1. The complete title of the Publication: A Multi-Objective Evolutionary Framework for Formulation of Nonlinear Structural Systems 2. Author information: * Amir H. Gandomi Professor of Data Science, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, Australia e-mail: Gandomi@uts.edu.au * David A. Roke Associate Professor of Civil Engineering, Department of Civil Engineering, University of Akron, OH, USA. e-mail: Roke@uakron.edu 3. Corresponding author Amir H. Gandomi Professor of Data Science, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, Australia Gandomi@uts.edu.au +61 (02) 9514 5081 4. Paper abstract In this study, an evolutionary framework is proposed for seismic response formulation of self-centering concentrically braced frame (SC-CBF) systems. A total of 75 different SC-CBF systems were designed, and their responses were recorded under 170 earthquake records. To select the most important earthquake intensity measures, an evolutionary feature selection strategy based on genetic programming is introduced, which tries to find the highest correlation by considering nonlinear correlations. For the formulation of the SC-CBF response, a hybrid multi-objective genetic programming and regression analysis is implemented, considering both model accuracy and model complexity as objectives. In the hybrid approach, regression tries to connect multiple genes. Non-dominated models are presented, and the best model is selected based on the practical approach proposed here. The best model is compared with four other genetic programming models. The results show that the evolutionary procedure is highly effective for designing the SC-CBF system using a simple and accurate model for such a complex system. 5. Competition criterion (B) The result is equal to or better than a result that was accepted as a new scientific result at the time when it was published in a peer-reviewed scientific journal. (G) The result solves a problem of indisputable difficulty in its field. 6. Statement why the result satisfies criteria (B and G): (B) Table II of the paper clearly shows how the proposed evolutionary correlation (Re) can capture nonlinear correlations and outperform well-known Pearson's correlation coefficient (R), which only measures linear correlation. The variable rankings were compared with F-test results, which score (-log(p-value)) the importance of each input variable individually for regression. The ranking is very similar to what is provided by Re2 in Table II validating our proposed approach. Note that the modification of R2 (Re2) can measure nonlinear correlations used for feature selection, can reveal the hidden nonlinearity (presented in percentages in Table II) missed by R2, and can provide an explicit equation to represent this nonlinearity. (G) Steel concentrically-braced frame (CBF) systems have been widely used as seismic lateral force-resisting systems in the United States and around the world. A damage-free earthquake-resistant structural system, called the self-centering CBF (SC-CBF) system, was proposed by Roke et al. (2006). This system has some special elements that permit rocking behavior under lateral loads, such as those generated by an earthquake. Findng the maximum response (maximum roof drift) of the SC-CBF structure is vital in order to design such system. Roke et al. (2010) used a general strategy for self-centering systems (called µ-R-T) for designing the SC-CBF systems and approximation of the median roof drift in the design stage. However, Roke et al. (2010) found this method is not accurate enough to predict the median design value of the maximum roof drift. There is no analytical solution to estimate the drift response and only empirical and semi-empirical models can be used in this case. As this system is relatively new, there are very limited studies in this field and there is lack of appropriate drift response predictions. The nominated study formulates and predicts the maximum response of SC-CBF systems of a specific earthquake record. For this challenging engineering problem, the goal is to develop an explicit and interpretable model that is applicable in practice and for designing such systems. References Roke, D., Sause, R., Ricles, J.M., Seo, C.-Y., and Lee, K.-S. (2006). Self-Centering Seismic-Resistant Steel Concentrically-Braced Frames. Proceedings of the 8th U.S. National Conference on Earthquake Engineering, EERI, San Francisco, April 18-22. Roke, D., Sause, R., Ricles, J.M., and Chancellor, N.B. (2010). Damage-Free Seismic-Resistant Self-Centering Concentrically-Braced Frames. ATLSS Report 10-09, Lehigh University, Bethlehem, PA, USA. 7. Full citation Gandomi, Amir H., and David Roke. "A Multi-Objective Evolutionary Framework for Formulation of Nonlinear Structural Systems." IEEE Transactions on Industrial Informatics (15 Nov 2021). DOI 10.1109/TII.2021.3126702 8. Prize breakdown statement Any prize money, if any, is to be divided equally among the co-authors. 9. Required statement indicating why this entry could be the "Best" The highly nonlinear nature of the structural response, combined with the stochastic nature of earthquake motion makes the problem challenging. An evolutionary correlation coefficient is proposed to select the best earthquake intensity features to account for Pearson's correlation coefficient, which only measures linear correlation. Introduce genetic programming-based framework found a simple yet accurate model (equation 7) for such a complex problem. The explicit model provided for the maximum response of the systems, addressed an important challenge in the SC-CBF design procedure and useful in practice. 10. Evolutionary computation type Genetic Programming (GP) 11. Publication date This paper has been made available online on 15 November 2021.