Analysis of gene expression programming for approximation in engineering design

To reduce the computational cost of implementing computer-based simulations and analyses in engineering design, a variety of metamodeling techniques have been developed and used for the construction of metamodels. Metamodels, also called approximation models and surrogate models, can be used to make a replacement of the expensive simulation codes for design and optimization. In this paper, gene expression programming (GEP) algorithm in the evolutionary computing area is investigated as an alternative metamodeling technique to provide the approximation of a design space. The approximation performance of GEP is tested on some low-dimensional mathematical and engineering problems. A comparative study is conducted on GEP and three common metamodeling techniques in engineering design (i.e., response surface methodology (RSM), kriging and radial basis functions (RBF)) for the approximation of the low-dimensional design space. Multiple evaluation criteria are considered in the comparison: accuracy, robustness, transparency and efficiency. Two different sample sizes are adopted: small and large. Comparative results indicate that GEP can achieve the most accurate and robust approximation of a low-dimensional design space for small sample sets. For large sample sets, GEP also presents good prediction accuracy and high robustness. Moreover, the transparency of GEP is the best since it can provide clear function relationships and factor contributions by means of compact expressions. As a novel metamodeling technique, GEP shows great promise for metamodeling applications in a low-dimensional design space, especially when only a few sample points are selected and used for training.