【正文】 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。(3) real design parameters are used rather than FEA node numbers。 Optimization1. IntroductionFixtures are used to locate and constrain a work 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 desig