【正文】 piece during a machining operation, minimizing work piece and fixture tooling deflections due to clamping and cutting forces are critical to ensuring accuracy of the machining operation. Traditionally, machining fixtures are designed and manufactured through trialanderror, which prove to be both expensive and timeconsuming to the manufacturing process. To ensure a work piece is manufactured according to specified dimensions and tolerances, it must be appropriately located and clamped, making it imperative to develop tools that will eliminate costly and timeconsuming trialanderror designs. Proper work piece location and fixture design are crucial to product quality in terms of precision, accuracy and finish of the machined part. Theoretically, the 321 locating principle can satisfactorily locate all prismatic shaped work pieces. This method provides the maximum rigidity with the minimum number of fixture elements. To position a part from a kinematic point of view means constraining the six degrees of freedom of a free moving body (three translations and three rotations). Three supports are positioned below the part to establish the location of the work piece on its vertical axis. Locators are placed on two peripheral edges and intended to establish the location of the work piece on the x and y horizontal axes. Properly locating the work piece in the fixture is vital to the overall accuracy and repeatability of the manufacturing process. Locators should be positioned as far apart as possible and should be placed on machined surfaces wherever possible. Supports are usually placed to enpass the center of gravity of a work piece and positioned as far apart as possible to maintain its stability. The primary responsibility of a clamp in fixture is to secure the part against the locators and supports. Clamps should not be expected to resist the cutting forces generated in the machining operation. For a given number of fixture elements, the machining fixture synthesis problem is the finding optimal layout or positions of the fixture elements around the work piece. In this paper, a method for fixture layout optimization using genetic algorithms is presented. The optimization objective is to search for a 2D fixture layout that minimizes the maximum elastic deformation at different locations of the work piece. ANSYS program has been used for calculating the deflection of the part under clamping and cutting forces. Two case studies are given to illustrate the proposed approach.2. Review of related worksFixture design has received considerable attention in recent years. However, little attention has been focused on the optimum fixture layout design. Manassas and Decries[1]used FEA for calculating deflections using the minimization of the work piece deflection at selected points as the design criterion. The design problem was to determine the position of supports. Meyer and Liou[2] presented an approach that uses linear programming technique to synthesize fixtures for dynamic machining conditions. Solution for the minimum clamping forces and locator forces is given. Li and Melkote[3]used a nonlinear programming method to solve the layout optimization problem. The method minimizes work piece location errors due to localized elastic deformation of the work piece. Roy andLiao[4]developed a heuristic method to plan for the best supporting and clamping positions. Tao et al.[5]presented a geometrical reasoning methodology for determining the optimal clamping points and clamping sequence for arbitrarily shaped workpieces. Liao and Hu[6]presented a system for fixture configuration analysis based on a dynamic model which analyses the fixture–work piece system subject to timevarying machining loads. The influence of clamping placement is also investigated. Li and Melkote[7]presented a fixture layout and clamping force optimal synthesis approach that accounts for work piece dynamics during machining. A bined fixture layout and clamping force optimization procedure presented. They used the contact elasticity modeling method that accounts for the influence of work piece rigid body dynamics during machining. Admiral et al. [8] used ANSYS to verify fixture design integrity. They employed 321 method. The optimization analysis is performed in ANSYS. Tan et al. [9] described the modeling, analysis and verification of optimal featuring configurations by the methods of force closure, optimization and finite element modeling. Most of the above studies use linear or nonlinear programming methods which often do not give global optimum solution. All of the fixture layout optimization procedures start with an initial feasible layout. Solutions from these methods are depending on the initial fixture layout. They do not consider the fixture layout optimization on overall work piece deformation. The GAs has been proven to be useful technique in solving optimization problems in engineering [10–12]. Fixture design has a large solution space and requires a search tool to find the best design. Few researchers have used the GAs for fixture design and fixture layout problems. Kumar et al. [13] have applied both GAs and neural networks for designing a fixture. Marcelin [14] has used GAs to the optimization of support positions. Vallapuzha et al. [15] presented GA based optimization method that uses spatial coordinates to represent the locations of fixture elements. Fixture layout optimization procedure was implemented using MATLAB and the genetic algorithm toolbox. HYPERMESH and MSC/NASTRAN were used for FE model. Vallapuzha et al. [16] presented results of an extensive investigation into the relative effectiveness of various optimization methods. They showed that continuous GA yielded the best quality solutions. Li and Shiu [17] determined the optimal fixture configuration design for sheet metal assembly using GA. MSC/NASTRAN has been used for fitness evaluation. Liao [18] presented a method to au