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Algorithm Research And Improve In Optimize Design

Posted on:2006-12-18Degree:MasterType:Thesis
Country:ChinaCandidate:S H ZhouFull Text:PDF
GTID:2120360182477339Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
People begin to realize the importance of resource rational scheme and efficiency improves along with the development of the society."Optimize design"has already been heard in any field. As the demand for"optimize design", it provides a new development to this subject, and at the same time puts forwards a higher request to this subject..In this paper, first we introduce a series of basis principles and corresponding solving methods. Second, on that basis, we have improved these methods. For linear programming, we point out the reason of iterative recurrence caused by degeneracy,and present a new simplex-like algorithm.The thought is that from any feasible basis finding the special basis solution series of the linear equation corresponding to constraint equation Ax =b,and along the feasible direction in which the length can not be zero and the function valve dropping most quickly,getting the next feasible basis.The numerical experiments illustrate that the speed of its convergency and stability is better than the method of biggest test count,and can be used for degeneracy problem.For nonlinear programming, firstly we introduce a series of basis principle of penalty function method, constrained variable metric method and genetic method. Secondly, we introduce a sort of novel adaptive penalty gene, transform the constrained problem into unconstrained problems. Get a solution for this unconstrained problem by genetic algorithm, and then use this solution as initial values for the constrained variable metric method to get the precise solution. The numerical experiments illustrate that this hybrid genetic algorithm is more efficient than the genetic algorithm, and at the most situation we can get globally optimal solution.
Keywords/Search Tags:linear programming, simplex-like algorithm, degeneracy, nonlinear programming problems, penalty function algorithm, genetic algorithm, the constrained variable metric method
PDF Full Text Request
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