Enhanced Collaborative Optimization: Application to an Analytic Test Problem and Aircraft Design Brian Roth ∗ and Ilan Kroo † Stanford University, Stanford, California, 94305, USA This paper provides an introduction to a new method for distributed optimization based on collaborative optimization, a decomposition-based method for the optimization of com- plex multidisciplinary designs. The key idea in this approach is to include models of the global objective and all of the subspace constraints in each subspace optimization problem while maintaining the low dimensionality of the system level (coordination) problem. Re- sults from an analytic test case and an aircraft family design problem suggest that the new approach is robust and leads to a substantial reduction in computational effort. I. Introduction Collaborative optimization (CO) is a method for the design of complex, multidisciplinary systems that was originally proposed 1 in 1994. CO is one of several decomposition-based methods that divides a design problem along disciplinary (or other convenient) boundaries. The idea is to mirror the natural divisions found in aerospace design companies. In these settings, engineers are often divided into design groups by disciplinary expertise. Disciplinary analysis tools tend to be complex in nature, and it is often impractical to integrate multiple analysis codes for the purpose of multidisciplinary optimization. Rather, CO offers a means of coordinating separate analyses, even leveraging discipline-specific optimization techniques. Relative to other decomposition-based methods, CO provides the disciplinary subspaces with an unusually high level of autonomy. This enhances their ability to independently make design decisions pertinent primarily to their discipline. Collaborative optimization has been successfully applied to a variety of mathematical test problems and practical engineering design problems. For example, it has been used for the conceptual design of launch vehicles, 2, 3 high speed civil transports 4 and unmanned aerial vehicles. 5 However, it also suffers from some challenges, as documented by Alexandrov, 6, 7 DiMiguel, 8 and others. DeMiguel highlights features of CO that have an adverse effect on robustness and computational efficiency. Three of these deficiencies are briefly reviewed in the following paragraph, since they strongly motivated the development of enhanced collaborative optimization (ECO). The basic CO formulation is composed of two levels. The system level (top level) is given by Equation 1. Note that the variable set (z) includes only those variables required by more than one subspace. The x * s are subspace target responses that provide each subspace’s best attempt to meet the system level targets (z). The x * s are treated as dependent variables, which means that the subspaces must be re-optimized each time that the system level evaluates its constraints. min z F (1) subject to J i = ‖z − x * s ‖ 2 2 ≤ 0, i =1,...,n where F (z) is the global objective z are variables (i.e., system level targets for shared variables) x * s are dependent variables (i.e., subspace target responses) n is the number of subspaces * Doctoral Candidate, Department of Aeronautics and Astronautics, AIAA Student Member † Professor, Department of Aeronautics and Astronautics, AIAA Fellow Copyright c 2008 by B. Roth. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. 1 of 14 American Institute of Aeronautics and Astronautics