Introduction to ANSYS DesignXplorer

Transcription

1 Lecture 5 Goal Driven Optimization Release Introduction to ANSYS DesignXplorer ANSYS, Inc. September 27, 2013

2 Goal Driven Optimization (GDO) 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 ANSYS, Inc. September 27, 2013

3 Goal Driven Optimization Outline 1. Goal Driven Optimization - 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 ANSYS, Inc. September 27, 2013

4 GDO Response Surface Optimization 1. Conduct an optimization study Define optimization domain, objectives and importance Select optimization model and settings ANSYS, Inc. September 27, 2013

5 GDO Response Surface Optimization 2. Review Candidate Points A number of gold stars or red crosses are displayed next to each objectivedriven 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 ANSYS, Inc. September 27, 2013

6 GDO Response Surface Optimization 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 ANSYS, Inc. September 27, 2013

7 GDO Response Surface Optimization 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 ANSYS, Inc. September 27, 2013

8 GDO Response Surface Optimization 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 ANSYS, Inc. September 27, 2013

9 GDO Direct Optimization 1. Conduct an optimization study ANSYS, Inc. September 27, 2013

10 GDO Direct Optimization - Select Optimization Method (discussed in the later slides) - Options under Optimization will change based on 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 ANSYS, Inc. September 27, 2013

11 GDO Direct Optimization 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 ANSYS, Inc. September 27, 2013

12 GDO Direct Optimization 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 ANSYS, Inc. September 27, 2013

13 GDO Direct Optimization 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 ANSYS, Inc. September 27, 2013

14 GDO Direct Optimization 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 ANSYS, Inc. September 27, 2013

15 GDO Direct Optimization 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 ANSYS, Inc. September 27, 2013

16 GDO Direct Optimization 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 ANSYS, Inc. September 27, 2013

17 GDO Direct Optimization 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 ANSYS, Inc. September 27, 2013

18 GDO Direct Optimization 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 ANSYS, Inc. September 27, 2013

19 GDO Direct Optimization ANSYS, Inc. September 27, 2013

20 Goal Driven Optimization Methods 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 ANSYS, Inc. September 27, 2013

21 Goal Driven Optimization Screening 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) ANSYS, Inc. September 27, 2013

22 Goal Driven Optimization MOGA 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 ANSYS, Inc. September 27, 2013

23 A gradient based single objective optimizer which is based on quasi-newton methods Ideally suited for local optimization Benefit: Accurate and fast Goal Driven Optimization NLPQL 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 ANSYS, Inc. September 27, 2013

24 Goal Driven Optimization MISQP 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) ANSYS, Inc. September 27, 2013

25 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: Goal Driven Optimization Adaptive Single Objective 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 ANSYS, Inc. September 27, 2013

26 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 ANSYS, Inc. September 27, 2013

27 Goal Driven Optimization Additional Points 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 ANSYS, Inc. September 27, 2013

28 Summary 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 ANSYS, Inc. September 27, 2013

29 Appendix ANSYS, Inc. September 27, 2013

30 Rating Candidate Design Points 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 is calculated as follows: (((Absolute( ))/( ))*6)-(6/2) = = -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 as = +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) ANSYS, Inc. September 27, 2013