Two-layered Surrogate Modeling for Tuning Optimization - - PowerPoint PPT Presentation

▶

Mar 23, 2023 372 likes •620 views

Two-layered Surrogate Modeling for Tuning Optimization Metaheuristics Gnter Rudolph, Mike Preuss & Jan Quadflieg Lehrstuhl fr Algorithm Engineering Fakultt fr Informatik TU Dortmund Outline Introduction: Main Goal and Ideas

SLIDE 1

Two-layered Surrogate Modeling for Tuning Optimization Metaheuristics

Günter Rudolph, Mike Preuss & Jan Quadflieg

Lehrstuhl für Algorithm Engineering Fakultät für Informatik TU Dortmund

SLIDE 2

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 2

Outline

Introduction: Main Goal and Ideas
Layer 1: Model-assisted Evolution Strategy (MAES)
Layer 2: Sequential parameter optimization (SPO)
Proof of Principle: Benchmark Problems
The Real Thing: Optimization of Ship Propulsion System (Linearjet)
Conclusions

SLIDE 3

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 3

Main Goal Introduction development of an efficient method for finding good parameterization of a stochastic optimization algorithm applied to problems with time-consuming objective function ) we do not focus on optimizing objective function, here ) rather, identify good parameterization of metaheuristic before spending time, effort, money etc. on optimization of true problem

SLIDE 4

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 4

Scenario – Part I Introduction

ptimization

metaheuristic

bjective

function f(x) time- consuming simulation x surrogate function fs(x) x good parameterization of metaheuristic?

SLIDE 5

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 5

Scenario – Part II Introduction

ptimizer

(SPO) performance metrics M(p) time- consuming metaheuristic p surrogate function Ms(p) p ) optimize parameters p of metaheuristic ) result M(p) is a random variable! ) kind of noisy optimization ) repeated evaluation & averaging (roughly)

SLIDE 6

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 6

Two Layers of Meta- / Surrogate Models Introduction Assumptions: 1. Parameter tuning easier than solving optimization problem 2. Rough approximation in layer 1 good enough to allow for tuning metaheuristic ad 1) fewer parameters (¼ 5) and prior knowledge about metaheuristic ad 2) to be tested experimentally

SLIDE 7

Two Layers of Meta- / Surrogate Models Introduction Minimal space filling design in parameter space Run metaheuristic for each design p Yields pair { p, M(p) } per run and many pairs { x, f(x) } over all runs Pairs { x, f(x) } used to build 1st layer surrogate model fs(x) SPO uses pairs { p, M(p) } to build 2nd layer surrogate model Ms(p) repeat SPO optimizes parameters p on Ms(p) Yields first candidate p* Validation runs on f(.) with parameterization p* Yields pairs { x, f(x) } → update surrogate model fs(x) Yields mean pair { p, M(p) } → update surrogate model Ms(p) until resources exhausted Phase 1 Phase 2

SLIDE 8

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 8

Model-assisted Evolution Strategy Layer 1 Parameters: ¹ , ¸ , k, ¾ , ¿ (º = ¸ / 2) also testing benefit of external databases → initial sizes: 0, 1000, 2000 pairs surrogate model:

rdinary kriging

SLIDE 9

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 9

Sequential Parameter Optimization Layer 2

Latin hypercube design in parameter space (here: 25 with 4 repeats)
Global ordinary kriging model to predict promising regions
Deploys expected improvement criterion of EGO
Considers predicted error and function value

Total budget of algorithm runs: 500 (here) Non-deterministic answers: increasing number of repeats

SLIDE 10

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 10

Benchmark Problems Proof of Principle f10(x) Rotated Rastrigin taken from IEEE CEC‘05 benchmark dimensions: 2 and 10

SLIDE 11

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 11

Benchmark Problems Proof of Principle f12(x) Schwefel 2.13 taken from IEEE CEC‘05 benchmark dimensions: 2 and 10

SLIDE 12

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 12

Tuning on 1st layer successful? Proof of Principle 20 runs for each database size 2 { 0, 1000, 2000 } initial: ¾ = 0.15, ¿ = 1.0, k = 10, ¹ = 1, ¸ = 5

Rotated Rastrigin Schwefel 2.13 D = 2000 D = 1000 D = 0 D = 2000 D = 1000 D = 0

SLIDE 13

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 13

Tuning on 1st layer successful? Proof of Principle Standard initial and tuned parameters of MAES

SLIDE 14

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 14

Tuning on 1st layer successful? Proof of Principle p-values of Wilcoxon rank-sum test at level 0.05 between 20 validation runs of different parameter sets

SLIDE 15

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 15

Linear-jet Engine Real-World Test Problem 15 design variables:

lengths
thicknesses
angles

basic fluid dynamic simulation needs 3 minutes full CFD simulation needs 8 hours in parallel

bjective:

minimum cavitation at a predefined efficiency caviatation = emergence of vacuum bubbles caused by extreme pressure differences due to high accelerations of the water (causes damage and noise)

SLIDE 16

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 16

Setup of Experiment Real-World Test Problem database of 2000 points from previous runs used to create ordinary kriging model SPO: run lengths of 300 evaluations on true problem MAES runn 9 times with best parameterization found note: a single run needs 12 to 24 hours on modern PC

SLIDE 17

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 17

Results Real-World Test Problem Good values: ¼ -1.6 different with p-value 0.02

SLIDE 18

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 18

Results Real-World Test Problem Good values: Parameterization found

SLIDE 19

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 19

Lessions learnt Conclusions Modelling of objective function needs revision → evidently, penalizations lead to rugged response surface 20x20 grid 2 rotor parameters 20x20 grid uncorrelated parameters

SLIDE 20

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 20

Lessions learnt and future work Conclusions Two-layered surrogate model approach works quite well … but needs more work Hypothesis: works since only main characteristics of true problem must be reflected by surrogate model → theoretical foundation possible? MAES not best choice → replace by other metaheuristic Future work: integrated / automatic procedure

SLIDE 21

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 21

Questions?

The End …

SLIDE 22

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 22

IEEE WCCI 2010, Barcelona, Spain Announcements

SLIDE 23

Rudolph / Preuss / Quadflieg @ ENBIS / EMSE 2009 23