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Analytical target cascading (ATC) is a hierarchical systems optimization method that works by decomposing a system into a hierarchy of subsystems and coordinating the optimization of subsystems so that the joint solution is consistent and optimal for the overall system.

Introduction

When designing complex systems, generally it is not possible or desirable to have a single decision-maker in charge of all decisions. Instead, such systems are routinely decomposed hierarchically into subsystems and components, and various design groups interact to coordinate their decisions and achieve a feasible and consistent system solution. For each system in such a hierarchy, target specifications are chosen for the subsystems below such that the system can meet targets set by the supersystem above. If targets cannot be met, negotiation and rebalancing is necessary to ensure that the final system solution is consistent and achieves system goals. Ford Motor Company refers to this process as target cascading, and the analogous model-based, computational process for such hierarchical systems has been termed analytical target cascading (ATC) [1]. In ATC, top level design targets are propagated to lower levels, which are optimized to meet the targets. The resulting responses are rebalanced at higher levels to achieve consistency. The optimal system solution is obtained through an iterative process until target/response consistency is achieved globally.

ATC approaches this target-setting and matching process through formal mathematical decomposition methods, and so it has similarities to many of the multidisciplinary design optimization (MDO) methods that have been developed to coordinate complex analysis models from various disciplines during optimization, such as collaborative optimization (CO), concurrent subspace optimization (CSSO), and bi-level integrated system synthesis (BLISS). In particular, Allison et al. [2] compare and contrast ATC and CO. Apart from the difference in initial motivation, the formulation of ATC also differs in that it is defined for an arbitrarily large hierarchy of subsystems, and formal convergence proofs ensure that the method will reach an optimal system solution under typical assumptions. More recently, methods for solving non-hierarchical quasiseparable, or dual block-angular, problems with proven convergence properties have also emerged [3,4]. This article focuses on hierarchical problems in the spirit of ATC; however, ATC works by translating a hierarchical problem into a quasiseparable problem through relaxation of target-response relationships between systems and their subsystems, and many of the methods posed for solving hierarchical ATC systems have or could also be used to approach general quasiseparable systems. ATC has been applied to complex systems such as automotive design [5], architectural design [6], and multidisciplinary product development [7,8].

References

[1] J. Allison, M. Kokkolaras, M. Zawislak, and P. Papalambros. “On the use of analytical target cascading and collaborative optimization for complex system design”. In Proceedings of the 6th World Congress on Structural and Multidisciplinary Optimization, Rio de Janeiro, Brazil, 2005.
[2] D.P. Bertsekas. Nonlinear Programming. Athena Scientific, Belmont, Massachusetts, 2 edition, 2003.
[3] D.P. Bertsekas and J.N. Tsitsiklis. Parallel and Distributed Computation. Prentice-Hall, 1989.
[4] R. Choudhary, A. Malkawi, and P.Y. Papalambros. “Analytic target cascading in simulation-based building design”. Automation in Construction, 14(4):551 – 568, 2005.
[5] R.T. Haftka and L.T. Watson. “Multidisciplinary design optimization with quasisepa- rable subsystems”. Optimization and Engineering, 6(1):9 – 20, March 2005.
[6] H.M. Kim, N.F. Michelena, P.Y. Papalambros, and T.Jiang. “Target cascading in optimal system design”. Journal of Mechanical Design, 125(3):474 – 480, September 2003.
[7] H.M. Kim, M.Kokkolaras, L.S. Louca, G.J. Delagrammatikas, N.F. Michelena, Z.S. Filipi, P.Y. Papalambros, J.L. Stein, and D.N. Assanis. “Target cascading in vehicle redesign: a class vi truck study”. International Journal of Vehicle Design, 29(3):199 – 225, 2002.
[8] H.M. Kim, W.Chen, and M.M. Wiecek. “Lagrangian coordination for enhancing the convergence of analytical target cascading”. AIAA Journal. To appear.
[9] J.B. Lassiter, M.M. Wiecek, and K.R. Andrighetti. “Lagrangian coordination and ana- lytical target cascading: Solving ATC-decomposed problems with lagrangian duality”. Optimization and Engineering, 6(3):361 – 381, September 2005.
[10] J.J. Michalek, O. Ceryan, P.Y. Papalambros, and Y.Koren. “Balancing marketabil- ity and manufacturability in product line design decision-making”. ASME Journal of Mechanical Design, 2006.
[11] J.J. Michalek, F.M. Feinberg, and P.Y. Papalambros. “Linking marketing and engi- neering product design decisions via analytical target cascading”. Journal of Product Innovation Management, 22:42 – 62, 2005.
[12] J.J Michalek and P.Y. Papalambros. “An efficient weighting update method to achieve acceptable inconsistency deviation in analytical target cascading”. Journal of Mechanical Design, 127(3):206 – 214, March 2005. 41