An Adaptive Sequential Linear Programming Algorithm for Optimal Design Problems With Probabilistic Constraints

2005 ◽  
Author(s):  
Kuei-Yuan Chan ◽  
Steven J. Skerlos ◽  
Panos Y. Papalambros
Keyword(s):  
Linear Programming ◽  
Optimal Design ◽  
Probabilistic Constraints ◽  
Programming Algorithm ◽  
Sequential Linear Programming ◽  
Design Problems ◽  
Reliability Based Design ◽  
Balance Accuracy ◽  
New Strategy ◽  
Solution Methods

Optimal design problems with probabilistic constraints, often referred to as Reliability-Based Design Optimization (RBDO) problems, have been the subject of extensive recent studies. Solution methods to date have focused more on improving efficiency rather than accuracy and the global convergence behavior of the solution. A new strategy utilizing an adaptive sequential linear programming (SLP) algorithm is proposed as a promising approach to balance accuracy, efficiency, and convergence. The strategy transforms the nonlinear probabilistic constraints into equivalent deterministic ones using both first order and second order approximations, and applies a filter-based SLP algorithm to reach the optimum. Simple numerical examples show promise for increased accuracy without sacrificing efficiency.

An Adaptive Sequential Linear Programming Algorithm for Optimal Design Problems With Probabilistic Constraints

2006 ◽  
Vol 129 (2) ◽  
pp. 140-149 ◽  
Author(s):  
Kuei-Yuan Chan ◽  
Steven J. Skerlos ◽  
Panos Papalambros
Keyword(s):  
Linear Programming ◽  
Optimal Design ◽  
Optimization Problems ◽  
Probabilistic Constraints ◽  
Programming Algorithm ◽  
Sequential Linear Programming ◽  
Design Problems ◽  
Reliability Based Design ◽  
New Strategy ◽  
Solution Methods

Optimal design problems with probabilistic constraints, often referred to as reliability-based design optimization problems, have been the subject of extensive recent studies. Solution methods to date have focused more on improving efficiency rather than accuracy and the global convergence behavior of the solution. A new strategy utilizing an adaptive sequential linear programming (SLP) algorithm is proposed as a promising approach to balance accuracy, efficiency, and convergence. The strategy transforms the nonlinear probabilistic constraints into equivalent deterministic ones using both first order and second order approximations, and applies a filter-based SLP algorithm to reach the optimum. Simple numerical examples show promise for increased accuracy without sacrificing efficiency.

Tuning a Hybrid Optimization Algorithm by Determining the Modality of the Design Space

2001 ◽  
Author(s):  
Kurt Hacker ◽  
John Eddy ◽  
Kemper Lewis
Keyword(s):  
Genetic Algorithm ◽  
Linear Programming ◽  
Optimization Algorithm ◽  
Design Space ◽  
Hybrid Optimization ◽  
Programming Algorithm ◽  
Sequential Linear Programming ◽  
Hybrid Optimization Algorithm ◽  
Linear Programming Algorithm ◽  
Algorithm Benchmarking

Abstract In this paper we present an approach for increasing the efficiency of a hybrid Genetic/Sequential Linear Programming algorithm. We introduce two metrics for evaluating the modality of the design space and then use this information to efficiently switch between the Genetic Algorithm and SLP algorithm. The motivation for this study is an effort to reduce the computational expense associated with the use of a Genetic Algorithm by reducing the number of function evaluations needed to find good solutions. In the paper the two metrics used to evaluate the modality of the design space are the variance in fitness of the population of the designs in the Genetic Algorithm and the error associated with fitting a response surface to the designs evaluates by the Genetic Algorithm. The effectiveness of this approach is demonstrated by considering a highly multimodal Genetic Algorithm benchmarking problem.

Optimal Design of Traction Drive Continuously Variable Transmissions

1989 ◽  
Vol 111 (2) ◽  
pp. 264-269 ◽  
Author(s):  
K. H. Lim ◽  
D. G. Ullman
Keyword(s):  
Optimal Design ◽  
Power Loss ◽  
Problem Formulation ◽  
Programming Algorithm ◽  
Design Technique ◽  
Optimal Design Problem ◽  
Design Problems ◽  
Traction Drive ◽  
Constraint Equations ◽  
Continuously Variable Transmissions

An optimal design technique for minimum power loss in traction drive continuously variable transmissions is developed. The general forms of the objective function and constraint equations are derived, and the formulated optimal design problems are implemented in a nonlinear programming algorithm. Kinematic analysis and optimal design problem formulation are performed for a selected traction drive configuration as an example of the procedures.

Optimization of Multibody Systems Using Sequential Linear Programming

1994 ◽  
Author(s):  
L. F. P. Etman ◽  
E. J. R. W. Thijssen ◽  
A. J. G. Schoofs ◽  
D. H. van Campen
Keyword(s):  
Linear Programming ◽  
Structural Analysis ◽  
Design Optimization ◽  
Software Package ◽  
Multibody Systems ◽  
Sequential Linear Programming ◽  
Analysis Software ◽  
Design Problems ◽  
Linear Programming Problems ◽  
Approximation Concept

Abstract Design optimization is far less developed for multibody analysis than for structural analysis. However, multibody design problems can be solved by optimization strategies applied in structural analysis. To illustrate this, a design optimization tool has been developed for a multibody analysis software package. It is based on a linear approximation concept. An optimization process results that consists of a sequence of linear programming problems. The design optimization tool has been successfully tested for three multibody design examples.

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