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.

Implementation of Semi-Heuristic Reasoning for Boundedness Analysis of Design Optimization Models

1987 ◽  
Author(s):  
J. R. J. Rao ◽  
P. Y. Papalambros
Keyword(s):  
Optimal Design ◽  
Heuristic Search ◽  
Optimization Models ◽  
Programming Environment ◽  
Initial Model ◽  
Active Set ◽  
Design Models ◽  
Active Set Strategy ◽  
Reasoning System ◽  
Global Boundedness

Abstract A production system performing global boundedness analysis of optimal design models has been implemented in the OPS5 programming environment. The system receives as input an initial model monotonicity table and derives global facts about boundedness and constraint activity using monotonicity principles. Additional facts may be discovered by heuristic search of implicit elimination sequences that examine boundedness of reduced models with active constraints eliminated. The 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.

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.

Optimal Design of Product Family Throughout Commonalization, Customization and Lineup Arrangement

2008 ◽  
Author(s):  
Kikuo Fujita ◽  
Ryota Akai
Keyword(s):  
Optimal Design ◽  
Design Problem ◽  
Product Family ◽  
Feasible Region ◽  
Product Family Design ◽  
Active Set ◽  
Active Set Strategy ◽  
Design Variables ◽  
Design Paradigm

Product family design is a framework for effectively and efficiently meeting with spread customers’ needs by sharing components or modules across a series of products. This paper systematizes product family design toward its extension to throughout consideration of commonalization, customization and lineup arrangement under the optimal design paradigm. That is, commonalization is viewed as the operation that restricts the feasible region by fixing a set of design variables related to commonalized components or modules against later customization and final lineup offered to customers. Customization is viewed as the operation that arranges lineup by adjusting another set of design variables related to reserved freedom for customers’ needs. Their mutual and bi-directional relationships must be a matter of optimal design. This paper discusses the mathematical fundamentals of optimal product family design throughout commonalization, customization and lineup arrangement under active set strategy, and demonstrates a case study with a design problem of centrifugal compressors for showing the meaning of throughout optimal design.

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.

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.

Structural Analysis and Optimal Design of Lightweight Skate for Loading and Unloading

2013 ◽  
Vol 785-786 ◽  
pp. 1258-1261
Author(s):  
In Pyo Cha ◽  
Hee Jae Shin ◽  
Neung Gu Lee ◽  
Lee Ku Kwac ◽  
Hong Gun Kim
Keyword(s):  
Topology Optimization ◽  
Structural Analysis ◽  
Optimal Design ◽  
Optimization Techniques ◽  
Normal Operation ◽  
Stress And Strain ◽  
Initial Model ◽  
Design Variables ◽  
Model Set ◽  
Main Frame

Topology optimization and shape optimization of structural optimization techniques are applied to transport skate the lightweight. Skate properties by varying the design variables and minimize the maximum stress and strain in the normal operation, while reducing the volume of the objective function of optimal design and Skate the static strength of the constraints that should not degrade compared to the performance of the initial model. The skates were used in this study consists of the main frame, sub frame, roll, pin main frame only structural analysis and optimal design was performed using the finite element method. Simplified initial model set design area and it compared to SM45C, AA7075, CFRP, GFRP was using the topology optimization. Strength does not degrade compared to the initial model, decreased volume while minimizing the stress and strain results, the optimum design was achieved efficient lightweight.

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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