On-line metamodel-assisted optimization with mixed variables

The optimization of complex civil engineering structures remains a major scientific challenge, mostly because of the high number of calls to the finite element analysis required by the complete design process. To achieve a significant reduction of this computational effort, a popular approach consists in substituting the high-fidelity simulation by a lower-fidelity regression model, also called a metamodel. However, most metamodels (like kriging, radial basis functions, etc.) focus on continuous variables, thereby neglecting the large amount of problems characterized by discrete, integer, or categorical data. Therefore, in this chapter, a complete metamodel-assisted optimization procedure is proposed to deal with mixed variables. The methodology includes a multi-objective evolutionary algorithm and a multiple kernel regression model, both adapted to mixed data, as well as an efficient on-line enrichment of the metamodel during the optimization. A structural benchmark test case illustrates the proposed approach, followed by a critical discussion about the generalization of the concepts introduced in this chapter for metamodel-assisted optimization.