An Automated Procedure for Local Monotonicity Analysis

1984 ◽  
Vol 106 (1) ◽  
pp. 82-89 ◽  
Author(s):  
S. Azarm ◽  
P. Papalambros
Keyword(s):  
Design Optimization ◽  
Active Set ◽  
Optimization Program ◽  
Active Set Strategy ◽  
Active Constraints ◽  
Automated Algorithm ◽  
Active Sets ◽  
Local Monotonicity ◽  
Monotonicity Analysis ◽  
Selection Of

A strategy for selecting active constraints in a design optimization program is implemented computationally. The strategy uses local monotonicity information to iterate on the active set. A fully automated algorithm is developed with the aid of constrained derivatives and conventional search methods. Four design examples are presented, one of which demonstrates how global rules derived from monotonicity analysis can be included in the active set strategy to enhance the performance of the algorithm. The procedure is flexible, so that any available rules that can bias the selection of active sets may be included in the strategy.

A Case for a Knowledge-Based Active Set Strategy

1984 ◽  
Vol 106 (1) ◽  
pp. 77-81 ◽  
Author(s):  
S. Azarm ◽  
P. Papalambros
Keyword(s):  
Design Optimization ◽  
Global Knowledge ◽  
Active Set ◽  
Optimization Program ◽  
Active Set Strategy ◽  
Active Constraints ◽  
Knowledge Based ◽  
The One ◽  
Monotonicity Analysis

A strategy for selecting active constraints in a design optimization program is proposed. The strategy differs from previous ones in that it suggests a combination of local and global knowledge. This knowledge may be analytical in nature, such as the one provided by monotonicity analysis. But it may also be provided by an expert. The strategy is proposed as a first attempt toward development of knowledge-based iteration procedures for optimization.

Remarks on Sufficiency of Constraint-Bound Solutions in Optimal Design

1993 ◽  
Vol 115 (3) ◽  
pp. 374-379
Author(s):  
P. Y. Papalambros
Keyword(s):  
Nonlinear Programming ◽  
Optimal Design ◽  
Active Set ◽  
Design Problems ◽  
Local Optima ◽  
Active Set Strategy ◽  
Active Constraints ◽  
Trade Offs ◽  
Design Variables ◽  
Monotonicity Analysis

Early preliminary models for optimal design problems in nonlinear programming formulations often have solutions that are constraint-bound points, i.e., the number of active constraints equals the number of design variables. Models leading to such solutions will typically offer little insight to design trade-offs, and it is desirable to identify them early in order to revise the model or to exclude the points from an active set strategy. Application of monotonicity analysis can quickly identify constraint-bound candidate solutions but not always prove their optimality. This article discusses some conditions under which these points are in fact global or local optima.

Monotonicity and Active Set Strategies in Probabilistic Design Optimization

2005 ◽  
Author(s):  
Kuei-Yuan Chan ◽  
Steven J. Skerlos ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Computational Cost ◽  
Inequality Constraints ◽  
Probabilistic Constraints ◽  
Programming Algorithm ◽  
Probabilistic Design ◽  
Active Set ◽  
Probability Metrics ◽  
Active Set Strategies ◽  
Monotonicity Analysis

Probabilistic design optimization addresses the presence of uncertainty in design problems. Extensive studies on Reliability-Based Design Optimization (RBDO), i.e., problems with random variables and probabilistic constraints, have focused on improving computational efficiency of estimating values for the probabilistic functions. In the presence of many probabilistic inequality constraints, computational costs can be reduced if probabilistic values are computed only for constraints that are known to be active or likely active. This article presents an extension of monotonicity analysis concepts from deterministic problems to probabilistic ones, based on the fact that several probability metrics are monotonic transformations. These concepts can be used to construct active set strategies that reduce the computational cost associated with handling inequality constraints, similarly to the deterministic case. Such a strategy is presented as part of a sequential linear programming algorithm along with a numerical example.

Monotonicity and Active Set Strategies in Probabilistic Design Optimization

2006 ◽  
Vol 128 (4) ◽  
pp. 893-900 ◽  
Author(s):  
Kuei-Yuan Chan ◽  
Steven Skerlos ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Computational Cost ◽  
Inequality Constraints ◽  
Probabilistic Constraints ◽  
Programming Algorithm ◽  
Probabilistic Design ◽  
Active Set ◽  
Probability Metrics ◽  
Active Set Strategies ◽  
Monotonicity Analysis

Probabilistic design optimization addresses the presence of uncertainty in design problems. Extensive studies on reliability-based design optimization, i.e., problems with random variables and probabilistic constraints, have focused on improving computational efficiency of estimating values for the probabilistic functions. In the presence of many probabilistic inequality constraints, computational costs can be reduced if probabilistic values are computed only for constraints that are known to be active or likely active. This article presents an extension of monotonicity analysis concepts from deterministic problems to probabilistic ones, based on the fact that several probability metrics are monotonic transformations. These concepts can be used to construct active set strategies that reduce the computational cost associated with handling inequality constraints, similarly to the deterministic case. Such a strategy is presented as part of a sequential linear programming algorithm along with numerical examples.

