility layout is time independent generally; it is not a constant numberespecially in non-automatic plant. Fuzzy interflow can be an estimation of material flow efficiently.By defining the flow volume i.e. best case, near-best case, near-worst case, and worse case, it can bereplaced by trapezoidal fuzzy number (TrFN). They can be used to estimate the flow volume betweendepartments.This kind of mentioned problem known as NP-Complete problem and classified in theclass of combinatorial optimization, and the material flow has to be formalized by using fuzzy set.This research proposes Multi Objective Fuzzy-Genetic Algorithms (MOFGA) for arrangingdepartments in facility layout with mentioned constraints, objective functions and fuzzy material flow.The objectives are to minimize cost of material flow, aisle relationship and total closeness rating, andto arrange departments or machines by restricted constraints of user.Because the performance of MOFGA depends on several parameters; pilot runs and experimentaldesigns have been used to test these parameters including population size, probability of crossover,probability of mutation, selection type, crossover type, and mutation type with many cases ofproblems for instance small number of department, medium number of department and large numberof department. Through performance comparisons, it is found that MOFGA performs equally well orsignificantly better than the MCRAFT heuristic. In addition, MOFGA is a promising solutiontechnique in searching for a good solution with an acceptable time limit.