Introduction to ANSYS DesignXplorer -...

© 2013 ANSYS, Inc. September 27, 2013 1 Release 14.5

14. 5 Release

Introduction to ANSYS DesignXplorer

Lecture 5 Goal Driven Optimization


Goal Driven Optimization (GDO) is a multi – objective technique in which the “best” possible designs are obtained from a sample set given the goals you set for parameters

Two different types of GDO systems are available: Response Surface Optimization and Direct Optimization

States a series of design goals which will be used to generate optimized design.

– Desired values for input and response parameters are specified

– Importance rankings are specified for parameters.

– A set of sample designs is generated.

– The most promising candidate designs are chosen.

Goal Driven Optimization (GDO)


1. Goal Driven Optimization Procedure

- Response Surface Optimization – draws information from response surface and it is dependant on the quality of response surface.

- Direct Optimization – single component system which utilizes real solve rather than response surface evaluations.

2. Optimization Methods

Goal Driven Optimization Outline


1. Conduct an optimization study

GDO – Response Surface Optimization Procedure

1

3

Select optimization

model and settings

Define optimization domain,

objectives and importance 2


2. Review Candidate Points

• A number of gold stars or red crosses are displayed next to each objective-driven parameter to indicate how well it meets the stated objective, from three red crosses (the worst) to three gold stars (the best)

• these results are not necessarily fully representative of the solution set, as this approach obtains results by ranking the solution by an aggregated weighted method



3. Generate Charts

• Tradeoff Chart

– Output parameters are displayed on each axis visualizing the displaying which output goals can be achieved and whether this entails sacrificing the goal attainment of other outputs

– A Pareto front is a group of solutions such that selecting any one of them in place of another will always sacrifice quality for at least one objective, while improving at least one other.

– The best set of samples (first Pareto front) is indicated in blue

– The worst set of samples (worst Pareto front) is indicated in red



3. Generate Charts

• Samples Chart

– Each sample is displayed as a group of line curves where each point is the value of one input or output parameter

– The color of the curve identifies the Pareto front that the sample belongs to, or the chart can be set so that the curves display the best candidates and all other samples

– Slide the yellow arrows at the top of each axis up or down in order to increase or decrease the axis bounds. Samples are dynamically hidden if they fall outside of the bounds.



4. Verify Candidates

• DesignXplorer verifies Candidate Points by creating and updating Design Points with a "real solve" using the input parameter values of the Candidate Points. The output parameter values from the real solve are displayed in the row below the response surface generated output values to allow for easy comparison

• If the results are not similar, it indicates that the response surface is not accurate enough in that area and perhaps refinement or other adjustments are necessary. It is possible to insert the Candidate Point as a refinement point.



GDO – Direct Optimization Procedure

1. Conduct an optimization study

1

2

3



- Options under Optimization will change based on Optimization Method (discussed in the later slides)

- Select Optimization Method (discussed in the later slides)

- Converged – indicates if optimization converged

- Number of Iterations – number of iterations executed

- Number of Evaluations – design point evaluations performed

- Number of Failures – number of failed design points

- Size of Generated Sample Set – number of samples successfully updated from the last population generated by the algorithm

- Number of Candidates – obtained candidates


• Screening

- Number of Samples – number of samples to generate for the optimization (generated from response surface), must be equal or greater than number of enabled input and output parameters

- Max Number of Candidates – max number of candidates to be generated by the algorithm

• MOGA

- Number of Initial Samples – minimum should be 10 times the number or continuous input parameters, the larger the better (default 100)

- Number of Samples Per Iteration – number of samples iterated and updated at each iteration. Must be grater or equal to the number of enabled input and output parameters but less than or equal to the number or initial samples (default 100 for Response Surface Optimization and 50 for Direct Optimization)

- Max Allowable Pareto Percentage – ratio of the number of desired Pareto points to the Number of Samples per iteration. Using between 55 and 75 works the best for most problems

- Max Number of Iterations – max possible number of iterations the algorithm executes



• NLPQL

- Allowable Convergence Percentage – the tolerance to which optimality creation is generated during NLPQL process. A smaller value indicates more convergence iterations and more accurate but slower solution. A larger number indicates less convergence iterations and less accurate but faster solution.

