Quantifying tradeoffs to reduce the dimensionality of complex design optimization problems and expedite trade space exploration

2016 ◽  
Vol 54 (2) ◽  
pp. 233-248 ◽  
Author(s):  
Mehmet Unal ◽  
Gordon P. Warn ◽  
Timothy W. Simpson
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Space Exploration ◽  
Complex Design ◽  
Trade Space Exploration

Introduction of a Tradeoff Index for Efficient Trade Space Exploration

2015 ◽  
Author(s):  
Mehmet Unal ◽  
Gordon Warn ◽  
Timothy W. Simpson
Keyword(s):  
Approximate Solution ◽  
Design Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Space Exploration ◽  
High Dimensional ◽  
Two Dimensional ◽  
Complex Design ◽  
Trade Space Exploration ◽  
Tradeoff Index

The development of many-objective evolutionary algorithms has facilitated solving complex design optimization problems, that is, optimization problems with four or more competing objectives. The outcome of many-objective optimization is often a rich set of solutions, including the non-dominated solutions, with varying degrees of tradeoff amongst the objectives, herein referred to as the trade space. As the number of objectives increases, exploring the trade space and identifying acceptable solutions becomes less straightforward. Visual analytic techniques that transform a high-dimensional trade space into two-dimensional (2D) presentations have been developed to overcome the cognitive challenges associated with exploring high-dimensional trade spaces. Existing visual analytic techniques either identify acceptable solutions using algorithms that do not allow preferences to be formed and applied iteratively, or they rely on exhaustive sets of 2D representations to identify tradeoffs from which acceptable solutions are selected. In this paper, an index is introduced to quantify tradeoffs between any two objectives and integrated into a visual analytic technique. The tradeoff index enables efficient trade space exploration by quickly pinpointing those objectives that have tradeoffs for further exploration, thus reducing the number of 2D representations that must be generated and interpreted while allowing preferences to be formed and applied when selecting a solution. Furthermore, the proposed index is scalable to any number of objectives. Finally, to illustrate the utility of the proposed tradeoff index, a visual analytic technique that is based on this index is applied to a Pareto approximate solution set from a design optimization problem with ten objectives.

Evaluating the Performance of Visual Steering Commands for User-Guided Pareto Frontier Sampling During Trade Space Exploration

2008 ◽  
Author(s):  
Dan Carlsen ◽  
Matthew Malone ◽  
Josh Kollat ◽  
Timothy W. Simpson
Keyword(s):  
Decision Making ◽  
Design Optimization ◽  
Optimization Problems ◽  
Space Exploration ◽  
Pareto Frontier ◽  
Optimization Process ◽  
Multi Objective Genetic Algorithm ◽  
Trade Space Exploration ◽  
Support Engineering ◽  
Visualization Techniques

Trade space exploration is a promising decision-making paradigm that provides a visual and more intuitive means for formulating, adjusting, and ultimately solving design optimization problems. This is achieved by combining multi-dimensional data visualization techniques with visual steering commands to allow designers to “steer” the optimization process while searching for the best, or Pareto optimal, designs. In this paper, we compare the performance of different combinations of visual steering commands implemented by two users to a multi-objective genetic algorithm that is executed “blindly” on the same problem with no human intervention. The results indicate that the visual steering commands — regardless of the combination in which they are invoked — provide a 4x–7x increase in the number of Pareto solutions that are obtained when the human is “in-the-loop” during the optimization process. As such, this study provides the first empirical evidence of the benefits of interactive visualization-based strategies to support engineering design optimization and decision-making. Future work is also discussed.

scholarly journals Improving the Performance of Visual Steering Commands for Multi-Dimensional Trade Space Exploration

2008 ◽  
Author(s):  
Christopher D. Congdon ◽  
Daniel E. Carlsen ◽  
Timothy W. Simpson ◽  
Jay D. Martin
Keyword(s):  
Optimization Problems ◽  
Space Exploration ◽  
Engineering Application ◽  
Region Of Interest ◽  
Monte Carlo Sampling ◽  
Test Problems ◽  
Design Decision ◽  
Support Design ◽  
Exploration Process ◽  
Trade Space Exploration

Designers perform many tasks when developing new products and systems, and making decisions may be among the most important of these tasks. The trade space exploration process advocated in this work provides a visual and intuitive approach for formulating and solving single- and multi-objective optimization problems to support design decision-making. In this paper, we introduce an advanced sampling method to improve the performance of the visual steering commands that have been developed to explore and navigate the trade space. This method combines speciation and crowding operations used within the Differential Evolution (DE) algorithm to generate new samples near the region of interest. The accuracy and diversity of the resulting samples are compared against simple Monte Carlo sampling as well as the current implementation of the visual steering commands using a suite of test problems and an engineering application. The proposed method substantially increases the efficiency and effectiveness of the sampling process while maintaining diversity within the trade space.

