Optimum Design Problem Formulation

2017 ◽  
pp. 19-70 ◽  
Author(s):  
Jasbir Singh Arora
Keyword(s):  
Optimum Design ◽  
Design Problem ◽  
Problem Formulation

scholarly journals The Optimum Design of Stepped Shafts: A Study in Computational Optimization

1982 ◽  
Author(s):  
C. J. Maday
Keyword(s):  
Optimum Design ◽  
Critical Speed ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Minimum Principle ◽  
Problem Formulation ◽  
Rayleigh Quotient ◽  
Computational Optimization ◽  
Stepped Shaft ◽  
Determine Step

Optimum stepped shaft designs are obtained through an application of Pontryagin’s Minimum Principle. Optimum designs are obtained for a given critical speed of specified order. Indexes of Performance to be minimized include mass and rotating inertia. A general problem formulation illustrates how constraints on stress, deflections, and geometric design are taken in account. Numerical solutions are obtained to nonlinear multi-point-boundary-value-problems. A Newton-Raphson algorithm was developed to determine step locations precisely in order to facilitate the convergence of the shooting method used to solve the boundary value problem. Numerical solutions are determined with an assumed critical speed; a Rayleigh quotient calculation is used to verify that the optimum design possesses the assumed value.

Hierarchical Arrangement of Characteristics in Product Design Optimization Problems for Deeper Insight Into Optimized Results

2004 ◽  
Author(s):  
Masataka Yoshimura ◽  
Masahiko Taniguchi ◽  
Kazuhiro Izui ◽  
Shinji Nishiwaki
Keyword(s):  
Design Optimization ◽  
Product Design ◽  
Optimum Design ◽  
Design Problem ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimization Method ◽  
Hierarchical Level ◽  
Hierarchical Arrangement ◽  
Insight Into

This paper proposes a design optimization method for machine products that is based on the decomposition of performance characteristics, or alternatively, extraction of simpler characteristics, to accommodate the specific features or difficulties of a particular design problem. The optimization problem is expressed using hierarchical constructions of the decomposed and extracted characteristics and the optimizations are sequentially repeated, starting with groups of characteristics having conflicting characteristics at the lowest hierarchical level and proceeding to higher levels. The proposed method not only effectively enables achieving optimum design solutions, but also facilitates deeper insight into the design optimization results, and aids obtaining ideas for breakthroughs in the optimum solutions. An applied example is given to demonstrate the effectiveness of the proposed method.

Design Optimization of Hydraulic Networks Using Mixed Integer Linear Programming

1982 ◽  
Vol 104 (4) ◽  
pp. 837-843
Author(s):  
T. F. Conry ◽  
J. A. Werhane
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Design Problem ◽  
Mixed Integer Linear Programming ◽  
Computer Aided Design ◽  
Water System ◽  
Cooling Water ◽  
Problem Formulation ◽  
Mixed Integer ◽  
Service Water

The optimum design problem is formulated for the selection of pipe sizes in a hydraulic network such as a power plant service water or bearing cooling water system. The flows in each branch of the network are taken to be known, which makes the design problem linear in the variables. The optimization problem is formulated as a mixed integer linear programming problem. A design example is given. The role of this problem formulation and solution method in an interactive computer aided design (CAD) system is discussed.

Multi-Objective Evolutionary Algorithms’ Performance in a Support Role

2015 ◽  
Author(s):  
Matthew J. Woodruff ◽  
Timothy W. Simpson ◽  
Patrick M. Reed
Keyword(s):  
Evolutionary Algorithms ◽  
Conceptual Design ◽  
Parameter Space ◽  
Design Problem ◽  
Problem Formulation ◽  
Diagnostic Assessment ◽  
Multi Objective ◽  
Assessment Study

This paper presents a diagnostic assessment study, evaluating five leading multi-objective evolutionary algorithms (MOEAs) on their effectiveness, efficiency, reliability, and controllability on four different formulations of the same benchmark conceptual design problem, using the same underlying model. This assessment entails a broad sampling of the parameter space of each MOEA, for each problem formulation, requiring millions of optimization runs and trillions of model evaluations. The results of this assessment show the strengths and limitations of these MOEAs, establishing the Borg MOEA as a leading algorithm.

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