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In multidisciplinary design optimization (MDO), if the relationships between design variables and some output parameters, which are important performance constraints, are complex implicit problems, plenty of time should be spent on computationally expensive simulations to identify whether the implicit constraints are satisfied with the given design variables during the optimization iteration process. The purpose of this paper is to propose an ensemble of surrogates-based analytical target cascading (ESATC) method to tackle such MDO engineering design problems with reduced computational cost and high optimization accuracy.

Different surrogate models are constructed based on the sample point sets obtained by Latin hypercube sampling (LHS) method. Then, according to the error metric of each surrogate model, the repeated ensemble of surrogates is constructed to approximate the implicit objective functions and constraints. Under the framework of analytical target cascading (ATC), the MDO problem is decomposed into several optimization subproblems and the function of analysis module of each subproblem is simulated by repeated ensemble of surrogates, working together to find the optimum solution.

The proposed method shows better modeling accuracy and robustness than other individual surrogate model-based ATC method. A numerical benchmark problem and an industrial case study of the structural design of a super heavy vertical lathe machine tool are utilized to demonstrate the accuracy and efficiency of the proposed method.

This paper integrates a repeated ensemble method with ATC strategy to construct the ESATC framework which is an effective method to solve MDO problems with implicit constraints and black-box objectives.