Efficient algorithms and models for mechanical and structural design optimization

Abstract

In the present work, different algorithms and penalty methods for design optimization of mechanical elements and structures are applied. Seven robust optimization techniques and seven penalty methods are thoroughly investigated and implemented in MATLAB codes. In addition, different optimization models are compared using two benchmark problems, namely, the minimal cost design of a welded beam structure and the optimal buckling design of a functionally graded material column. A performance measure factor is defined to determine the best technique among the implemented optimization algorithms. The results are arranged and nested to make it easy for the reader to figure out each technique characteristics, and hence choose the suitable one for a specific design problem and/or application. Comprehensive computer experimentations were performed, and the best optimization techniques and models have been thoroughly demonstrated. The attained optimal solutions show that, in general, the hybrid algorithms worked better than the stand-alone ones and the sequential quadratic programming (SQP) with global search indicates a superior performance than other techniques. Finally, based on the present study, the adaptive and dynamic penalties need further investigation to become more consistent with the implemented optimization algorithms.