Discrete Optimal Design Formulations: Application to Gear Train Design

1992 ◽  
Author(s):  
Leonard P. Pomrehn ◽  
Panos Y. Papalambros
Keyword(s):  
Optimal Design ◽  
Spur Gear ◽  
Gear Train ◽  
Continuous Variables ◽  
Discrete Variables ◽  
Interesting Aspect ◽  
Model Formulation ◽  
Design Models ◽  
Different Types

Abstract The use of discrete variables in optimal design models offers the opportunity to deal rigorously with an expanded variety of design situations, as opposed to using only continuous variables. However, complexity and solution difficulty increase dramatically and model formulation becomes very important. A particular problem arising from the design of a gear train employing four spur gear pairs is introduced and formulated in several different ways. An interesting aspect of the problem is its exhibition of three different types of discreteness. The problem could serve as a test for a variety of optimization or artificial intellegence techniques. The best known solution is included in this article, while its derivation is given in a sequel article.

Discrete Optimal Design Formulations With Application to Gear Train Design

1995 ◽  
Vol 117 (3) ◽  
pp. 419-424 ◽  
Author(s):  
L. P. Pomrehn ◽  
P. Y. Papalambros
Keyword(s):  
Artificial Intelligence ◽  
Optimal Design ◽  
Spur Gear ◽  
Gear Train ◽  
Continuous Variables ◽  
Discrete Variables ◽  
Interesting Aspect ◽  
Model Formulation ◽  
Design Models ◽  
Different Types

The use of discrete variables in optimal design models offers the opportunity to deal rigorously with an expanded variety of design situations, as opposed to using only continuous variables. However, complexity and solution difficulty increase dramatically and model formulation becomes very important. A particular problem arising from the design of a gear train employing four spur gear pairs is introduced and formulated in several different ways. An interesting aspect of the problem is its exhibition of three different types of discreteness. The problem could serve as a test for a variety of optimization or artificial intelligence techniques. The best known solution is included in this article, while its derivation is given in a sequel article.

Infeasibility and Non-Optimality Tests for Solution Space Reduction in Discrete Optimal Design

1992 ◽  
Author(s):  
Leonard P. Pomrehn ◽  
Panos Y. Papalambros
Keyword(s):  
Mathematical Model ◽  
Solution Space ◽  
Global Optimum ◽  
Gear Train ◽  
Discrete Variables ◽  
Multistage Process ◽  
Model Formulation ◽  
Space Reduction ◽  
Nonlinear Design ◽  
The Mathematical Model

Abstract Techniques to be employed for nonlinear design optimization with discrete variables are studied in the context of a particular problem arising from the design of a gear train. The mathematical model formulation was presented in an earlier article. In this sequel, a solution derivation is described, patterned as a multistage process. After certain reformulation and relaxation, a variety of infeasibility and non-optimality tests are performed, greatly reducing the size of the space containing the global optimum. Methods used to investigate the remaining space do not guarantee a global optimum, but could be replaced by more costly methods that do provide such guarantees. A global infimum is generated, bounding any improvements on the best known solution.

Robust Design Optimization Based on Improved Ant Colony Algorithm with Application

2010 ◽  
Vol 29-32 ◽  
pp. 2273-2277
Author(s):  
Shi Ming Hao ◽  
Hui Xin Guo ◽  
Juan Dai ◽  
Li Zhi Cheng
Keyword(s):  
Optimal Design ◽  
Ant Colony Algorithm ◽  
Electric Circuit ◽  
Ant Colony ◽  
Robust Design Optimization ◽  
Continuous Variables ◽  
Discrete Variables ◽  
Design Problems ◽  
Discrete Search ◽  
Improved Ant Colony Algorithm

The basic ant colony algorithm is improved by introducing chaos model of Logistic and discrete search in order to improve the global convergence. A program of improved ant colony algorithm has been designed by using Matlab. It can be used for solving optimal design problems with continuous variables, discrete variables or mixed-discrete variables. For an electric circuit, the design problem about the robustness of electric current is discussed and a model of robust optimal design is established. The solution of established model is achieved by using the proposed method and the robustness of the electric circuit has been improved. The example shows that the proposed method is effective in engineering design.

scholarly journals Optimal Design of Compact Spur Gear Reductions

1992 ◽  
Author(s):  
M. Savage ◽  
S. B. Lattime ◽  
J. A. Kimmel ◽  
H. H. Coe
Keyword(s):  
Optimal Design ◽  
Search Algorithm ◽  
Spur Gear ◽  
Optimal Designs ◽  
Continuous Variables ◽  
Gear Mesh ◽  
System Life ◽  
Optimal Configurations ◽  
System Volume ◽  
Selection Of

Abstract The optimal design of compact spur gear reductions includes the selection of bearing and shaft proportions in addition to the gear mesh parameters. Designs for single mesh spur gear reductions are based on optimization of system life, system volume, and system weight including gears, support shafts, and the four bearings. The overall optimization allows component properties to interact, yielding the best composite design. A modified feasible directions search algorithm directs the optimization through a continuous design space. Interpolated polynomials expand the discrete bearing properties and proportions into continuous variables for optimization. After finding the continuous optimum, the designer can analyze near optimal designs for comparison and selection. Design examples show the influence of the bearings on the optimal configurations.

