Activity Analysis: Simplifying Optimal Design Problems Through Qualitative Partitioning

1995 ◽  
Author(s):  
Brian C. Williams ◽  
Jonathan Cagan
Keyword(s):  
Numerical Analysis ◽  
Optimal Design ◽  
Design Problem ◽  
Optimization Problem ◽  
Activity Analysis ◽  
Design Problems ◽  
Gradient Based ◽  
Monotonicity Analysis

Abstract Activity analysis is introduced as a means to strategically cut away subspaces of a design problem that can quickly be ruled out as suboptimal. This results in focused regions of the space in which additional symbolic or numerical analysis can take place. Activity analysis is derived from a qualitative abstraction of the Karush-Kuhn-Tucker conditions of optimality, used to partition an optimization problem into regions which are nonstationary and qualitatively stationary (qstationary). Activity analysis draws from the fields of gradient-based optimization, conflict-based approaches of combinatorial satisficing search, and monotonicity analysis.

scholarly journals Optimal design of a DC MHD pump by simulated annealing method

2014 ◽  
Vol 11 (2) ◽  
pp. 339-350
Author(s):  
Khadidja Bouali ◽  
Fatima Kadid ◽  
Rachid Abdessemed
Keyword(s):  
Simulated Annealing ◽  
Optimal Design ◽  
Objective Function ◽  
Design Problem ◽  
Design Methodology ◽  
Optimization Problem ◽  
Optimization Procedure ◽  
Simulated Annealing Method ◽  
Direct Interpretation ◽  
Annealing Method

In this paper a design methodology of a magnetohydrodynamic pump is proposed. The methodology is based on direct interpretation of the design problem as an optimization problem. The simulated annealing method is used for an optimal design of a DC MHD pump. The optimization procedure uses an objective function which can be the minimum of the mass. The constraints are both of geometrics and electromagnetic in type. The obtained results are reported.

A Framework for Algorithms in Globally Optimal Design

1989 ◽  
Vol 111 (3) ◽  
pp. 353-360 ◽  
Author(s):  
P. Hansen ◽  
B. Jaumard ◽  
S. H. Lu
Keyword(s):  
Combinatorial Optimization ◽  
Optimal Design ◽  
Branch And Bound ◽  
General Framework ◽  
Ad Hoc ◽  
Design Problems ◽  
Branch And Bound Algorithms ◽  
Monotonicity Analysis

Many problems of globally optimal design have been solved in the literature using monotonicity analysis and a variety of tests, often applied in an ad hoc way. These tests are developed here, expressed mathematically and classified according to the conclusions they yield. Moreover, many new tests, similar to those used in combinatorial optimization, are presented. Finally, a general framework is proposed in which branch-and-bound algorithms for globally optimal design problems can be expressed.

Synergy and transitivity in constraint dominance methods: Demonstration with linear motor design problem

2006 ◽  
Vol 20 (4) ◽  
pp. 383-397
Author(s):  
ASHISH DESHPANDE ◽  
JAMES R. RINDERLE
Keyword(s):  
Design Problem ◽  
Optimal Solution ◽  
Design Problems ◽  
Electric Actuator ◽  
Constraint Reasoning ◽  
Effective Decision ◽  
Determination Methods ◽  
Effective Decision Making ◽  
Propagation Methods ◽  
Monotonicity Analysis

Reasoning about relationships among design constraints can facilitate objective and effective decision making at various stages of engineering design. Exploiting dominance among constraints is one particularly strong approach to simplifying design problems and to focusing designers' attention on critical design issues. Three distinct approaches to constraint dominance identification have been reported in the literature. We lay down the basic principles of these approaches with simple examples, and we apply these methods to a practical linear electric actuator design problem. With the help of the design problem we demonstrate strategies to synergistically employ the dominance identification methods. Specifically, we present an approach that utilizes the transitive nature of the dominance relation. The identification of dominance provides insight into the design of linear actuators, which leads to effective decisions at the conceptual stage of the design. We show that the dominance determination methods can be synergistically employed with other constraint reasoning methods such as interval propagation methods and monotonicity analysis to achieve an optimal solution for a particular design configuration of the linear actuator. The dominance determination methods and strategies for their employment are amenable for automation and can be part of a suite of tools available to assist the designer in detailed as well as conceptual design.

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 of Taguchi’s Robust Circuit Design Problem

1990 ◽  
Author(s):  
Douglass J. Wilde
Keyword(s):  
Circuit Design ◽  
Design Problem ◽  
Recent Article ◽  
Optimization Problem ◽  
Algebraic Function ◽  
Necessary Condition ◽  
Control Range ◽  
Design Variables ◽  
Numerical Iteration ◽  
Monotonicity Analysis

Abstract A recent article showed how to formulate Taguchi’s robust circuit design problem rigorously as an optimization problem. A necessary condition for optimality was found to be that the control range be centered about the target value. This generates a constraint on the two design variables which cannot be solved for either variable. The present article shows that by approximating this unsolvable constraint with a simpler constraint that is solvable, one variable can be eliminated and the problem reduced to an unconstrained one in a single variable. Since this reduced objective turns out to be monotonic in the remaining design variable, its optimum value must be at the limit of its range. The corresponding optimum value of the other variable is then determined exactly from the true, not approximate, constraint. Since no model construction, experimentation, statistical analysis or numerical iteration is needed, this procedure is recommended whenever the input-output relation is known to be a monotonic algebraic function.

