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Analytical target cascading (ATC) method has been widely applied to solve multilevel decomposed system design optimization problems. In the ATC method, concurrent design is achieved by target cascading. However, due to the complexity and the presence of uncertainty, it is a challenging task to set proper targets. In this article, instead of using point value targets, interval targets are analyzed and propagated through the multilevel system with the goal of reducing the effects of uncertainty while providing more flexibility to a design process. In the proposed method, the design of a hierarchical system at each level is taken as a single-objective optimization problem, by minimizing the degree of deviation between the target response interval and the achievable response interval. Not only the optimal design performance is considered in this method, but also the acceptable variation range of the performance is analyzed. When the present target for a lower level system and the achievable response from a lower level system are not point values, but rather intervals, their probability distributions are not available. Therefore, these variables are treated as interval variables. When the random and interval variables are present, the most probable point-based first-order reliability and the interval analysis methods are used to calculate the reliability bounds. The proposed method for flexibility under uncertainty provides more degree of freedom to the design of lower level systems, while also keeping the performance of the upper systems stable within a tolerable range. The accuracy of the proposed method is demonstrated via comparing results from both the proposed and traditional methods. [ABSTRACT FROM AUTHOR]

A novel non-probabilistic robust design optimization model using interval analysis is presented. Based on non-linear interval number programming and function interval extension, the robustness was assessed, and the uncertain robust optimization model with interval parameters was transformed into a deterministic form, which can achieve the objective with any expected robustness level according to decision-maker, and a bi-level mathematical model is established. This model doesn't require the presumed probability distribution of uncertain factors and gradient or continuous information of constraints and objective functions. Experimental results demonstrate the effectiveness of the given method. [ABSTRACT FROM AUTHOR]

The conflictive and fuzzy coupling relationships between product quality and tolerances of design variables always bring out the deviation between optimization results and design intention to a certain extent. Considering the fuzzy subjective and objective factors, which exist in engineering robust design problem, a fuzzy robust optimization model based on tolerance objectives is established using interval weighted coefficient method. Physical programming is used to describe the designers' progressive preference. A Pareto design set is obtained by controlling the interval weighted coefficients. A map from Pareto designs to their corresponding evaluation value is established using compromise programming. An interactive decision-making is carried out through improving the progressive preference by the tradeoff of the conflictive degree between objectives. The given numerical example illustrates that the proposed method can get the optimal solution which satisfies the subjective and objective uncertainties of robust design requirements. [ABSTRACT FROM AUTHOR]