Managing Function Constraints in Design Sheet™

1998 ◽  
Author(s):  
Sudhakar Y. Reddy ◽  
Kenneth W. Fertig
Keyword(s):  
Optimization Problems ◽  
Systems Of Nonlinear Equations ◽  
Graph Theoretic ◽  
Constraint Management ◽  
Constraint Network ◽  
Design Variables ◽  
Large Systems ◽  
And Performance ◽  
Design Cost ◽  
Performance Tradeoff

Abstract Design Sheet™ is a constraint management system specially designed for doing conceptual design cost and performance tradeoff studies. It represents the design models as constraints between design variables, and uses graph-theoretic algorithms to decompose large systems of nonlinear equations into smaller pieces that can be solved robustly. This paper describes extensions to Design Sheet that enable it to manage functions as variables in a constraint network. The paper also discusses the new capabilities of function encapsulation and explicit differentiation that are built on top of these extensions. The ability to encapsulate a part of the constraint network into a function, and use it in other constraints, promotes model reuse and improves computational efficiency. The capability to automatically differentiate certain variables with respect to other design variables allows Design Sheet to be used for solving practical optimization problems. In combination with the tradeoff capability, this enables the designer to track changing optima in trade studies. The paper also provides a couple of optimization examples to demonstrate these new capabilities.

An Approach to Identify Six Sigma Robust Solutions of Multi/Many-Objective Engineering Design Optimization Problems

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Tapabrata Ray ◽  
Md Asafuddoula ◽  
Hemant Kumar Singh ◽  
Khairul Alam
Keyword(s):  
Design Optimization ◽  
Engineering Design ◽  
Optimization Problems ◽  
Product Family ◽  
Latin Hypercube Sampling ◽  
General Aviation ◽  
Design Variables ◽  
Engineering Design Optimization ◽  
The Face ◽  
And Performance

In order to be practical, solutions of engineering design optimization problems must be robust, i.e., competent and reliable in the face of uncertainties. While such uncertainties can emerge from a number of sources (imprecise variable values, errors in performance estimates, varying environmental conditions, etc.), this study focuses on problems where uncertainties emanate from the design variables. While approaches to identify robust optimal solutions of single and multi-objective optimization problems have been proposed in the past, we introduce a practical approach that is capable of solving robust optimization problems involving many objectives building on authors’ previous work. Two formulations of robustness have been considered in this paper, (a) feasibility robustness (FR), i.e., robustness against design failure and (b) feasibility and performance robustness (FPR), i.e., robustness against design failure and variation in performance. In order to solve such formulations, a decomposition based evolutionary algorithm (DBEA) relying on a generational model is proposed in this study. The algorithm is capable of identifying a set of uniformly distributed nondominated solutions with different sigma levels (feasibility and performance) simultaneously in a single run. Computational benefits offered by using polynomial chaos (PC) in conjunction with Latin hypercube sampling (LHS) for estimating expected mean and variance of the objective/constraint functions has also been studied in this paper. Last, the idea of redesign for robustness has been explored, wherein selective component(s) of an existing design are altered to improve its robustness. The performance of the strategies have been illustrated using two practical design optimization problems, namely, vehicle crash-worthiness optimization problem (VCOP) and a general aviation aircraft (GAA) product family design problem.

scholarly journals Metamodels for Planar 3R Workspace Optimization

2002 ◽  
Author(s):  
Cameron J. Turner
Keyword(s):  
Computer Aided Design ◽  
Optimization Problems ◽  
Nonlinear Modeling ◽  
Central Element ◽  
B Spline ◽  
Spline Models ◽  
Design Variables ◽  
And Performance ◽  
Complex Relationships ◽  
Workspace Optimization

Robotic workspace optimization is a central element of robot system design. To formulate the optimization problem, the complex relationships between design variables, tuning parameters, and performance indices need to be accurately and efficiently represented. The nature of the relationships suggests that metamodels, or models of the models, should be used to derive suitable objective functions. A comparison of two metamodeling techniques for robotic workspace optimization problems for several trial cases suggests that non-uniform rational B-spline models, derived from computer graphics and computer-aided design techniques, are as suitable as response surface models to solve planar 3R workspace optimization problems. Promising nonlinear modeling results with B-spline models suggest future work is justified and performance gains can be realized.

