Convergence using variable fidelity approximation data in a trust region managed augmented Lagrangian approximate optimization

1998 ◽  
Author(s):  
Jose Rodriguez ◽  
John Renaud ◽  
Layne Watson
Keyword(s):  
Augmented Lagrangian ◽  
Trust Region ◽  
Approximate Optimization ◽  
Variable Fidelity

Trust Region Augmented Lagrangian Methods for Sequential Response Surface Approximation and Optimization

1997 ◽  
Author(s):  
José F. Rodríguez ◽  
John E. Renaud ◽  
Layne T. Watson
Keyword(s):  
Response Surface ◽  
Computer Simulations ◽  
Design Problem ◽  
Augmented Lagrangian ◽  
Original Problem ◽  
Trust Region ◽  
Model Management ◽  
Response Surface Approximation ◽  
Approximate Optimization ◽  
Region Model

Abstract A common engineering practice is the use of approximation models in place of expensive computer simulations to drive a multidisciplinary design process based on nonlinear programming techniques. The use of approximation strategies is designed to reduce the number of detailed, costly computer simulations required during optimization while maintaining the pertinent features of the design problem. To date the primary focus of most approximate optimization strategies is that application of the method should lead to improved designs. This is a laudable attribute and certainly relevant for practicing designers. However to date few researchers have focused on the development of approximate optimization strategies that are assured of converging to a solution of the original problem. Recent works based on trust region model management strategies have shown promise in managing convergence in unconstrained approximate minimization. In this research we extend these well established notions from the literature on trust-region methods to manage the convergence of the more general approximate optimization problem where equality, inequality and variable bound constraints are present. The primary concern addressed in this study is how to manage the interaction between the optimization and the fidelity of the approximation models to ensure that the process converges to a solution of the original constrained design problem. Using a trust-region model management strategy, coupled with an augmented Lagrangian approach for constrained approximate optimization, one can show that the optimization process converges to a solution of the original problem. In this research an approximate optimization strategy is developed in which a cumulative response surface approximation of the augmented Lagrangian is sequentially optimized subject to a trust region constraint. Results for several test problems are presented in which convergence to a Karush-Kuhn-Tucker (KKT) point is observed.

Trust Region Augmented Lagrangian Methods for Sequential Response Surface Approximation and Optimization

1998 ◽  
Vol 120 (1) ◽  
pp. 58-66 ◽  
Author(s):  
J. F. Rodri´guez ◽  
J. E. Renaud ◽  
L. T. Watson
Keyword(s):  
Response Surface ◽  
Computer Simulations ◽  
Design Problem ◽  
Augmented Lagrangian ◽  
Original Problem ◽  
Trust Region ◽  
Model Management ◽  
Response Surface Approximation ◽  
Approximate Optimization ◽  
Region Model

A common engineering practice is the use of approximation models in place of expensive computer simulations to drive a multidisciplinary design process based on nonlinear programming techniques. The use of approximation strategies is designed to reduce the number of detailed, costly computer simulations required during optimization while maintaining the pertinent features of the design problem. To date the primary focus of most approximate optimization strategies is that application of the method should lead to improved designs. This is a laudable attribute and certainly relevant for practicing designers. However to date few researchers have focused on the development of approximate optimization strategies that are assured of converging to a solution of the original problem. Recent works based on trust region model management strategies have shown promise in managing convergence in unconstrained approximate minimization. In this research we extend these well established notions from the literature on trust-region methods to manage the convergence of the more general approximate optimization problem where equality, inequality and variable bound constraints are present. The primary concern addressed in this study is how to manage the interaction between the optimization and the fidelity of the approximation models to ensure that the process converges to a solution of the original constrained design problem. Using a trust-region model management strategy, coupled with an augmented Lagrangian approach for constrained approximate optimization, one can show that the optimization process converges to a solution of the original problem. In this research an approximate optimization strategy is developed in which a cumulative response surface approximation of the augmented Lagrangian is sequentially optimized subject to a trust region constraint. Results for several test problems are presented in which convergence to a Karush-Kuhn-Tucker (KKT) point is observed.

Improved Trust Region Model Management for Approximate Optimization

1998 ◽  
Author(s):  
Brett A. Wujek ◽  
John E. Renaud
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Low Cost ◽  
Approximation Error ◽  
Trust Region ◽  
Model Management ◽  
Multidisciplinary Design ◽  
Test Problems ◽  
Approximation Techniques ◽  
Approximate Optimization

Abstract Approximations play an important role in multidisciplinary design optimization (MDO) by offering system behavior information at a relatively low cost. Most approximate optimization strategies are sequential in which an optimization of an approximate problem subject to design variable move limits is iteratively repeated until convergence. The move limits are imposed to restrict the optimization to regions of the design space in which the approximations provide meaningful information. In order to insure convergence of the sequence of approximate optimizations to a Karush Kuhn Tucker solution a move limit management strategy is required. In this paper, issues of move-limit management are reviewed and a new adaptive strategy for move limit management is developed. With its basis in the provably convergent trust region methodology, the TRAM (Trust region Ratio Approximation Method) strategy utilizes available gradient information and employs a backtracking process using various two-point approximation techniques to provide a flexible move-limit adjustment factor. The new strategy is successfully implemented in application to a suite of multidisciplinary design optimization test problems. These implementation studies highlight the ability of the TRAM strategy to control the amount of approximation error and efficiently manage the convergence to a Karush Kuhn Tucker solution.

