0-1 Programming Problem Continuous Solution and Application to Topological Optimization of the Continuum Structure
|School||Beijing University of Technology|
|Keywords||0-1 programming ICM method high order contraction Generalized Geometric Programming topology optimization design software|
Structural topology optimization belongs to 0-1 programming problem essentially. The structural topology optimization model, which is established by ICM (Independent Continuous Mapping) method, is extremely nonlinear. In this thesis, according to the high order contraction method, the object functions and the constraint functions of the structural topology optimization model are expanded in logarithm space; consequently, it gets a more precise approximate description than the model expanded by Tyler expansion, the procedure of model optimization is a more precise solution. The ICM method based on this thesis, the topology optimization problem of continuum structures is solved.The central content is:(1) Generalized Geometric Programming problem is solved by high order contraction method.(2) The discrete 0-1 programming problem is translated into continuous nonlinear optimization problem by polish function, and the nonlinear optimization problem is solved by contraction algorithm.(3) The topology optimization problem is approximately modeled of continuum structures by filter function, then the optimization problem is solved by contraction algorithm.(4) Two software are designed: Solve 0-1 Programming Software based Contraction Algorithm and Continuum Structures Optimization Software based Contraction Algorithm.