Sequential Approximate Optimization (SAO) is a class of methods available for the multidisciplinary design optimization (MDO) of complex systems that are composed of several disciplines coupled together. One of the approaches used for SAO, is based on a quadratic response surface approximation, where zero and first order information are required. In these methods, designers must generate and query a database of order O(n²) in order to compute the second order terms of the quadratic response surface approximation. As the number of design variables grows, the computational cost of generating the required database becomes a concern. In this paper, we present an new approach in which we require just O(n) parameters for constructing a second order approximation. This is accomplished by transforming the matrix of second order terms into the canonical form. The method periodically requires an order O(n²) update of the second order approximation to maintain accuracy. Results show

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.

Response Surface Approximations (RSA's) are widely used in the design community to provide designers with an approximate representation of a system. The use of RSA's allow designers to query the system while avoiding the high computational costs associated with today's advanced simulation codes. Sequential Approximate Optimization (SAO) methodologies have proved to be effective in managing the optimization of multidisciplinary design problems. In SAO the sampling required to build the RSA's often takes place within the same bounds as imposed on the current optimization iterate. This assures a good representation of the system in the region where it will be optimized. However it may restrict the approximation from extrapolating beyond the design space, and therefore improve the convergence rate of the algorithm. In this research a decoupling of the sampling region from the trust region is proposed.

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.

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.

The MATLAB program and computing language has seen increased usage both in industry and academia in recent years. This is due to the ease in which it handles matrices and numerical computations. This computing environment also has an array of toolboxes for different mathematical and engineering tasks (e.g., controls, optimization). These toolboxes provide a general suite of numerical tools within a specific discipline for the user. The toolbox codes are general tools and are not typically as robust or as efficient as state of the art numerical codes develop by advanced users in a given discipline. In this research a MATLAB driver which links an existing robust and efficient optimization program SNOPT is developed and tested. The resulting program and driver have proved to be more efficient than the existing MATLAB toolbox codes for optimization. 1

The MATLAB program and computing language has seen increased usage both in industry and academia in recent years. This is due to the ease in which it handles matrices and numerical computations. This computing environment also has an array of toolboxes for different mathematical and engineering tasks (e.g., controls, optimization). These toolboxes provide a general suite of numerical tools within a specific discipline for the user. The toolbox codes are general tools and are not typically as robust or as efficient as state of the art numerical codes develop by advanced users in a given discipline. In this research a MATLAB driver which links an existing robust and efficient optimization program SNOPT is developed and tested. The resulting program and driver have proved to be more efficient than the existing MATLAB toolbox codes for optimization.

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