The Optimal Layout Algorithm Research Of Punching Parts Based On Artificial Neural Networks

Optimal layout with computer assistant is to arrange more and more parts on a board as reasoned and efficaciously in some limited condition. The aim is to reduce waste and improve the stuff using rate. Optimal layout with computer assistant is a typical problem about combination and optimizing. It is very complex in calculating. Cutting stock 2D is filiations of optimal layout with computer assistant. It has practice value.Optimal layout problem is applied in lots of industries broadly. Its economy and society benefit is very considerable. But because of the complexity, in some fields manual layout is adopted. So not only the manpower resource and time resource are wasted, but also in some time the best layout project can not be got cause of the people's faction. At first people brought forward the optimal layout as a pure arithmetic. Some simple layout problem such as layout 1D, rectangle layout, circularity layout, triangle layout, looking like simply, are very difficult to resolve. There will be appeared combination explode phenomenon in layout of regular objects because the answer room of layout is extended by index times when the number of layout object is increased. As for irregular objects, because the unbending of their modality, the problem becomes thundering complex. Optimal layout problem in engineering is more complex than it in the theory. At present, there is a few of software on irregular-parts optimal layout. And those software need proving in more aspects. As following is the study content of this paper.Punching parts are regarded as closed two-dimension geometry graphics. Then optimal layout problem between punching parts changes to the operation problem between graphics. That is to say, it takes two-dimension geometry graphics as operation objects and as a result of output. In order to describe the graphics'insidesand outsides effectively, loops are used to describe the graphics'boundary. Loop is composed by a set of border vectors which are joined from beginning to end. Each loop is described by a circle and order positive integer gather. The positive integer gather is L1 , L2,Ln ,L1. Positive integer index the loop peak coordinates. Two border upon integer(s Li , Li+1)composed a loop border vector. The operation of two graphics is two-dimension Boolean operation between two loops, including intersection,union and subtraction. The calculation of between punching parts is the Boolean intersection operation of two graphics. And the superposition area can get trough polygon area formula.The paper also introduces two-dimension graphics geometry transform, such as shift,rotation,symmetry and combination transform. In order to unified express the graphics geometry transform by matrix, homogeneous coordinate is used to express the special point. So any two-dimension transform can be obtained by matrix multiplication. In the process of optimal layout, graphics geometry combination transforms make the relative movement between punching parts come true.In process of punching and layout, the join side between work-pieces or work-piece and bar side is required to satisfy the request of concave model. In order to calculate and distinguish in process of layout conveniently, we don't make use of the original figure dimension of work-piece to layout, but the isometric magnifying figure which is enlarge along with the normal direction of original figure outline. On the other side, punching parts data-bases are founded to realize the information storage of punching parts. The information of punching parts include engineering information and craftwork information such as the parts name, fig number, material thickness and so on. So these data are numerical and character frame, they can be stored in relation database by two dimension list.In the 90th of last century, the technology of computer was improved and artificial intelligence appeared. Genetic algorithms,simulated annealing,ant algorithm and artificial neural networks gradually become the hotspots of research. In the same time, there were researches based on the arithmetic. This paper studies the punching parts optimal layout problem in system and figures out how to solve it using Hopfield artificial neural networks.In 1982, American physical scientist J. Hopfield put forward a monolayer interlinked completely recursion network with symmetry synapses. Hopfield formed a new calculation method using the thinking of constructing an energy function. And illuminate the relation of neural networks and dynamics, and then used the non-linearity dynamics to study this neural networks'characteristic, and founded the criterion of neural networks'stability. Energy function is a scalar quantity function which can reflect excessive dimension nerve cell states. It can be used to estimate the stability of monolayer dynamic neural networks. In 1984, Hopfield designed and studied the Hopfield neural networks model circuit. He pointed that nerve cell could be substituted by operation amplifier and all connects of nerve cell could simulate through electron circuitry. This is continuous Hopfield neural networks (CHNN). Hopfield dissolved traveler (TSP) difficult problem (optimized problem).The thoughts of CHNN used to dissolve optimized problem are as follows. At first, optimized problem is mapped to neural networks'specifically configurations. The configurations correspond to optimized problem'potential answers. And then a corresponded energy function is constructed. The format is E =(1/2)V~T WV-I~TVThe energy function is the direct ratio of optimized problem'aim function. When the system is in imbecility state, the output of every deal unit is closed to zero or max. At last, the answers in steady state change to optimized problem'answers.According to the principle of Hopfield NN solving optimal problem, thispaper mapped the layout problem of irregular punching parts on fixed configuration of NN, and make the stable output of nerve cell corresponding the answer of problem. Then on the foundation of aim function f(x) of layout of irregular punching parts the first item of energy function is written out. According to the limit condition g(x), the penalize function as second item of energy function is written out. When the limit condition is satisfied, the penalize function get the least value. So the energy function is constructed as E ( x)= f(x)+c(g(x))2 (c is limit intension). Therefore the limit optimal problem is transformed unlimited optimal problem. The power matrix, threshold matrix and original state expression of net are educed. At the same time, the net parameters are selected according to the requirement of problem.Based on the optimal model and Hopfield NN arithmetic on the text, this paper applies VB which is a computer language face to the objects to compile program and make interface. At the same time, some sample parts are tested in this layout system, and some reasonable results are got.At the end of this paper, the application of Hopfield NN in punching parts layout is analyzed, and then some advise of research direction is provide to reference.