A Single-Stage Gradient-Based Approach for Solving the Joint Product Family Platform Selection and Design Problem Using Decomposition

2007 ◽  
Author(s):  
Aida Khajavirad ◽  
Jeremy J. Michalek
Keyword(s):  
Design Problem ◽  
Optimization Problem ◽  
Computational Cost ◽  
Product Family ◽  
Single Stage ◽  
System Level ◽  
Continuous Space ◽  
Joint Product ◽  
Product Family Optimization ◽  
Gradient Based

A core challenge in product family optimization is to develop a single-stage approach that can optimally select the set of variables to be shared in the platform(s) while simultaneously designing the platform(s) and variants within an algorithm that is efficient and scalable. However, solving the joint product family platform selection and design problem involves significant complexity and computational cost, so most prior methods have narrowed the scope by treating the platform as fixed or have relied on stochastic algorithms or heuristic two-stage approaches that may sacrifice optimality. In this paper, we propose a single-stage approach for optimizing the joint problem using gradient-based methods. The combinatorial platform-selection variables are relaxed to the continuous space by applying the commonality index and consistency relaxation function introduced in a companion paper. In order to improve scalability properties, we exploit the structure of the product family problem and decompose the joint product family optimization problem into a two-level optimization problem using analytical target cascading so that the system-level problem determines the optimal platform configuration while each subsystem optimizes a single product in the family. Finally, we demonstrate the approach through optimization of a family of ten bathroom scales; Results indicate encouraging success with scalability and computational expense.

Monotonicity Analysis of Taguchi’s Robust Circuit Design Problem

1992 ◽  
Vol 114 (4) ◽  
pp. 616-619 ◽  
Author(s):  
D. J. Wilde
Keyword(s):  
Circuit Design ◽  
Design Problem ◽  
Optimization Problem ◽  
Algebraic Function ◽  
The Other ◽  
Necessary Condition ◽  
Control Range ◽  
Design Variables ◽  
Numerical Iteration ◽  
Monotonicity Analysis

Taguchi’s robust circuit design problem can be formulated rigorously as an optimization problem. A necessary condition for optimality is that the control range be centered about the target value. This generates a constraint on the two design variables which cannot be solved for either variable. The present article shows that by approximating this unsolvable constraint with a simpler constraint that is solvable, one variable can be eliminated and the problem reduced to an unconstrained one in a single variable. Since this reduced objective turns out to be monotonic in the remaining design variable, its optimum value must be at the limit of its range. The corresponding optimum value of the other variable is then determined exactly from the true, not approximate, constraint. Since no model construction, experimentation, statistical analysis, or numerical iteration is needed, this procedure is recommended whenever the input-output relation is known to be a monotonic algebraic function.

Monotonicity Analysis in Optimum Design of Marine Risers

1982 ◽  
Vol 104 (4) ◽  
pp. 849-854 ◽  
Author(s):  
P. Papalambros ◽  
M. M. Bernitsas
Keyword(s):  
Optimal Design ◽  
Optimization Problem ◽  
Static Pressure ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Design Rules ◽  
Marine Risers ◽  
Two Dimensional Model ◽  
Polynomial Expression ◽  
Monotonicity Analysis

The optimal design of marine risers used for drilling and production of oil in offshore operations is studied. The optimization problem is formulated on a two-dimensional model for bending of circular tubular beams under tension and internal and external static pressure. A general polynomial expression describes the external hydrodynamic loads. Monotonicity analysis is used to identify active constraints, determine design rules, and reduce the size of the problem.

APPLICATION OF IMPROVED COLLABORATIVE OPTIMIZATION METHOD TO MECHANICAL MULTI-OBJECTIVE OPTIMAL DESIGN PROBLEM

2012 ◽  
Vol 11 (02) ◽  
pp. 151-157 ◽  
Author(s):  
FENGTAO WEI ◽  
LI SONG ◽  
YAN LI ◽  
KUN SHI
Keyword(s):  
Optimal Design ◽  
Efficient Method ◽  
Design Problem ◽  
Optimization Method ◽  
Collaborative Optimization ◽  
Flow Chart ◽  
Optimal Design Problem ◽  
Design Problems ◽  
Multi Objective ◽  
Result Show

In order to solve the mechanical multi-objective optimal design problems, the basic idea and flow chart of collaborative optimization method are introduced in this paper. In view of the shortcomings that exist in standard collaborative optimization method, this method has been improved by applying the dynamic slack factor method. Taking a mechanical multi-objective optimal design of spring as an example, the multi-objective optimal design problem has been solved by the improved collaborative optimization method. The process and result show that the improved collaborative optimization method has higher accuracy and efficiency. This paper has provided an efficient method to solve the complicated mechanical multi-objective optimal design problems.

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