Faster Evolutionary Multi-Objective Optimization via GALE: the Geometric Active Learner
description
Transcript of Faster Evolutionary Multi-Objective Optimization via GALE: the Geometric Active Learner
Joseph Krall
In partial fulfillment of the requirements for the degree of Doctor of Philosophy in Computer Science.
College of Engineering and Mineral Resources
Faster Evolutionary Multi-Objective Optimization via GALE, the Geometric Active Learner
a Ph.D. Final Defense Presentation for the
Special Thanks to the NASA Ames Research Center
The Lane Department of Computer Science and Electrical Engineering
at
April 21, 2014
Estimated Duration: 45 minutes
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A Thesis Proposal
- “JMOO: Tools for Faster Multi-Objective Optimization”
Comments from Committee
- Lacking Rigor
- Generalizability of Proposal
- Lacking Details / Misunderstandings
- Some Missing Related Works
- Validity Concerns
- Needed More – Not Substantial Enough
Last Time 1. Introduction
November, 2013
SE or CS?
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Final Dissertation - “Faster Multi-Objective Optimization via GALE” Key Changes from Proposal - Focus on Contributions of GALE - Focus on Assessing and Validating GALE - Very rigorous experimental methodology - Addressing Comments from Proposal - Expansive Related Works - Formalizing the Field - MANY more experimental results
This Time
Spring!
…Sort of
April, 2014
1. Introduction
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Search & Optimization of Goals - the art of decision making - e.g. shortest time city navigation - e.g. managing calorie intake for diets Not always trivial - Landing an airplane safely - Maximizing software project profits
MOO = Multi-Objective Optimization - Draft solutions to a problem (red) - Find Pareto Frontiers (green) - Report to a decision maker
This Thesis
Areas on the Pareto frontier
Rejected Solutions
Who do I pick???
1. Introduction
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Increasing Interest
The Field of MOO
Agile Project Studies
Aircraft Studies
Software Engineering (SE) General MOO
(MOO) Coello: http://delta.cs.cinvestav.mx/˜ccoello/EMOO/EMOObib.html (SE) CREST: http://crestweb.cs.ucl.ac.uk/resources/sbse_repository/repository.html
* Data from :
8000 Papers Since the
1950’s
1. Introduction
In this thesis: SE and CS
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[Sayyad & Ammar 2013] Report:
- NSGA-II and SPEA2 are the most popular search tools today
Popular Search Tools Evaluate Too Much - O(N2) internal search: fast if solution evaluation is a cheap operation
- Need to count number of evaluations instead: O(2NG)
This Thesis Proposes GALE: O(2Log2(NG)) - GALE adds data mining to evaluate only the most-informative solutions
Main Message Introduction
GALE: 597s
NSGA-II: 14,018s
N = population size G = number of generations
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Aircraft Studies for Safety Assurance
- Complex Simulations at NASA [8 seconds per run]
Standard MOO Tools
- Many [300] weeks
GALE
- Many [300] hours
Applications of MOO
!
* Asiana Flight Wreckage, Summer 2013
(50400 hrs)
(1.8 wks)
1. Introduction
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GALE is a Meta-heuristic Search Tool
- Too difficult (maybe impossible) to “prove”
- Can only be experimented -> Generalizability (External Validity) concerns
-> A MOO Critique to Improve Validity
Research Questions
- Evaluations
- Runtime
- Solution Quality
Assessing GALE
4 Experimental Areas: - #1 Aircraft Safety (CDA)
- #2 Agile Projects (POM3) - #3 Constrained Lab Problems
- #4 Unconstrained Lab Problems
SE or CS?