scholarly journals NeuSE: A Neural Snapshot Ensemble Method for Collaborative Filtering

2021 ◽  
Vol 15 (6) ◽  
pp. 1-20
Author(s):  
Dongsheng Li ◽  
Haodong Liu ◽  
Chao Chen ◽  
Yingying Zhao ◽  
Stephen M. Chu ◽  
...  
Keyword(s):  
Collaborative Filtering ◽  
Optimization Problems ◽  
Empirical Studies ◽  
Large Datasets ◽  
Model Learning ◽  
Global Models ◽  
Convex Optimization Problems ◽  
Memory Network ◽  
Real World Datasets ◽  
Performance Tradeoff

In collaborative filtering (CF) algorithms, the optimal models are usually learned by globally minimizing the empirical risks averaged over all the observed data. However, the global models are often obtained via a performance tradeoff among users/items, i.e., not all users/items are perfectly fitted by the global models due to the hard non-convex optimization problems in CF algorithms. Ensemble learning can address this issue by learning multiple diverse models but usually suffer from efficiency issue on large datasets or complex algorithms. In this article, we keep the intermediate models obtained during global model learning as the snapshot models, and then adaptively combine the snapshot models for individual user-item pairs using a memory network-based method. Empirical studies on three real-world datasets show that the proposed method can extensively and significantly improve the accuracy (up to 15.9% relatively) when applied to a variety of existing collaborative filtering methods.

Improved Particle Swarm Optimizer with Dynamically Adjusted Search Space and Velocity Limits for Global Optimization

2015 ◽  
Vol 24 (05) ◽  
pp. 1550017 ◽  
Author(s):  
Aderemi Oluyinka Adewumi ◽  
Akugbe Martins Arasomwan
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Search Space ◽  
Particle Swarm Optimizer ◽  
Search Range ◽  
Original Algorithm ◽  
Inertia Weight ◽  
And Performance

This paper presents an improved particle swarm optimization (PSO) technique for global optimization. Many variants of the technique have been proposed in literature. However, two major things characterize many of these variants namely, static search space and velocity limits, which bound their flexibilities in obtaining optimal solutions for many optimization problems. Furthermore, the problem of premature convergence persists in many variants despite the introduction of additional parameters such as inertia weight and extra computation ability. This paper proposes an improved PSO algorithm without inertia weight. The proposed algorithm dynamically adjusts the search space and velocity limits for the swarm in each iteration by picking the highest and lowest values among all the dimensions of the particles, calculates their absolute values and then uses the higher of the two values to define a new search range and velocity limits for next iteration. The efficiency and performance of the proposed algorithm was shown using popular benchmark global optimization problems with low and high dimensions. Results obtained demonstrate better convergence speed and precision, stability, robustness with better global search ability when compared with six recent variants of the original algorithm.

Shape Synthesis and Optimization Using Intrinsic Geometry

1990 ◽  
Author(s):  
Shahriar Tavakkoli ◽  
Sanjay G. Dhande
Keyword(s):  
Optimization Problems ◽  
Piecewise Linear ◽  
Shape Design ◽  
Arc Length ◽  
Intrinsic Geometry ◽  
Shape Model ◽  
Design Variables ◽  
Dimensional Shape ◽  
Variable Geometry Truss ◽  
Arc Lengths

Abstract The present paper outlines a method of shape synthesis using intrinsic geometry to be used for two-dimensional shape optimization problems. It is observed that the shape of a curve can be defined in terms of intrinsic parameters such as the curvature as a function of the arc length. The method of shape synthesis, proposed here, consists of selecting a shape model, defining a set of shape design variables and then evaluating Cartesian coordinates of a curve. A shape model is conceived as a set of continuous piecewise linear segments of the curvature; each segment defined as a function of the arc length. The shape design variables are the values of curvature and/or arc lengths at some of the end-points of the linear segments. The proposed method of shape synthesis and optimization is general in nature. It has been shown how the proposed method can be used to find the optimal shape of a planar Variable Geometry Truss (VGT) manipulator for a pre-specified position and orientation of the end-effector. In conclusion, it can be said that the proposed approach requires fewer design variables as compared to the methods where shape is represented using spline-like functions.

