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 workpiece 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 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 built-in 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 workpiece。 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 commercial finite element solver;

(2) GA uses chromosome library in order to decrease the computation 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 workpiece。

3。 Genetic algorithm concepts

Genetic 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 inpiduals 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 computed 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。