SE CS
CS CS
1. Introduction
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GALE shown to be a strong rival to NSGA-II & SPEA2
And The Results
Two orders of magnitude fewer evaluations for all
models
Two orders of magnitude faster (seconds) for big
models
Better Solution Quality
SPEA2 much slower
GALE Never worse NSGA-II/SPEA2 Never better
1. Introduction
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Background 2
In this chapter: - Formalities - Definitions
- Related Works
1. Introduction
2. Background
3. MOO Critique
4. GALE
5. Models
6. Experiments
7. Validity
8. Conclusion
10 Slides
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Mathematical Programming: [Dantzig] - The aim is to find solutions that optimize objectives - Transformation functions transform decisions (x) into objectives (y) - Solutions are infeasible if they do not satisfy constraint functions
Formalities 2. Background
objectives
Constraint functions Optimality direction
Transformation functions
a. Defines
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Lab Problems
- Schaffer, Viennet, Tanaka, etc.
Real-world Problems
- Simulations
- Too complex for math
- Aircraft Safety
- Software Dev. Profit
Kinds of Models
The Schaffer Model
2. Background a. Defines
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Early methods assumed math models
- A bad assumption for real world practicality
They also assume other aspects:
- Concave vs. Convex
- Differentiability
- Linear vs. Non-linear
- Single vs. Multi-objective
- Objective Functions vs. Simulation
Numerical Optimization 2. Background b. Early Methods
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Exterior Search [Dantzig]
- For Linear problems ( [Nelder & Mead 1965] made a non-linear version)
- Embed a simplex with solutions along the vertices
- Traverse along the nodes
- Good average Complexity
- But bad O(N3) worst case
Simplex Search
Nelder, John A.; R. Mead (1965). "A simplex method for function minimization". Computer Journal 7: 308–313.
2. Background b. Early Methods
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Karmarkar’s Algorithm – [Karmarkar 1984]
- Good for big data
- Fast convergence
- Polynomial complexity
- 50x faster than Simplex
- Single-Objective Only
- Requires Concavity
Interior Point Methods
Narendra Karmarkar (1984). "A New Polynomial Time Algorithm for Linear Programming", Combinatorica, Vol 4, nr. 4, p. 373–395.
2. Background b. Early Methods
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Moving onward from Numerical Methods
- Improve a heuristic, not the actual objectives
- Hill Climbing: Accept only improved steps
- Tabu Search: Refuse only recently attempted steps
- Simulated Annealing: Early bad okay, late bad refused
Heuristic-based Searches 2. Background c. Recent Methods
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Particle Swarm Optimization [Kennedy 1995]
- Real life swarms; flocks of birds, etc
- Swarm towards good solutions
- Self best and Pack best
Ant Colony Optimization [Dorigo 1992]
- Ant Colony Path Searches
- Pheromone density = best path
PSO & ACO
Kennedy, J.; Eberhart, R. (1995). "Particle Swarm Optimization". Proceedings of IEEE International Conference on Neural Networks IV. pp. 1942–1948.
M. Dorigo, Optimization, Learning and Natural Algorithms, PhD thesis, Politecnico di Milano, Italy, 1992.
2. Background c. Recent Methods
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Standard EA (Evolutionary Algorithm): 1) Build initial population
2) Repeat for max_generations:
a) crossover
b) mutation
c) select
3) Return final population
Evolutionary Algorithms
a+b) Build Offspring: Perturb Population c) Combine Offspring + Population c) Cull the worst solutions to retain Population Size
* Malin Åberg: http://physiol.gu.se/maberg/images.html
2. Background c. Recent Methods
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NSGA-II [Deb 2002]
- Non-dominated Sorting Genetic Algorithm
- Standard select+crossover+mutation
- Sort by ‘bands’, or domination ‘depth’
- Break ties based on density
- crowding distance
NSGA-II
Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T. (2002). "A fast and elitist multiobjective genetic algorithm: NSGA-II". IEEE Transactions on Evolutionary Computation 6 (2): 182
2. Background c. Recent Methods
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SPEA2 [Zitzler2002]
- Strength Pareto Evolutionary Algorithm
- Standard select+crossover+mutation
- Sort by ‘strength’: count of solutions someone dominates
- Truncate crowded solutions via nearest neighbor
SPEA2
E. Zitzler, M. Laumanns, and L. Thiele. SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization. Evolutionary Methods for Design Optimization and Control with Applications to Industrial Problems, 95--100, 2001.
