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Truss Structural Optimization

by Real-Coded Probabilistic Model-Building GA Tomoyuki Hiroyasu,

^††

Mitsunori Miki

^††

and Hisashi Shimosaka

^†

In this paper, real-coded probabilistic model-building genetic algorithm (PMBGA) is ap- plied to structural optimization problems. In order to find an optimum in the problem which has a strong correlation among the parameters, principal component analysis (PCA) is ap- plied to the construction of the probabilistic model. To deal with the constraints, penalty function and pulling back methods are also applied to PMBGA. Using the proposed methods, a truss structure is designed to minimize its volume as a numerical example. Through the numerical example, the comparison between PMBGA and sequential quadratic programming method (SQP) shows the effectiveness of PMBGA and the handling methods of constraints.

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2 Comparison of PMBGA with penalty function method, PMBGA with pulling back method and SQP (Success Rate)

Success Rate

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Penalty Function 20/20 Pulling Back 20/20

3 Comparison of PMBGA with penalty function method, PMBGA with pulling back method and SQP (Number of Function Calls)

Number of Function Calls

SQP 67,370

Penalty Function 41,608

Pulling Back 169,726

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1) Goldberg,D.E. Genetic Algorithms in Search Optimization and Machine Learnig, Addison- Wesley, 1989.

2) Holland,J.H. Adaptation In Natural and Artificial Systems, University of Michigan Press,1975.

3) Pelikan,M. and Goldberg,D.E. and Fernando Lobo, A Servey of Optimization by Building and Using Probabilistic Models, illiGAL Report No.99018, 1999.

4) Michalewicz,Z. and Janikow,C.Z. Handling Constraints in Genetic Algorithms, Proc. of the International conference on Genetic Algo- rithms 4,pp.151-157

5) Tanese,R. Distributed Genetic Algorithms, Proc. of the 3rd International Conference on Genetic Algorithms,1989.

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