Optimization Algorithm Based On Geometric Constraint Solving Techniques

In the application of the engineering, most machine designs come from the grass diagram and existing sketch. In the grass diagram design, customers are careless of sketch of accurate size, but just delineate the shape of spare parts roughly; and customers will do a small improvement on the foundation of the existing sketch. It is normal to adjustment of the size. It is hard for the traditional method of making a diagram to adjust the shape, and the method has not inherit, so people put forward to parameter method.Geometric constraint is the core of Parametric Technology, given the size of designed draft and the bound of topological relations, system can generate corresponding designed draft automatic. At present, the geometric constraint solving method: numerical methods, symbolic methods, rules methods, graph theory. The use of graph theory and practical issues related to the theory of constraints to information on the constraint graph decomposition and assembly. Decomposition of the strong coupling of the geometric constraint graph into a body as small as possible of the Statute, the Statute of the assembly when the body-by-solving, and integration solutions as a whole. Geometric constraint graph can be expressed as geometric constraint undirected graph (GCG) and the geometric constraint has to map (DGCG), one of the geometric constraint graph has given full consideration to the direction of transmission constraints, but also with the geometric interpretability.The quality and maturity of geometric constraint solving technology decide the computational complexity and the speed and efficiency. So, it is import for a good algorithm of geometric constraint model for solving problems using geometric constraint.For the problems of Geometric constraint, some scholars launched a series of research, and some problems are to be resolved. Such as the speed and convergence of the Aalgorithm; under-constrained and over-constrained problem; classic Newton iteration more sensitive to the initial value, improper initial users will not want to cause convergence of the solution and so on. This article from the following aspects of the problem studied, a new geometric constraint solving methodFirst, for the sensitive problems of initial value of quasi-Newton method, I proposed quasi-Newton method. The idea of the algorithms: for the selection of the initial value of Quasi-Newton algorithm,we select the genetic algorithm global as master class , and local neighborhood search algorithm of particle swarm as cong class. We make the algorithm not depend on complicated coding way and the overall evolution operator accuracy searching,K on behalf of the finish for the evolution of the genetic groups to assess the fitness of one of the higher S elite individual as a quasi-Newton algorithm sets the initial value,then Simulate-Newton algorithm use the first value in the set S as its initial value,if it is not convergent after N times iterative operation,turn to the next element in the S,repeat until we find the root which is satisfied us with our precision request.The statute of the entities can be converted into nonlinear equations after decomposition of geometric constraint , and can be resolved in numerial methods。Newton method is the most classic numerical methods ,however,this method for the selection of initial value is more sensitive,resulting in no solution for some problem。The Simulate-Newton method is a betterment of Newton-Raphson method,compared with Newton-Raphson method,it has many advantages as follows:⑴only one-rank differential coefficient is needed,but Newton-Raphson method need two-rank differential coefficient,⑵the defect that Jacobi matrix is too huge and hard to compute is solved,In large-scale CAD,it is hard to compute Jacobi matrix,so Stimu-Newton method is more adaptable.⑶The time complexity of one iterative computation is ,but the Newton-Raphson method is ,time is saved greatly and accords with the characteristic of real time in CAD system.But it still unable to extricate itself from the initial value sensitive"bottleneck"Real-coded genetic algorithm for the solution space can be directly encoded,it is good at huge space searching,high efficiency,but an the latter phase ,the efficiency is low and immature convergence will happened,for the high-dimensional accuracy of complex numerical optimization function is not high.PSO has the advantage of a simple calculation and fast convergence ,but easy to fall into local optimum.Quasi-Newton solving problem in on the shortcomings,this paper presents a quasi-Newton optimization algorithm.Take full asvantage of the algorithm of genetic algorithm global search capability,is responsible for the problem solution space at RC optimal solution search ,particle swarm optimization to achieve a genetic chromosome as the center of the local neighborhood search more accurate,give the correct initial value range of feasible region,Quasi-Newton algorithm in the feasible solution space to complete the iteration ,and finally find a solution to meet the accuraty requirements.Experimental results show that the method is effective to solve the sensitive problem of the initial value ,the probability algorithm and the accuracy has improved.In the actual engineering sketch , exists many under-constraint system, the under-constrainde geometric of the less constraint system has many status, and it can't promise the rationality of the bounding directed graph , after matching constraint initial value, for the less constraint system, the main resolving idea is like this: If there are strongly connected component in the bounding directed graph, we hope that can be bound by adjusting the direction of the match,there is a change to the plans within the constraint distribution,reducing the maximum strongly connected component of the scale ,try to be a strongly connected component for solving the order of the smallest sequence.The idea of algorithms is like this: less constraint system, when you add a new Ct to the DGCG,firstly find the vertex'V'which RDOF is >0 in the related Vertex set of Ct,if exist,Ct matches with it,else, recursively search for the reversible path of vi, ,if failed,it indicate that Ct is redundant,if succeed,reverse the arc of vi.If vi has many reverse paths that can be matched transimition,we can do matching the results of any cohesion plan as there is evolution,adjust matching and point precipitation,finally,we can get a sort a better graph.Adding adjusted to optimize matching of the strongly connected component can gather real-time operation will be required to match polymorphism generated by the non-linear numerical solution of the compound to do further decomposition .The implementation of adaptive constraint solving optimal adjustment , effective restraint systems have improved the quality of the solution.In conclusion, the achievements of this dissertation make the applied research on the geometric constraint solving theory progress. It has a certain theory significance and application importance. It provides effective methods and means for the research on the geometric constraint solving.