Hider: A Methodology for Early-Stage Exploration of Design Space

1996 ◽  
Author(s):  
Sudhakar Y. Reddy
Keyword(s):  
Design Space ◽  
Optimization Problems ◽  
Early Stage ◽  
Simulation Models ◽  
Design Tool ◽  
System Level ◽  
Complex Simulation ◽  
Machine Learning Approach ◽  
Detailed Simulation ◽  
And Performance

Abstract This paper describes HIDER, a methodology that enables detailed simulation models to be used during the early stages of system design. HIDER uses a machine learning approach to form abstract models from the detailed models. The abstract models are used for multiple-objective optimization to obtain sets of non-dominated designs. The tradeoffs between design and performance attributes in the non-dominated sets are used to interactively refine the design space. A prototype design tool has been developed to assist the designer in easily forming abstract models, flexibly defining optimization problems, and interactively exploring and refining the design space. To demonstrate the practical applicability of this approach, the paper presents results from the application of HIDER to the system-level design of a wheel loader. In this demonstration, complex simulation models for cycle time evaluation and stability analysis are used together for early-stage exploration of design space.

Improved Trust Region Based MPS Method for High-Dimensional Expensive Black-Box Problems

2013 ◽  
Author(s):  
George H. Cheng ◽  
Adel Younis ◽  
Kambiz Haji Hajikolaei ◽  
G. Gary Wang
Keyword(s):  
Optimization Problems ◽  
Trust Region ◽  
Black Box ◽  
High Dimensional ◽  
Test Problems ◽  
Design Variables ◽  
Low Dimensionality ◽  
Improve Algorithm ◽  
Improved Performance ◽  
Better Than

Mode Pursuing Sampling (MPS) was developed as a global optimization algorithm for optimization problems involving expensive black box functions. MPS has been found to be effective and efficient for problems of low dimensionality, i.e., the number of design variables is less than ten. A previous conference publication integrated the concept of trust regions into the MPS framework to create a new algorithm, TRMPS, which dramatically improved performance and efficiency for high dimensional problems. However, although TRMPS performed better than MPS, it was unproven against other established algorithms such as GA. This paper introduces an improved algorithm, TRMPS2, which incorporates guided sampling and low function value criterion to further improve algorithm performance for high dimensional problems. TRMPS2 is benchmarked against MPS and GA using a suite of test problems. The results show that TRMPS2 performs better than MPS and GA on average for high dimensional, expensive, and black box (HEB) problems.

Multi Objective Design Optimization of Two Bar Truss Using NSGA II and TOPSIS

2014 ◽  
Vol 984-985 ◽  
pp. 419-424
Author(s):  
P. Sabarinath ◽  
M.R. Thansekhar ◽  
R. Saravanan
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Nsga Ii ◽  
Multi Objective ◽  
Total Displacement ◽  
Design Variables ◽  
Conflicting Objectives

Arriving optimal solutions is one of the important tasks in engineering design. Many real-world design optimization problems involve multiple conflicting objectives. The design variables are of continuous or discrete in nature. In general, for solving Multi Objective Optimization methods weight method is preferred. In this method, all the objective functions are converted into a single objective function by assigning suitable weights to each objective functions. The main drawback lies in the selection of proper weights. Recently, evolutionary algorithms are used to find the nondominated optimal solutions called as Pareto optimal front in a single run. In recent years, Non-dominated Sorting Genetic Algorithm II (NSGA-II) finds increasing applications in solving multi objective problems comprising of conflicting objectives because of low computational requirements, elitism and parameter-less sharing approach. In this work, we propose a methodology which integrates NSGA-II and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for solving a two bar truss problem. NSGA-II searches for the Pareto set where two bar truss is evaluated in terms of minimizing the weight of the truss and minimizing the total displacement of the joint under the given load. Subsequently, TOPSIS selects the best compromise solution.

Emitter resistance and performance tradeoff of submicrometer self-aligned double-polysilicon bipolar devices

1988 ◽  
Vol 35 (12) ◽  
pp. 2397-2405 ◽  
Author(s):  
T. Yamaguchi ◽  
Y.-C.S. Yu ◽  
V.F. Drobny ◽  
A.M. Witkowski
Keyword(s):  
Bipolar Devices ◽  
And Performance ◽  
Performance Tradeoff
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