【正文】 n 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 automatically select the optimal numbers of locators and clamps as well as their optimal positions in sheet metal assembly fixtures. Krishnakumar and Melkote [19] developed a fixture layout optimization technique that uses the GA to find the fixture layout that minimizes the deformation of the machined surface due to clamping and machining forces over the entire tool path. Locator and clamp positions are specified by node numbers. A builtin finite element solver was developed. Some of the studies do not consider the optimization of the layout for entire tool path and chip removal is not taken into account. Some of the studies used node numbers as design parameters. In this study, a GA tool has been developed to find the optimal locator and clamp positions in 2D work piece. Distances from the reference edges as design parameters are used rather than FEA node numbers. Fitness values of real encoded GA chromosomes are obtained from the results of FEA. ANSYS has been used for FEA calculations. A chromosome library approach is used in order to decrease the solution time. Developed GA tool is tested on two test problems. Two case studies are given to illustrate the developed approach. Main contributions of this paper can be summarized as follows:(1) developed a GA code integrated with a mercial finite element solver。(2) GA uses chromosome library in order to decrease the putation time。(3) real design parameters are used rather than FEA node numbers。(4) chip removal is taken into account while tool forces moving on the work piece..3. Genetic algorithm conceptsGenetic algorithms were first developed by John Holland. Goldberg [10] published a book explaining the theory and application examples of genetic algorithm in details. A genetic algorithm is a random search technique that mimics some mechanisms of natural evolution. The algorithm works on a population of designs. The population evolves from generation to generation, gradually improving its adaptation to the environment through natural selection。 fitter individuals have better chances of transmitting their characteristics to later generations.In the algorithm, the selection of the natural environment is replaced by artificial selection based on a puted fitness for each design. The term fitness is used to designate the chromosome’s chances of survival and it is essentially the objective function of the optimization problem. The chromosomes that define characteristics of biological beings are replaced by strings of numerical values representing the design variables.GA is recognized to be different than traditional gradient based optimization techniques in the following four major ways [10]:1. GAs work with a coding of the design variables and parameters in the problem, rather than with the actual parameters themselves.2. GAs makes use of populationtype search. Many different design points are evaluated during each iteration instead of sequentially moving from one point to the next.3. GAs needs only a fitness or objective function value. No derivatives or gradients are necessary.4. GAs use probabilistic transition rules to find new design points for exploration rather than using deterministic rules based on gradient information to find these new points.4. Approach. Fixture positioning principlesIn machining process, fixtures are used to keep workpieces in a desirable position for operations. The most important criteria for featuring are work piece position accuracy and work piece deformation. A good fixture design minimizes work piece geometric and machining accuracy errors. Another featuring requirement is that the fixture must limit deformation of the work piece. It is important to consider the cutting forces as well as the clamping forces. Without adequate fixture support, machining operations do not conform to designed tolerances. Finite element analysis is a powerful tool in the resolution of some of these problems [22].Common locating method for prismatic parts is 321 method. This method provides the maximum rigidity with the minimum number of fixture elements. A work piece in 3D may be positively located by means of six points positioned so that they restrict nine degrees of freedom of the work piece. The other three degrees of freedom are removed by clamp elements. An example layout for 2D work piece based 321 locating principle is shown in Fig. 4.Fig. 4. 321 locating layout for 2D prismatic work pieceThe number of locating faces must not exceed two so as to avoid a redundant location. Based on the 321 featuring principle there are two locating planes for accurate location containing two and one locators. Therefore, there are maximum of two side clamping against each locating plane. Clamping forces are always directed towards the locators in order to force the work piece to contact all locators. The clamping point should be positioned opposite the positioning points to prevent the work piece from being distorted by the