Applying nonlinear optimization strategies directly to complex multidisciplinary systems can be prohibitive when the complexity of the simulation codes is large. Increasingly, response surface approximations(RSAs), and specifically quadratic approximations, are being integrated with nonlinear optimizers in order to reduce the CPU time required for the optimization of complex multidisciplinary systems. RSAs provide a computationally inexpensive lower fidelity representation of the system performance. The curse of dimensionality is a major drawback in the implementation of these approximations as the amount of required data grows quadratically with the number of design variables.

The use of optimization in a simulation based design environment has become a common trend in industry today. Computer simulation tools are common place in many engineering disciplines, providing the designers with tools to evaluate a design's performance without building a physical prototype. This has triggered the development of optimization techniques suitable for dealing with such simulations. One of these approaches is known as sequential approximate optimization. In sequential approximate minimization a sequence of optimizations are performed over local response surface approximations of the system. This paper details the development of an interior point approach for trust region managed sequential approximate optimization. The interior point approach will insure that approximate feasibility is maintained throughout the optimization process. This facilitates the delivery of a usable design at each iteration when subject to reduced design cycle time constraints. In order to deal with infeasible starting points, homotopy methods are used to relax constraints and push designs toward feasibility. Results of application studies are presented, illustrating the applicability of the proposed algorithm.

Surrogate-based-optimization methods provide a means to minimize expensive highfidelity models at reduced computational cost. The methods are useful in problems for which two models of the same physical system exist: a high-fidelity model which is accurate and expensive, and a low-fidelity model which is less costly but less accurate. A number of model management techniques have been developed and shown to work well for the case in which both models are defined over the same design space. However, many systems exist with variable fidelity models for which the design variables are defined over different spaces, and a mapping is required between the spaces. Previous work showed that two mapping methods, corrected space mapping and POD mapping, used in conjunction with a trust-region model management method, provide improved performance over conventional non-surrogate-based optimization methods for unconstrained problems. This paper extends that work to constrained problems. Three constraint-management methods are demonstrated with each of the mapping methods: Lagrangian minimization, an sequential quadratic programming-like surrogate method, and MAESTRO. The methods are demonstrated on a fixed-complexity analytical test problem and a variable-complexity wing design problem. The SQP-like method consistently outperformed optimization in the high-fidelity space and the other variable complexity methods. Corrected space mapping performed slightly better on average than POD mapping. On the wing design problem, the combination of the SQP-like method and corrected space mapping achieved 58 % savings in high-fidelity function calls over optimization directly in the high-fidelity space. I.

The use of computer simulations has revolutionized the way engineers design and improve products and affects all design stages from concept to realization. As a consequence optimization has become an important tool for the engineer to realize better designs without the need of extensive prototype building. One of the algorithms that has shown an important ability to deal with this type of optimization is known as sequential approximate optimization. In sequential approximate optimization a series of local minimizations are performed over local response surface approximations of the system.

The paper presents a first level of coarse-grained parallelization in a sequential approximate optimization framework. A sequential approximate optimization framework builds local approximations of the system every iteration by evaluating a set of design points around the current design. In this research the database is generated by distributing the data sampling process among several processors in a cluster. Two test problems are implemented in a 32 processor cluster. Communications and process control is performed using a message passing interface (MPI) implementation called LAM (Local area multicomputer). The MPI application sends to each processor a set of points to evaluate during the database generation step. Results demonstrate that the use of a cluster of computers to perform the optimization reduces significantly the overall computational time.

Simulation-based design has become a major tool in the design of automotive, aerospace and consumer products. Designers are faced with the continuous challenge of reducing manufacturing costs and design cycle times while improving the system's performance and reliability. Simulation-based design plays an increasingly prominent role in facilitating the conceptualization and realization of products under these competitive conditions. Single discipline simulations used for analysis are being coupled together to create complex coupled simulation systems. This investigation focuses on the development of methodologies that help designers reduce the cost of using optimization to manage the simulation based design process. The computational cost of executing a single complex coupled simulation and the total number of simulations required per iteration are the two factors which most influence an optimization framework's design. Original contributions