Improving Penalty Functions for Structural Optimization

New penalty functions, which have better convergence properties, as compared to the commonly used exterior and interior penalty functions, have been proposed in this paper. the convergence behavior and accuracy of ordinary penalty functions depend on the selection of appropriate penalty parameters. the optimization of ordinary penalty functions is accomplished after several rounds of optimization where, at each round a different but fixed value of penalty parameter is used. while some useful hints and rules for the selection of suitable penalty parameter values have been provided by different authors, the objective of this paper has been to improve this procedure by including the penalty parameter in the design vector, so that it can be modi ed during the optimization, automatically, in order to improve the convergence characteristics. this can also help accomplish optimization in only one round, which is of considerable importance when it is desired to solve a constrained problem by using genetic algorithms. the proof of convergence to the optimum solution of the proposed functions is also included in the paper. ten-bar and three-bar truss examples are used for illustration through which the convergence of ordinary and new functions are evaluated and compared. the results show that the new penalty functions can outperform the ordinary functions, especially in combination with genetic algorithms.