Analytical Target Cascading (ATC) is a method for design optimization of hierarchically decomposed multilevel systems. ATC subproblems are defined by introducing target and response variables that couple the subsystems of the original system. During the iterative solution inconsistencies between target and response variable values are minimized using a quadratic penalty function. Typically, a nested solution strategy is used consisting of an inner and an outer loop. In the inner loop subproblems are solved with fixed penalty weights while in the outer loop these weights are updated with information from the inner loop. Two sources of computational cost associated with solving the decomposed ATC problem are observed. First, accurate solutions can often be obtained only with large penalty weights, which can also introduce ill-conditioning of the subproblems. Second, subproblems are not independent and their solution has to be coordinated within the inner loop, meaning that subproblems may have to be solved many times before the algorithm can return to the outer loop. The article introduces the use of an augmented Lagrangian function to obtain accurate subproblem solutions for relatively small weights. To reduce the computational cost of coordination in the inner loop, an alternating directions method of multipliers is used. Instead of updating penalty parameters at convergence of the inner loop, the alternating direction method updates the penalty parameters after a single inner loop iteration. Inner loop coordination is reduced to solving subproblems only once. These new strategies are demonstrated on two example problems and compared to the quadratic penalty function currently used for ATC. Computational costs for the tested problems are decreased by orders of magnitude ranging between ten and one thousand.

This paper explores the use of decomposition-based methods for aircraft family design. The traditional approach in multidisciplinary design optimization is to decompose a problem along disciplinary lines. For aircraft family design problems, a more natural approach is decomposition by individual aircraft. This decomposition facilitates the concurrent development of several aircraft variants, providing substantial autonomy to individual aircraft development programs. Two decomposition-based methods are applied to the aircraft family problem: collaborative optimization and analytical target cascading. This paper marks the beginning of a collaborative effort to clarify the distinctions between these two methods, and to identify how these differences impact the relative performance and applicability of these methods. Initial product family results illustrate how decomposition-based methods can be applied to the aircraft family problem. I.

This paper critically examines the use of Analytic Target Cascading as a multi-level, hierarchical design optimization model for formulating simulation-based design tasks in architecture. A case study is used to illustrate the main steps involved in posing and solving an ATC problem. With an emphasis on problem formulation, this study is used as the basis of highlighting issues confronted while posing design analysis problems in a model-based systems framework.

In this research, a reliability based topology optimization (RBTO) for structural design methodology using the Hybrid Cellular Automata (HCA) method is proposed. More specifically, a decoupled reliability based design optimization (RBDO) approach is utilized, so that the topology optimization is separate from the reliability analysis. In this paper, a maximum allowable displacement failure mode is considered. In this methodology, starting from a continuum design space of uniform material distribution and initial uncertain variable values, a deterministic topology optimization is followed by a reliability assessment of the resulting structure to determine the most probable point of failure (MPP) for the current structure. The MPP is determined with respect to the maximum allowable deflection of the structure when loaded. This is generally a computationally expensive process using traditional techniques due to the large number of design variables associated with topology optimization problem. However, combining the e#cient methods of the non-gradient HCA algorithm with the decoupled approach for RBDO aims to reduce this burden. The topology optimization was without constraint in previous applications of the HCA method. To accommodate RTBO, a mechanism for a global constraint for maximum allowable displacement is developed. This paper details the methodology for the six-sigma design of structures using topology optimization.

Astute choices made early in the design process provide the best opportunity for reducing the life cycle cost of a new product. Optimal decisions require reasonably detailed disciplinary analyses, which pose coordination challenges. These types of complex multidisciplinary problems are best addressed through the use of decomposition-based methods, several of which have recently been developed. Two of these methods are collaborative optimization (CO) and analytical target cascading (ATC). CO was conceived in 1994 in response to multidisciplinary design needs in the aerospace industry. Recent progress has led to an updated version, enhanced collaborative optimization (ECO), that is introduced in this paper. ECO addresses many of the computational challenges inherent in CO, yielding significant computational savings and more robust solutions. ATC was formalized in 2000 to address needs in the automotive industry. While ATC was originally developed for object-based decomposition, it is also applicable to multidisciplinary design problems. In this paper, both methods are applied to a set of test cases. The goal is to introduce the ECO methodology by comparing and contrasting it with ATC, a method familiar within the mechanical engineering design community. Comparison of ECO and ATC is not intended to establish the computational superiority of either method. Rather, these two methods are compared as a means of highlighting several promising approaches to the coordination of distributed design problems.