Infeasibility and Non-Optimality Tests for Solution Space Reduction in Discrete Optimal Design

1995 ◽  
Vol 117 (3) ◽  
pp. 425-432 ◽  
Author(s):  
L. P. Pomrehn ◽  
P. Y. Papalambros
Keyword(s):  
Mathematical Model ◽  
Solution Space ◽  
Global Optimum ◽  
Gear Train ◽  
Discrete Variables ◽  
Multistage Process ◽  
Model Formulation ◽  
Space Reduction ◽  
Nonlinear Design ◽  
The Mathematical Model

Techniques employed for nonlinear design optimization with discrete variables are studied in the context of a particular problem arising from the design of a gear train. The mathematical model formulation was presented in an earlier article. In this sequel, a solution derivation is described, patterned as a multistage process. After certain reformulation and relaxation, a variety of infeasibility and non-optimality tests are performed, greatly reducing the size of the space containing the global optimum. Methods used to investigate the remaining space do not guarantee a global optimum, but could be replaced by more costly methods that do provide such guarantees. A global infimum is generated, bounding any improvements on the best known solution.

scholarly journals Optimal Design of Compact Spur Gear Reductions

1994 ◽  
Vol 116 (3) ◽  
pp. 690-696 ◽  
Author(s):  
M. Savage ◽  
S. B. Lattime ◽  
J. A. Kimmel ◽  
H. H. Coe
Keyword(s):  
Optimal Design ◽  
Search Algorithm ◽  
Spur Gear ◽  
Optimal Designs ◽  
Continuous Variables ◽  
Gear Mesh ◽  
System Life ◽  
Optimal Configurations ◽  
System Volume ◽  
Selection Of

The optimal design of compact spur gear reductions includes the selection of bearing and shaft proportions in addition to the gear mesh parameters. Designs for single mesh spur gear reductions are based on optimization of system life, system volume, and system weight including gears, support shafts, and the four bearings. The overall optimization allows component properties to interact, yielding the best composite design. A modified feasible directions search algorithm directs the optimization through a continuous design space. Interpolated polynomials expand the discrete bearing properties and proportions into continuous variables for optimization. After finding the continuous optimum, the designer can analyze near optimal designs for comparison and selection. Design examples show the influence of the bearings on the optimal configurations.

Foraging-Directed Adaptive Linear Programming: An Algorithm for Solving Nonlinear Mixed Discrete/Continuous Design Problems

1996 ◽  
Author(s):  
Kemper Lewis ◽  
Farrokh Mistree
Keyword(s):  
Linear Programming ◽  
Continuous Variables ◽  
Design Problems ◽  
Design Studies ◽  
Design Models ◽  
Sequential Linearization ◽  
And Behavior

Abstract Design models often contain a combination of discrete, integer, and continuous variables. Previously, the Adaptive Linear Programming (ALP) Algorithm, which is based on sequential linearization, has been used to solve design models composed of continuous and Boolean variables. In this paper, we extend the ALP Algorithm using a discrete heuristic based on the analogy of an animal foraging for food. This algorithm for mixed discrete/continuous design problems integrates ALP and the foraging search and is called Foraging-directed Adaptive Linear Programming (FALP). Two design studies are presented to illustrate the effectiveness and behavior of the algorithm.

scholarly journals Optimal design for population pk/pd models

2012 ◽  
Vol 51 (1) ◽  
pp. 115-130
Author(s):  
Sergei Leonov ◽  
Alexander Aliev
Keyword(s):  
Optimal Design ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Optimal Sampling ◽  
Design Algorithm ◽  
Sampling Schemes ◽  
Population Pk ◽  
Different Types

ABSTRACT We provide some details of the implementation of optimal design algorithm in the PkStaMp library which is intended for constructing optimal sampling schemes for pharmacokinetic (PK) and pharmacodynamic (PD) studies. We discuss different types of approximation of individual Fisher information matrix and describe a user-defined option of the library.

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.

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