Quantifying the Shape of a Pareto Front in Support of Many-Objective Trade Space Exploration

2016 ◽  
Author(s):  
Mehmet Unal ◽  
Gordon P. Warn ◽  
Timothy W. Simpson
Keyword(s):  
Pareto Front ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Space Exploration ◽  
Shape Index ◽  
Analytical Geometry ◽  
Conflicting Objectives ◽  
Diminishing Returns ◽  
Final Design ◽  
Trade Space Exploration

Complex design optimization problems typically include many conflicting objectives, and the resulting trade space is comprised of numerous design solutions. To efficiently explore a many-objective trade space, form preferences, and select a final design, one must identify and negotiate tradeoffs between multiple, often conflicting, objectives. Identifying conflicting objective pairs allows decision-makers to concentrate on these objectives when selecting preferred designs from the non-dominated solution set, i.e., the Pareto front. Techniques exist to identify and visualize tradeoffs between these conflicting objectives to support trade space exploration; however, these techniques do not quantify, or differentiate, the shape of the Pareto front, which might be useful information for a decision-maker. More specifically, designers could gain insight from the degree of diminishing returns among solutions on the Pareto front, which can be used to understand the extent of the tradeoffs in the problem. Therefore, the shape of the Pareto front could be used to prioritize exploration of conflicting objective pairs. In this paper, we introduce a novel index that quantifies the shape of the Pareto front to provide information about the degree of diminishing returns. The aim of the index is to help designers gain insight into the underlying tradeoffs in a many-objective optimization problem and support trade space exploration by prioritizing the negotiation of conflicting objectives. The proposed Pareto Shape Index is based on analytical geometry and derived from the coordinates of the Pareto solutions in the n objective trade space. The utility of the Pareto Shape Index in differentiating diminishing returns between conflicting objectives is demonstrated by application to an eight-objective benchmark optimization problem.

A Comprehensive Investigation of Ensembles of Gaussian-Based and Gradient-Based Transformed Reliability Analyses: When and How to Use Them

2016 ◽  
Author(s):  
Po Ting Lin ◽  
Wei-Hao Lu ◽  
Shu-Ping Lin
Keyword(s):  
Design Optimization ◽  
Design Space ◽  
Optimization Problems ◽  
Nonlinear Problems ◽  
Kernel Functions ◽  
Sensitivity Analyses ◽  
Normal Space ◽  
Highly Nonlinear ◽  
Standard Normal ◽  
Gradient Based

In the past few years, researchers have begun to investigate the existence of arbitrary uncertainties in the design optimization problems. Most traditional reliability-based design optimization (RBDO) methods transform the design space to the standard normal space for reliability analysis but may not work well when the random variables are arbitrarily distributed. It is because that the transformation to the standard normal space cannot be determined or the distribution type is unknown. The methods of Ensemble of Gaussian-based Reliability Analyses (EoGRA) and Ensemble of Gradient-based Transformed Reliability Analyses (EGTRA) have been developed to estimate the joint probability density function using the ensemble of kernel functions. EoGRA performs a series of Gaussian-based kernel reliability analyses and merged them together to compute the reliability of the design point. EGTRA transforms the design space to the single-variate design space toward the constraint gradient, where the kernel reliability analyses become much less costly. In this paper, a series of comprehensive investigations were performed to study the similarities and differences between EoGRA and EGTRA. The results showed that EGTRA performs accurate and effective reliability analyses for both linear and nonlinear problems. When the constraints are highly nonlinear, EGTRA may have little problem but still can be effective in terms of starting from deterministic optimal points. On the other hands, the sensitivity analyses of EoGRA may be ineffective when the random distribution is completely inside the feasible space or infeasible space. However, EoGRA can find acceptable design points when starting from deterministic optimal points. Moreover, EoGRA is capable of delivering estimated failure probability of each constraint during the optimization processes, which may be convenient for some applications.

Study on Mix-Variable Collaborative Design Optimization

2012 ◽  
Vol 215-216 ◽  
pp. 592-596
Author(s):  
Li Gao ◽  
Rong Rong Wang
Keyword(s):  
Design Optimization ◽  
Product Design ◽  
Optimization Algorithm ◽  
Collaborative Design ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Collaborative Optimization ◽  
Continuous Variables ◽  
Complex Product ◽  
Divide And Rule

In order to deal with complex product design optimization problems with both discrete and continuous variables, mix-variable collaborative design optimization algorithm is put forward based on collaborative optimization, which is an efficient way to solve mix-variable design optimization problems. On the rule of “divide and rule”, the algorithm decouples the problem into some relatively simple subsystems. Then by using collaborative mechanism, the optimal solution is obtained. Finally, the result of a case shows the feasibility and effectiveness of the new algorithm.

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