2. Background c. Recent Methods
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MOO Critique 3
In this chapter: - Survey - Rigor
1. Introduction
2. Background
3. MOO Critique
4. GALE
5. Models
6. Experiments
7. Validity
8. Conclusion
4 Slides
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Experimental Rigor
- Want to maximize validity
- Because reasons to doubt GALE
- Still does good with few evals?
- Can still run fast?
We looked at literature for advice - Search query targeted these questions:
- Ended up selecting 21 papers
Survey of MOO
Statistical Methods? - [Demsar2006]: recommends KS-Test + Friedman + Nemenyi
* J. Demsar, “Statistical comparisons of classifiers over multiple data sets,” ˇ J. Mach. Learn. Res., vol. 7, pp. 1–30, Dec. 2006.
Population size? - 20 ~ 100 is good. - Over 200 is a waste
Number of Repeats? - [Harman 2012]: 30-50 is common. - This Thesis: 20.
* M. Harman et al., Search based software engineering: techniques, taxonomy, tutorial. In Empirical Software Engineering and Verification, Bertrand Meyer and Martin Nordio (Eds.). Springer-Verlag, Berlin, Heidelberg 1-59.
3. MOO Critique
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1. Use variety of models – Real World Models: Practicality.
– Standard Models: Reproducibility.
– Constrained and Unconstrained: Generalizability
2. How many Repeats – Pragmatics: Keep repeats low to save on computational cost
– Statistics: Want high repeats for statistical stability
– The middle ground: for n in 20,30,40: no change. So 20 is good.
Principles 1 & 2
Many papers used only lab models
- 7 Constrained - 13 Unconstrained - 1 Privatized (CDA) - 1 Public (POM3)
In this thesis: Standard Models Real World Models
Constrained Lab
Unconstrained Lab Public
Privatized Use models from all quadrants:
3. MOO Critique
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3. Statistical Methods – Based on Demsar’s Recommendations
– Begin with Kolmogorov-Smirnov (KS-Test) to test normality
• Data rarely conforms to normality assumptions
– For two-group testing, use Wilcoxon Rank Sum (WRS) Test
– For Multi-group testing, use Friedman Test + Nemenyi
4. Runtimes – Report runtimes to aid reproducibility arguments
– Report details of machine
Principles 3 & 4 3. MOO Critique
Most papers failed to address number of groups
Half of the papers neglected to report runtimes
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5. Number of Evaluations – Report number of evaluations
– Because they dominate runtime of real-world models
6. Parameters – Define all parameters carefully
– Reproducibility concerns: pop. Size, #gens, stopping criteria
7. Discuss Threats of Validity – Don’t make the reader do all the work
– Rigorous Experimental Methods = Stronger Conclusions
Principles 5-7
Half of the papers neglected to report evaluations
Almost no one had a threats to validity section in their paper
3. MOO Critique
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GALE 4
1. Introduction
2. Background
3. MOO Critique
4. GALE
5. Models
6. Experiments
7. Validity
8. Conclusion
In this chapter: - Spectral Learning - Active Learning
5 Slides
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GALE: Geometric Active Learning (Evolution)
- At most O(2Log2N) evaluations per generation
- Exactly Θ(2N) evaluations for NSGA-II, SPEA2
Main Differences in GALE:
- cluster solutions
- evaluate some, not all
- Directed vs random
- More on these later
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Introducing GALE 4. GALE
GALE NSGA-II SPEA2
Asymptotic Notation: Big-O: worst case
Big-Theta: Exact case
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Three key phrases to talk about
1. Active Learning - Minimize cost of evaluation
- Learn more from using less [Settles 2009]
2. Spectral Learning (WHERE) - Reasoning with eigenvectors via covariance matrix
- “Spectral Clustering” – via eigenvectors
- FastMap finds eigenvectors faster than PCA
3. Directed Search - Shove solutions along promising directions
Components to GALE
some, not all
clustered spectrally
Directed mutation
4. GALE
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Algorithm shown here and explained over next several slides - WHERE algorithm - WHERE uses FastMap - Directed Mutation
1. Build initial population, P0. Initialize generation: t = 0. Set Life = 3. 2. Repeat until stopping criteria is met (stop if life == 0):
a. Run WHERE (with pruning) to select Rt = dominant leafs from WHERE. b. Perform Directed Mutation on members of Rt. c. Copy Rt into Pt+1 and generate new random candidates until new population is full. d. Increment generation number t = t + 1. e. Collect stats and evaluate stopping criteria. Decrement life if no improvement to any
objective.
