## 1 Introduction  
The manufacturing system comprises many components; fixture is considered to be the most important component. The purpose of fixture is to hold the work piece at a specific position and orientation in the assembly, manufacturing, and verification process [1]. Fixtures restrain workpieces in such a way that the deformation is minimized during the manufacturing process. They also reduce the deformation due to the weight of the workpiece under the effect of gravity. A fixture comprises locators and clamps. Locators are used to determine the position and orientation of a work piece. On other hand, clamps scrutiny clamping force to hold a workpiece against the locators [2]. Fixture design and fabrication cost is quite high and it comprises almost 10-20% of the cost of the manufacturing system. Product cost also depends on fixture cost. Fixture eliminates frequent checking, individual marking, positioning and non-uniform quality in manufacturing process. This results in a reduction in operation time and an increase in productivity. As defined by [PERSON] et al. [3]: fixture layout is to arrange fixture elements within the fixture, and optimized fixture layout is the arrangement of fixture elements that results in the minimum deformation of a workpiece. Different techniques of fixture layout optimization are used. The most popular are genetic algorithms, simulated annealing, mathematical programming methods, and ant colony algorithms. Due to the flexible nature of the sheet metal's rigid body, fixturing methods are not applicable to sheet metals. The research work on sheet metal is very limited in the literature and many researchers are focusing on sheet metal due to its many applications. In this research, the flexible workpiece is considered. First, the literature review regarding rigid body is explained, and later sheet metals. [PERSON] et al. [4] proposed a method to optimize fixture layout, considering dynamic conditions. Minimize deflection was set as the objective function and was achieved in terms of clamping force. [PERSON] et al. [5] worked on arbitrarily shaped workpieces while applying a computational geometric approach. [PERSON] et al. [6] developed a technique to find optimal support locations using FEA. Workpiece stability and minimization of maximum deformation is set as the objective function. [PERSON] et al. [7] proposed a method by combining the force closure method, optimization technique, and Finite Element Method (FEM) for optimal fixture modelling design and validation. [PERSON] et al. [8] optimized the fixture design using FEM. This research targets deformation and minimizes it during drilling and milling operations. The case study used involved the reduction of deformation up to 30% from initial deformation. [PERSON] et al. [9] optimized the machining fixture layout using the Genetic Algorithm (GA). Authors modified GA to optimize six locators using the 3-2-1 method. It was found that modified GA results in better stability and quality of the workpiece [10]. Most researchers are focusing on sheet metal fixture; the literature review regarding sheet metals is described below. [PERSON] et al. [11] were the first to consider fixture elements' number and position to optimize the fixture layout of sheet metal assembly used in laser welding using GA. [PERSON] et al. [12] developed a method known as the fixture configuration method for laser welding form on a newly suggested locating scheme. Authors verified the proposed method by applying it to an automotive assembly. [PERSON] et al. [13] developed the fixture optimization method to reduce variations in assembly undergoing welding gun variations. It was found that by using the welding gun variation model need of the Monte Carlo simulation was eliminated, because assembly variation simulation is converted into the deterministic assembly model. [PERSON] et al. [14] developed the N-2-1-1 fixture layout optimization method with integrating genetic algorithm and FEM. [PERSON] et al.