# American Institute of Mathematical Sciences

2007, 3(3): 543-552. doi: 10.3934/jimo.2007.3.543

## A two-step algorithm for layout optimization of structures with discrete variables

 1 Department of Computer Science, Tianjin University of Technology and Education, Tianjin 300222, P.R., China 2 Department of Mathematics, Dalian University of Technology, Dalian 116023, P.R., China 3 Department of Mechanics, Dalian University of Technology, Dalian 116023, P.R., China 4 Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78541

Received  December 2006 Revised  January 2007 Published  July 2007

This paper presents a mathematical model for Layout optimization of structure with discrete variables. The optimization procedure is composed of two kinds of sub-procedures of optimization: the topological optimization and the shape optimization. In each one, a comprehensive algorithm is used to treat the problem. The two kinds of optimization procedures are used in turn until convergence appears. After the dimension of the structure is reduced, the delimiting combinatorial algorithm is used to search for the better objective value. A couple of classical examples are presented to show the efficiency of the method. Numerical results indicate that the method is efficient and the optimal results are satisfactory.
Citation: Lianshuan Shi, Enmin Feng, Huanchun Sun, Zhaosheng Feng. A two-step algorithm for layout optimization of structures with discrete variables. Journal of Industrial & Management Optimization, 2007, 3 (3) : 543-552. doi: 10.3934/jimo.2007.3.543
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