3. Run WHERE (without pruning) to select Rt = dominant leafs from WHERE. 4. Rt contains approximations to the Pareto frontier.
GALE Pseudo-Code GALE
Spectral Learning Active Learning Directed Search
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Spectral clustering is O(n3) [Kumar12]
- Common method: PCA
- The Nystrom Method reduces to near-linear
- Low-rank approx. of covariance matrix
e.g.: FastMap is a Nystrom Algorithm [Platt05] - 1) Pick an arbitrary point, z.
- 2) Let ‘east’ be the furthest point from z.
- 3) Let ‘west’ be the furthest point from ‘east’.
- 4) Project all points onto the line east-west
- 5) east-west is the first principal component
Nystrom Method GALE
east
west
c
b
a x
Active Learning: - Only evaluate East & West!
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WHERE = Spectral Learning in GALE
- Similar to Boley’s PDDP: find first eigenvector and recursively split
- PDDP uses PCA. WHERE uses FastMap.
The WHERE Tool GALE
Initial population
WHERE clusters initial population = Spectral Learning
Only evaluate the best clusters =
Active Learning
Mutate along those clusters = Directed Search
At Most 2Log2(NG) Evaluations (N=Population Size. G=Number of Generations)
Refill the Population
Non-dominated clusters
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Models 5
1. Introduction
2. Background
3. MOO Critique
4. GALE
5. Models
6. Experiments
7. Validity
8. Conclusion
In this chapter: - CDA
- POM3 - Lab Models
4 Slides
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5. Models
Continuous Descent Arrival
- NASA wants to know if CDA is doable
- Standard descents are less efficient than CDA -> more {noise, time, fuel, $$$}
- CDA might unnecessarily strain air traffic control (ATC)
CDA Model a. CDA
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Lots of work - 2 months at NASA Ames Research Center
- CDA not pre-assembled
Inspiration from 2013 Asiana Flight Crash - Pilots had to do unusually more tasks than normal
- Keeping airspeed nominal was a task they ‘forgot’
- Human Factors model a pilot ‘HTM’ = maximum human taskload
Goal of CDA: less forgetting, less time from delays and missed tasks
* based on Work Models that Compute by Pritchett, Kim and Feigh, 2011-2013
Building CDA 5. Models a. CDA
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POM3
- Model of Agile Software Requirements Engineering
Agile Software Projects
- Programmers rush to complete tasks
- But what tasks get most priority?
