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The purpose of this paper is to present a modified bi-level integrated system collaborative optimization (BLISCO) to avoid the non-separability of the original BLISCO. Besides, to mitigate the computational burden caused by expensive simulation codes and employ both efficiently simplified and expensively detailed information in multidisciplinary design optimization (MDO), an effective framework combining variable fidelity metamodels (VFM) and modified BLISCO (MBLISCO) (VFM-MBLISCO) is proposed.

The concept of the quasi-separable MDO problems is introduced to limit range of applicability about the BLISCO method and then based on the quasi-separable MDO form, the modification of BLISCO method without any derivatives is presented to solve the problems of BLISCO. Besides, an effective framework combining VFM-MBLISCO is presented.

One mathematical problem conforms to the quasi-separable MDO form is tested and the overall results illustrate the feasibility and robustness of the MBLISCO. The design of a Small Waterplane Area Twin Hull catamaran demonstrates that the proposed VFM-MBLISCO framework is a feasible and efficient design methodology in support of design of engineering products.

The proposed approach exhibits great capability for MDO problems with tremendous computational costs.

A MBLISCO is proposed which can avoid the non-separability of the original BLISCO and an effective framework combining VFM-MBLISCO is presented to efficiently integrate the different fidelities information in MDO.

Uncertainty is inevitable in real-world engineering optimization. With an outer-inner optimization structure, most previous robust optimization (RO) approaches under interval uncertainty can become computationally intractable because the inner level must perform robust evaluation for each design alternative delivered from the outer level. This paper aims to propose an on-line Kriging metamodel-assisted variable adjustment robust optimization (OLK-VARO) to ease the computational burden of previous VARO approach.

In OLK-VARO, Kriging metamodels are constructed for replacing robust evaluations of the design alternative delivered from the outer level, reducing the nested optimization structure of previous VARO approach into a single loop optimization structure. An on-line updating mechanism is introduced in OLK-VARO to exploit the obtained data from previous iterations.

One nonlinear numerical example and two engineering cases have been used to demonstrate the applicability and efficiency of the proposed OLK-VARO approach. Results illustrate that OLK-VARO is able to obtain comparable robust optimums as to that obtained by previous VARO, while at the same time significantly reducing computational cost.

The proposed approach exhibits great capability for practical engineering design optimization problems under interval uncertainty.

The main contribution of this paper lies in the following: an OLK-VARO approach under interval uncertainty is proposed, which can significantly ease the computational burden of previous VARO approach.