PRIMA: A Production-Based Implicit Elimination System for Monotonicity Analysis of Optimal Design Models

1991 ◽  
Vol 113 (4) ◽  
pp. 408-415 ◽  
Author(s):  
J. R. Rao ◽  
P. Y. Papalambros
Keyword(s):  
Optimal Design ◽  
Heuristic Search ◽  
Programming Environment ◽  
Initial Model ◽  
Active Set ◽  
Design Models ◽  
Active Set Strategy ◽  
Knowledge Based ◽  
Reasoning System ◽  
Monotonicity Analysis

Monotonicity analysis is a useful method for analyzing optimal design models prior to numerical computation. Much of the information required for such analysis is represented in the monotonicity table. Rigorous procedures using the monotonicity principles and the implicit function theorem have been combined with heuristics, to extract additional constraint activity knowledge based only on the information contained in the monotonicity table. PRIMA is a production system implemented in the OPS5 programming environment. The system receives as input the monotonicity table of the initial model and derives global facts about boundedness and constraint activity by heuristic search of sequences of successively reduced models. Such reduction is obtained by implicit elimination of active constraints. Global facts generated automatically by this reasoning system can be used either for a global solution, or for a combined local-global active set strategy.

Remarks on Sufficiency of Constraint-Bound Solutions in Optimal Design

1988 ◽  
Author(s):  
P. Y. Papalambros
Keyword(s):  
Nonlinear Programming ◽  
Optimal Design ◽  
Design Problems ◽  
Local Optima ◽  
Solution Strategies ◽  
Active Constraints ◽  
Active Sets ◽  
Trade Offs ◽  
Design Variables ◽  
Monotonicity Analysis

Abstract Solution strategies for optimal design problems in nonlinear programming formulations may require verification of optimality for constraint-bound points. These points are candidate solutions where the number of active constraints is equal to the number of design variables. Models leading to such solutions will typically offer little insight to design trade-offs and it would be desirable to identify them early, or exclude them in a strategy using active sets. Potential constrained-bound solutions are usually identified based on the principles of monotonicity analysis. This article discusses some cases where these points are in fact global or local optima.

Monotonicity Analysis and Recursive Quadratic Programming in Constrained Optimization

1985 ◽  
Vol 107 (4) ◽  
pp. 459-462 ◽  
Author(s):  
J. Zhou ◽  
R. W. Mayne
Keyword(s):  
Quadratic Programming ◽  
Constrained Optimization ◽  
Nonlinear Optimization ◽  
Active Set ◽  
Active Set Strategy ◽  
Constrained Nonlinear Optimization ◽  
Recursive Quadratic Programming ◽  
Analysis Strategy ◽  
Original Procedure ◽  
Monotonicity Analysis

This paper considers the use of an active set strategy based on monotonicity analysis as an integral part of a recursive quadratic programming (RQP) algorithm for constrained nonlinear optimization. Biggs’ RQP method employing equality constrained subproblems is the basis for the algorithm developed here and requires active set information. The monotonicity analysis strategy is applied to the sequence of search directions selected by the RQP method. As each direction is considered, progress toward optimum occurs and a new constraint is added to the active set. As the active set is finalized the basic RQP method is followed unless a constraint is to be dropped. Testing of the proposed algorithm illustrates its promise as an enhancement to Biggs’ original procedure.

An Active Set Sequential Linearization Algorithm for Nonlinear Design Optimization

1987 ◽  
Author(s):  
N. Tzannetakis ◽  
P. Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Programming Algorithm ◽  
Linear Programs ◽  
Chemical Process Design ◽  
Active Set ◽  
Active Set Strategy ◽  
Nonlinear Design ◽  
Working Set ◽  
Sequential Linearization

Abstract Solution of nonlinear design optimization problems via a sequence of linear programs is regaining attention for solving certain model classes, such as in structural design and chemical process design. An active set strategy modification of an algorithm by Palacios-Gomez is presented. A special interior linear programming algorithm with active set strategy is used also for solving the subproblem and generating the working set of the outer iterations. Examples are included.

Active set strategy of optimized extreme learning machine

2014 ◽  
Vol 59 (31) ◽  
pp. 4152-4160 ◽  
Author(s):  
Xiao-Jian Ding ◽  
Bao-Fang Chang
Keyword(s):  
Extreme Learning Machine ◽  
Active Set ◽  
Active Set Strategy ◽  
Learning Machine
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