ALBERT

Description: In recent years there have been several hierarchic multilevel optimization algorithms proposed and implemented in design studies. Equality constraints are often imposed between levels in these multilevel optimizations to maintain system and subsystem variable continuity. Equality constraints of this nature will be referred to as coupling equality constraints. In many implementation studies these coupling equality constraints have been handled indirectly. This indirect handling has been accomplished using the coupling equality constraints' explicit functional relations to eliminate design variables (generally at the subsystem level), with the resulting optimization taking place in a reduced design space. In one multilevel optimization study where the coupling equality constraints were handled directly, the researchers encountered numerical difficulties which prevented their multilevel optimization from reaching the same minimum found in conventional single level solutions. The researchers did not explain the exact nature of the numerical difficulties other than to associate them with the direct handling of the coupling equality constraints. The coupling equality constraints are handled directly, by employing the Generalized Reduced Gradient (GRG) method as the optimizer within a multilevel linear decomposition scheme based on the Sobieski hierarchic algorithm. Two engineering design examples are solved using this approach. The results show that the direct handling of coupling equality constraints in a multilevel optimization does not introduce any problems when the GRG method is employed as the internal optimizer. The optimums achieved are comparable to those achieved in single level solutions and in multilevel studies where the equality constraints have been handled indirectly.

Description: In this research a Collaborative Optimization (CO) approach for multidisciplinary systems design is used to develop a decision based design framework for non-deterministic optimization. To date CO strategies have been developed for use in application to deterministic systems design problems. In this research the decision based design (DBD) framework proposed by Hazelrigg is modified for use in a collaborative optimization framework. The Hazelrigg framework as originally proposed provides a single level optimization strategy that combines engineering decisions with business decisions in a single level optimization. By transforming this framework for use in collaborative optimization one can decompose the business and engineering decision making processes. In the new multilevel framework of Decision Based Collaborative Optimization (DBCO) the business decisions are made at the system level. These business decisions result in a set of engineering performance targets that disciplinary engineering design teams seek to satisfy as part of subspace optimizations. The Decision Based Collaborative Optimization framework more accurately models the existing relationship between business and engineering in multidisciplinary systems design.

Description: This research effort is a joint program between the Departments of Aerospace and Mechanical Engineering and the Computer Science and Engineering Department at the University of Notre Dame. The purpose of the project was to develop a framework and systematic methodology to facilitate the application of Multidisciplinary Design Optimization (MDO) to a diverse class of system design problems. For all practical aerospace systems, the design of a systems is a complex sequence of events which integrates the activities of a variety of discipline "experts" and their associated "tools". The development, archiving and exchange of information between these individual experts is central to the design task and it is this information which provides the basis for these experts to make coordinated design decisions (i.e., compromises and trade-offs) - resulting in the final product design. Grant efforts focused on developing and evaluating frameworks for effective design coordination within a MDO environment. Central to these research efforts was the concept that the individual discipline "expert", using the most appropriate "tools" available and the most complete description of the system should be empowered to have the greatest impact on the design decisions and final design. This means that the overall process must be highly interactive and efficiently conducted if the resulting design is to be developed in a manner consistent with cost and time requirements. The methods developed as part of this research effort include; extensions to a sensitivity based Concurrent Subspace Optimization (CSSO) NMO algorithm; the development of a neural network response surface based CSSO-MDO algorithm; and the integration of distributed computing and process scheduling into the MDO environment. This report overviews research efforts in each of these focus. A complete bibliography of research produced with support of this grant is attached.

Description: This research effort is a joint program between the Departments of Aerospace and Mechanical Engineering and the Computer Science and Engineering Department at the University of Notre Dame. Three Principal Investigators; Drs. Renaud, Brockman and Batill directed this effort. During the four and a half year grant period, six Aerospace and Mechanical Engineering Ph.D. students and one Masters student received full or partial support, while four Computer Science and Engineering Ph.D. students and one Masters student were supported. During each of the summers up to four undergraduate students were involved in related research activities. The purpose of the project was to develop a framework and systematic methodology to facilitate the application of Multidisciplinary Design Optimization (N4DO) to a diverse class of system design problems. For all practical aerospace systems, the design of a systems is a complex sequence of events which integrates the activities of a variety of discipline "experts" and their associated "tools". The development, archiving and exchange of information between these individual experts is central to the design task and it is this information which provides the basis for these experts to make coordinated design decisions (i.e., compromises and trade-offs) - resulting in the final product design. Grant efforts focused on developing and evaluating frameworks for effective design coordination within a MDO environment. Central to these research efforts was the concept that the individual discipline "expert", using the most appropriate "tools" available and the most complete description of the system should be empowered to have the greatest impact on the design decisions and final design. This means that the overall process must be highly interactive and efficiently conducted if the resulting design is to be developed in a manner consistent with cost and time requirements. The methods developed as part of this research effort include; extensions to a sensitivity based Concurrent Subspace Optimization (CSSO) MDO algorithm; the development of a neural network response surface based CSSO-MDO algorithm; and the integration of distributed computing and process scheduling into the MDO environment. This report overviews research efforts in each of these focus. A complete bibliography of research produced with support of this grant is attached.