Rapid design optimization of antennas using variable-fidelity EM models and adjoint sensitivities

2016 ◽  
Vol 33 (7) ◽  
pp. 2007-2018 ◽  
Author(s):  
Slawomir Koziel ◽  
Adrian Bekasiewicz
Keyword(s):  
Design Optimization ◽  
Optimization Technique ◽  
Computational Cost ◽  
Trust Region ◽  
Simulation Models ◽  
Direct Optimization ◽  
Content Type ◽  
Variable Fidelity ◽  
Em Simulation ◽  
Conventional Methods

Purpose Development of techniques for expedited design optimization of complex and numerically expensive electromagnetic (EM) simulation models of antenna structures validated both numerically and experimentally. The paper aims to discuss these issues. Design/methodology/approach The optimization task is performed using a technique that combines gradient search with adjoint sensitivities, trust region framework, as well as EM simulation models with various levels of fidelity (coarse, medium and fine). Adaptive procedure for switching between the models of increasing accuracy in the course of the optimization process is implemented. Numerical and experimental case studies are provided to validate correctness of the design approach. Findings Appropriate combination of suitable design optimization algorithm embedded in a trust region framework, as well as model selection techniques, allows for considerable reduction of the antenna optimization cost compared to conventional methods. Research limitations/implications The study demonstrates feasibility of EM-simulation-driven design optimization of antennas at low computational cost. The presented techniques reach beyond the common design approaches based on direct optimization of EM models using conventional gradient-based or derivative-free methods, particularly in terms of reliability and reduction of the computational costs of the design processes. Originality/value Simulation-driven design optimization of contemporary antenna structures is very challenging when high-fidelity EM simulations are utilized for performance utilization of structure at hand. The proposed variable-fidelity optimization technique with adjoint sensitivity and trust regions permits rapid optimization of numerically demanding antenna designs (here, dielectric resonator antenna and compact monopole), which cannot be achieved when conventional methods are of use. The design cost of proposed strategy is up to 60 percent lower than direct optimization exploiting adjoint sensitivities. Experimental validation of the results is also provided.

Expedited antenna optimization with numerical derivatives and gradient change tracking

2019 ◽  
Vol 37 (4) ◽  
pp. 1179-1193
Author(s):  
Anna Pietrenko-Dabrowska ◽  
Slawomir Koziel
Keyword(s):  
Computational Cost ◽  
Trust Region ◽  
Optimization Process ◽  
System Response ◽  
Design Quality ◽  
Direct Optimization ◽  
Content Type ◽  
Variable Fidelity ◽  
Relative Design ◽  
Response Gradient

Purpose The purpose of this study is to propose a framework for expedited antenna optimization with numerical derivatives involving gradient variation monitoring throughout the optimization run and demonstrate it using a benchmark set of real-world wideband antennas. A comprehensive analysis of the algorithm performance involving multiple starting points is provided. The optimization results are compared with a conventional trust-region (TR) procedure, as well as the state-of-the-art accelerated TR algorithms. Design/methodology/approach The proposed algorithm is a modification of the TR gradient-based algorithm with numerical derivatives in which a monitoring of changes of the system response gradients is performed throughout the algorithm run. The gradient variations between consecutive iterations are quantified by an appropriately developed metric. Upon detecting stable patterns for particular parameter sensitivities, the costly finite differentiation (FD)-based gradient updates are suppressed; hence, the overall number of full-wave electromagnetic (EM) simulations is significantly reduced. This leads to considerable computational savings without compromising the design quality. Findings Monitoring of the antenna response sensitivity variations during the optimization process enables to detect the parameters for which updating the gradient information is not necessary at every iteration. When incorporated into the TR gradient-search procedures, the approach permits reduction of the computational cost of the optimization process. The proposed technique is dedicated to expedite direct optimization of antenna structures, but it can also be applied to speed up surrogate-assisted tasks, especially solving sub-problems that involve performing numerous evaluations of coarse-discretization models. Research limitations/implications The introduced methodology opens up new possibilities for future developments of accelerated antenna optimization procedures. In particular, the presented routine can be combined with the previously reported techniques that involve replacing FD with the Broyden formula for directions that are satisfactorily well aligned with the most recent design relocation and/or performing FD in a sparse manner based on relative design relocation (with respect to the current search region) in consecutive algorithm iterations. Originality/value Benchmarking against a conventional TR procedure, as well as previously reported methods, confirms improved efficiency and reliability of the proposed approach. The applications of the framework include direct EM-driven design closure, along with surrogate-based optimization within variable-fidelity surrogate-assisted procedures. To the best of the authors’ knowledge, no comparable approach to antenna optimization has been reported elsewhere. Particularly, it surmounts established methodology by carrying out constant supervision of the antenna response gradient throughout successive algorithm iterations and using gathered observations to properly guide the optimization routine.

Decoupling the Design Sampling Region From the Trust Region in Approximate Optimization

2000 ◽  
Author(s):  
Victor M. Pérez ◽  
John E. Renaud
Keyword(s):  
Convergence Rate ◽  
Response Surface ◽  
Design Space ◽  
Trust Region ◽  
Good Representation ◽  
Approximate Representation ◽  
Design Problems ◽  
Computational Costs ◽  
Approximate Optimization ◽  
Response Surface Approximations

Abstract 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 multi-disciplinary 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.

Sign in / Sign up

Export Citation Format

Share Document