Multidisciplinary collaborative optimization using fuzzy satisfaction degree and fuzzy sufficiency degree model

Collaborative optimization (CO) is a bi-level multidisciplinary design optimization (MDO) method for large-scale and distributed-analysis engineering design problems. Its architecture consists of optimization at both the system-level and autonomous discipline levels. The system-level optimization maintains the compatibility among coupled subsystems. In many engineering design applications, there are uncertainties associated with optimization models. These will cause the design objective and constraints, such as weight, price and volume, and their boundaries, to be fuzzy sets. In addition the multiple design objectives are generally not independent of each other, that makes the decision-making become complicated in the presence of conflicting objectives. The above factors considerably increase the modeling and computational difficulties in CO. To relieve the aforementioned difficulties, this paper proposes a new method that uses a fuzzy satisfaction degree model and a fuzzy sufficiency degree model in optimization at both the system level and the discipline level. In addition, two fuzzy multi-objective collaborative optimization strategies (Max-Min and alpha-cut method) are introduced. The former constructs the sufficiency degree for constraints and the satisfaction degree for design objectives in each discipline respectively, and adopts the Weighted Max-Min method to maximize an aggregation of them. The acceptable level is set up as the shared design variable between disciplines, and is maximized at the system level. In the second strategy, the decision-making space of the constraints is distributed in each discipline independently through the allocation of the levels of alpha. At the system level, the overall satisfaction degree for all disciplines is finally maximized. The illustrative mathematical example and engineering design problem are provided to demonstrate the feasibility of the proposed methods.