Derivative Approximation – specify the method of approximating the gradient of the objective function. Central Difference – calculates output derivatives, doubles the number of design point evaluations (default for Response surface optimization), Forward Difference – calculates output derivatives, fewer design point evaluations, and less accuracy of the gradient calculation (default for the Direct Optimization

• MISQP – similar to NLPQL



• Single – Objective

- Number of LHS Initial Samples – samples for the initial Kriging and for the construction of the next Kriging

- Number of Screening Samples – samples for screening generation on the current Kriging

- Number of Starting Points – determines the number of the local optima to be explored, the larger the starting points set, the more local optima will be explored

- Max Number of Evaluations – Stop criterion. If the convergence occurs before the number is reached, evaluations will stop

- Max Number of Domain Reductions – max possible number of domain reductions for input variation

- Percentage of Domain Reductions – min size of the current domain according to the initial domain

• Multiple – Objective – Similar to MOGA



• Objectives and Constraints – allows you to define design goals in the form of objectives and constraints that will be used to generate optimized design.

• Objective type

• Constraint type

• Objective Target



• History Chart varies based on the input parameter, the objective/constraint, and optimization method being used.

• Objective values are listed vertically

• Number of points is shown horizontally

• Red curve – evaluation of the objective

• Gray dashed line – bounds for constraints

• Blue dashed line – target values




• Define Optimization Domain by Select Domain and edit the domain via Table or select input parameter and define domain via the Parameters view • Define Lower bound, Upper bound, and Starting value



• Raw design point data is stored for future reference

•This list is compiled of raw design point data only; no analysis is applied and

it does not show feasibility, ratings, Pareto fronts, etc. for the included points



• Each Candidate Point is displayed along with its input values, output values, and candidate rating • Percentage of variation for all parameters is calculated with regard to an initial reference point • Custom candidate points can be created • When the optimization is stopped, candidate points are generated from the data available at that time


There are six optimization methods in DX

1. Screening (Shifted Hammersley) [default]

2. MOGA (Multi-objective Genetic Algorithm)

3. NLPQL (Non-linear Programming by Quadratic Lagrangian)

4. MISQP (Mixed – Integer Sequential Quadratic Programming Method for Direct Optimization and Response Surface Optimization systems)

5. Adaptive Single – Objective Method for Direct Optimization systems

6. Adaptive Multiple – Objective Method for Direct Optimization systems

Goal Driven Optimization Methods


A non-iterative direct sampling method by a quasi-random number generator

Generates a large collection of samples from the response surfaces and sort its samples based on objectives and weighting

Usually used for preliminary designs

Benefit:

• Provides a global overview of the design space

• Allows you to identify global and local minima

• Provides several candidates

• Available for both continuous and discrete input parameters

Drawbacks:

• Not fully accurate (accuracy improves with more sample points)

Goal Driven Optimization Screening


An iterative multi-objective genetic algorithm

Provides a more refined approach than Screening

It goes through several iterations retaining the “elite” percentage of the samples through each iteration allowing the samples to “genetically” evolve until the best pareto set has been found

Ideally suited for calculating global maxima/minima (designed to avoid local optima traps)

Benefit:

• Helps identify global and local minima

• Provides several candidates in different regions

• Accurate solution

• Can handle multiple goals

Drawback:

• Might concentrate on a single region in the design space

• Available for continuous input parameters only

Goal Driven Optimization MOGA


A gradient based single objective optimizer which is based on quasi-Newton methods

Ideally suited for local optimization

Benefit:

• Accurate and fast

Drawback:

• Might fall into a local minimum

• Does not handle multiple objectives (although other output parameters can be defined as constraints)

