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.

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.

A Fuzzy Sequential Linear Programming Algorithm for Engineering Design Optimization

1995 ◽  
Author(s):  
Yeh-Liang Hsu ◽  
Yu-Fa Lin ◽  
Yu-Shuei Guo
Keyword(s):  
Linear Programming ◽  
Design Optimization ◽  
Engineering Design ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Optimization Process ◽  
Programming Algorithm ◽  
Sequential Linear Programming ◽  
Original Algorithm ◽  
Engineering Design Optimization

Abstract An optimization process can be viewed as a closed-loop control system. Traditional “controllers”, the numerical optimization algorithms, are usually “crisply” designed for well defined mathematical models. However, when applied to engineering design optimization problems in which function evaluations can be expensive and imprecise, very often the crisp algorithms will become impractical or will not converge. A common strategy for designers is to monitor the optimization process and keep “tuning” the process in an interactive manner, using their judgment on the information obtained from previous iterations, and their knowledge of the problem. This paper presents how the heuristics of this human supervision can be modeled into the optimization algorithms using fuzzy set theory. A fuzzy version of sequential linear programming is used to demonstrate this idea. Fuzzy rules, which describe the human supervision during the optimization process, are combined with the numerical rules of the original algorithm to refine the output of each iteration. Several design optimization problems are used to show the feasibility and practicality of this approach.

scholarly journals A decoupling algorithm with first-order asymptotic integration for reliability-based design optimization

2018 ◽  
Vol 10 (9) ◽  
pp. 168781401879333 ◽  
Author(s):  
Zhiliang Huang ◽  
Tongguang Yang ◽  
Fangyi Li
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Optimization Problems ◽  
Asymptotic Integration ◽  
Probabilistic Constraints ◽  
Reliability Based Design Optimization ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Based Design ◽  
Reliability Method

Conventional decoupling approaches usually employ first-order reliability method to deal with probabilistic constraints in a reliability-based design optimization problem. In first-order reliability method, constraint functions are transformed into a standard normal space. Extra non-linearity introduced by the non-normal-to-normal transformation may increase the error in reliability analysis and then result in the reliability-based design optimization analysis with insufficient accuracy. In this article, a decoupling approach is proposed to provide an alternative tool for the reliability-based design optimization problems. To improve accuracy, the reliability analysis is performed by first-order asymptotic integration method without any extra non-linearity transformation. To achieve high efficiency, an approximate technique of reliability analysis is given to avoid calculating time-consuming performance function. Two numerical examples and an application of practical laptop structural design are presented to validate the effectiveness of the proposed approach.

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.

A Filter-Based Sample Average SQP for Optimization Problems With Highly Nonlinear Probabilistic Constraints

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Kai-Shian Hsu ◽  
Kuei-Yuan Chan
Keyword(s):  
Optimization Problems ◽  
Limit State ◽  
Trust Region ◽  
Probabilistic Constraints ◽  
Iteration Step ◽  
Reliability Based Design ◽  
Sample Average ◽  
Highly Nonlinear ◽  
Reliability Method ◽  
Low Probability

In this work, we develop a filter-based sequential quadratic programming (SQP) algorithm for solving reliability-based design optimization (RBDO) problems with highly nonlinear constraints. The proposed filter-based SQP uses the approach of average importance sampling (AAIS) in calculating the values and gradients of probabilistic constraints. AAIS allocates samples at the limit state boundaries such that relatively few samples are required in calculating constraint probability values to achieve high accuracy and low variance. The accuracy of probabilistic constraint gradients using AAIS is improved by a sample filter that eliminates sample outliers that have low probability of occurrence and high gradient values. To ensure convergence, the algorithm uses an iteration filter in place of the penalty function to avoid the ill-conditioning problems of the penalty parameters in the acceptance of a design update. A sample reuse mechanism that improves the efficiency of the algorithm by avoiding redundant samples is introduced. The “unsampled” region, the region not covered by previous samples, is identified using iteration step lengths, the trust region, and constraint reliability levels. As a result, the filter-based sampling SQP efficiently handles highly nonlinear probabilistic constraints with multiple most probable points or functions without analytical forms. Several examples are demonstrated, and the results are compared with those from first order reliability method/second order reliability method and Monte Carlo simulations. Results show that by integrating the modified AAIS with the filter-based SQP, the overall computation cost of solving RBDO problems can be significantly reduced.

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.

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