Requirements Prioritization Strategies
- Find good schemes that optimize objectives
POM3
Repeat 2 < N < 6 times: 1. Collect Tasks 2. Prioritize Tasks 3. Execute Tasks 4. Find New Tasks 5. Adjust Priorities
Objectives to Minimize - Total Cost - % Idle Rate of Teams
Objectives to Maximize - % Completion of Tasks
* POM3 based on POM2 based on POM by Portman, Owens, Menzies (2008, 2009)
5. Models b. POM3
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We explore all these: The Constrex Model
Standard Lab Models
Unconstrained Constrained
Fonseca BNH
Golinski Constrex
Kursawe Osyczka2
Poloni Srinivas
Schaffer Tanaka
Viennet2-3-4 TwoBarTruss
ZDT1-2-3 Water
ZDT4-6
5. Models c. Lab
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Experiments 6
3. MOO Critique
4. GALE
5. Models
6. Experiments
7. Validity
8. Conclusion
1. Introduction
2. Background
4 Slides
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In this chapter: - Results - Analysis
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Research Questions:
- Number of Evaluations
- Runtime
- Quality of Solutions
4 Experiment Areas:
- #1 Aircraft Safety
- #2 Agile Software Development
- #3 Constrained Lab Models
- #4 Unconstrained Lab Models
Experimental Methods 6. Experiments
1. Run the Model 500 times 2. Collect an average-case baseline 3. Compute loss (x, baseline) for each solution x
4. The median loss is the “Quality Score”
o = number of objectives
Quality Score: > 1.0: Loss in Quality from Baseline = 1.0: No Change from Baseline < 1.0: Improvement from Baseline
[Zitzler & Kunzli 2004]
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Experiment GALE NSGA-II SPEA2
#1 Aircraft Safety (CDA Model)
50 +++
2800 =
2450 =
#2 Agile Software (POM3 Models)
36-46 +++
3000-3550 =
3050-3300 =
#3 Constrained Lab Models
28-88 +++
1050-3250 =
950-3150 =
#4 Unconstrained Lab models
26-45 +++
1250-3550 =
1250-3250 =
RQ1: Number of Evaluations
GALE needed two orders of magnitude fewer evaluations
6. Experiments
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Experiment GALE NSGA-II SPEA2
#1 Aircraft Safety (CDA Model)
6 – 20mins +++
3 – 5hrs =
3 – 5hrs =
#2 Agile Software (POM3 Models)
1.5 – 9.5s ++
4.0 – 108s =
12 – 109s =
#3 Constrained Lab Models
0.5 – 1.5s =
0.5 – 1.0s =
3 – 30s –
#4 Unconstrained Lab models
0.5 – 2.5s =
0.5 – 1.0s =
3 – 30s –
#5 – 16 Modes of the CDA Model
83 hours 6 months 6 months
RQ2: Runtime
GALE needed two orders of magnitude lesser runtime
6. Experiments
GALE enabled an even larger
study on CDA
NSGA-II and SPEA
weren’t used in #5,
so these values were extrapolated
from #1
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Experiment GALE NSGA-II SPEA2
#1 Aircraft Safety (CDA Model)
0-0-2 =
0-0-2 =
0-0-2 =
#2 Agile Software (POM3 Models)
0-0-6 =
0-1-5 =
1-0-5 =
#3 Constrained Lab Models
12-0-2 +
0-6-8 =
0-6-8 =
#4 Unconstrained Lab models
10-3-13 +
1-5-20 =
2-5-19 =
RQ3: Solution Quality
Displays are ‘Wins-Losses-Ties’ Format GALE never loses. GALE usually wins.
KS-Test + Friedman + Nemenyi at the 99% Level
6. Experiments
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Threats to Validity
3. MOO Critique
4. GALE
5. Models
6. Experiments
7. Validity
8. Conclusion
7
1. Introduction
2. Background
1 Slide
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In this chapter: - Validity
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Most threats were already addressed
Others too trivial for this presentation
Threats to Validity 7. Validity
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Conclusion
3. MOO Critique
4. GALE
5. Models
6. Experiments
7. Validity
8. Conclusion
8
1. Introduction
2. Background
3 Slides
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In this chapter: - Summary
- Ending
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Popular MOO Tools Need O(2NG) Evaluations
- Very slow for large models
GALE: Geometric Active Learning (Evolution)
- Add Data Mining to Search
- Evaluate only most informative Solutions
- At most O(2LogNG) Evaluations (usually less than that)
- Enables large studies with large models
- Finds good solutions for wide
variety of models
Summary 8. Conclusion
N = population size G = number of generations
Active Learning: - Only evaluate East & West!
Standard Models Real World Models
Constrained Lab
Unconstrained Lab Public
Privatized
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Developed principles for rigorous experiments
Employed those principles for our experiments
Principles 8. Conclusion
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GALE a clear winner
Results of Experiments
#1 #2 #3
8. Conclusion
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The End
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