• Available for continuous input parameters only

• Provides a single solution

Goal Driven Optimization NLPQL


Mixed-Integer Sequential Quadratic Programming is mathematical optimization algorithm that solves MINLP (Mixed-Integer Non-Linear Programming) by modified sequential quadratic programming method

Benefit:

• Can be used for both Response Surface Optimization and Direct Optimization

• Provides more refined approach than Screening method

• Available for both discrete and continuous input parameters

Drawback:

• It can only handle one output parameter goal (other output parameters can be defined as constraints)

Goal Driven Optimization MISQP


Adaptive Single-Objective is a mathematical optimization method that combines an LHS Design of Experiments, a Kriging response surface, and the NLPQL optimization algorithm. It is a gradient-based algorithm based on a response surface which provides a refined, global, optimized result

Benefit:

• Employs automatic intelligent refinement to provide the global optima

• Reduces the number of design points necessary for the optimization

• Failed design points are treated as inequality constraints, making it fault-tolerant

Drawback:

• Supports a single objective

• It can only handle one output parameter goal (other output parameters can be defined as constraints)

• Limited to continuous parameters

• It is available only for Direct Optimization systems

Goal Driven Optimization Adaptive Single – Objective


Goal Driven Optimization Adaptive Multiple – Objective

Adaptive Multiple-Objective is a mathematical optimization that combines a Kriging and the MOGA optimization algorithm. It allows you to either generate a new sample set or use an existing set. Part of the population is “simulated” by evaluations of the Kriging and the Kriging error predictor reduces the number of evaluations used in finding the first Pareto front solutions

Benefit:

• Provides more refined approach than the Screening method

• The optimizer does not evaluate all design points

• Supports multiple objectives

• Supports multiple constraints

Drawback:

• Limited to continuous parameters

• Available only for Direct Optimization systems


• At least one of the output parameters should have an Objective of

Maximize, Minimize, or Seek Target in order to do optimization with

the MOGA or NLPQL methods (only one output can have an

objective for the NLPQL method). The same applies to ASO, AMO,

and MISQP.

• If this is not done, then the optimization problem is either undefined

(No Objective) or is merely a constraint satisfaction problem

(Objective set to >= Target or <= Target). When the problem is not

defined, the MOGA or NLPQL analysis cannot be run. The same

applies to ASO, AMO, and MISQP.

• Screening method does not depend on any parameter settings and

can be used to perform preliminary design studies.

Goal Driven Optimization Additional Points


If parameters are discontinuous:

• Screening

If one objective and parameters are continuous:

• Screening (to find global maxima/minima)

• NLPQL (with solution space narrowed to be near global maxima/minima)

or

• MOGA (if you want to select from multiple candidates)

If more than one objective and parameters are continuous:

• Screening (optional)

• MOGA

Good default approach: Screening followed by MOGA

Summary


Appendix


Each parameter range is divided into 6 zones, or rating scales. The location of a design candidate value in the range is measured according to the rating scales. For example, for parameter X with a range of 0.9 to 1.1, the rating scale for a design candidate value of 1.0333 is calculated as follows:

(((Absolute(1.0333-1.1))/(1.1-0.9))*6)-(6/2) = 2.01-3 = -1 [one star] (as 0 indicating neutral, negative values indicating closer to the target, up to -3; positive value indicating farther away from the target, up to +3)

Following the same procedures, you will get rating scale for design candidate value of 0.9333 as 5.001-3 = +2 [two crosses] (away from target). Therefore, the extreme cases are as follows:

1. Design Candidate value of 0.9 (the worst), the rating scale is 6-3 = +3 [three crosses]

2. Design Candidate value of 1.1 (the best), the rating scale is 0-3 = -3 [three stars]

3. Design Candidate value of 1.0 (neutral), the rating scale is 3-3 = 0 [dash]

Note:

Objective-driven parameter values with inequality constraints receive either three stars (the constraint is met) or three red crosses (the constraint is violated).

Rating Candidate Design Points

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