Masters Defense, WVU Dept. CSEE. April 7, 2010.

1. The Robust Optimization of Non-
Linear Requirements Models
GREGORY GAY
THESIS DEFENSE
WEST VIRGINIA UNIVERSITY
GREG@GREGGAY.COM

2. 2
Consider a requirements model…
 Contains:
 Various goals of a project.
 Methods for reaching those goals.
 Risks that prevent those goals.
 Mitigations that remove risks.
 (but carry costs)
 A solution: balance between cost and attainment.
 This is a non-linear optimization problem!

3. 3
Understanding the Solution Space
 Open and pressing issue. [Harman ‘07]
 Many SE problems are over-constrained.
 No right answer, so give partial solutions.
 Robustness of solutions is key – many algorithms
give brittle results. [Harman ‘01]
 Important to present insight into the neighborhood.
 What happens if I do B instead of A?

4. 4
The Naïve Approach
 Naive approaches to understanding neighborhood:
 Run N times and report (a) the solutions appearing in more
than N/2 cases, or (b) results with a 95% confidence interval.
 Both are flawed – they require multiple trials!
 Neighborhood assessment must be fast [Feather ’08]
 Real-time if possible.
 [Nielson ‘93] states that results must be within:
 1Second before the mind begins to drift.
 10 seconds before the mind has completely moved on.

5. 5
Research Goals
 Two important concerns:
 Is demonstrating solution
robustness a time-consuming
task?
 Must solution quality be traded
against solution robustness?

6. 6
What We Want
 These are the features we want out of an algorithm:
Feature Algorithm
High-Quality Results* Yes
Low Result Variance Yes
Neighborhood (Tame)
Assessment
Scores Plateau to Stability Yes
(Well-behaved)
Speed Real-Time Results Yes
Scalability Yes
*(We want “more for less”)

7. 7
Why Do We Care?
 The later in the development process that a defect is
identified, the more exponentially expensive it
becomes to fix it
(Paraphrased from Barry Boehm [Boehm ‘81])

8. 8
Roadmap
 Model
 Algorithms
 Experiments
 Future Work
 Conclusions

9. 9
The Defect Detection and Prevention Model
 Used at NASA JPL by Martin Feather’s “Team X”
 [Cornford ’01, Feather ‘02, Feather ’08, Jalali ‘08]
 Early-lifecycle requirements model
 Light-weight ontology represents:
 Requirements: project objectives, weighted by importance.
 Risks: events that damage attainment of requirements.
 Mitigations: precautions that remove risk, carry a cost value.
 Mappings: Directed, weighted edges between requirements
and risks and between risks and mitigations.
 Part-of-relations: Provide structure between model
components.

10. 10
Light-weight != Trivial

11. 11
Why Use DDP?
 Three Reasons:
 1. Demonstrably useful. [Feather ‘02, Feather ‘08]
 Costsavings often over $100,000
 Numerous design improvements seen in DDP sessions
 Overall shift in risks in JPL projects.
 2. Availability of real-world models [Jalali ‘08]
 Now and in the future.

12. 12
The Third Reason
 DDP is representative of other requirements tools.
 Set of influences, expressed in a hierarchy, with relationships
modeled through equations.
QOC [MacLean ‘96]
Soft-Goals [Myloupolus ‘99]
 Sensitivity analysis [Cruz ‘73] not applicable to DDP.

13. 13
Using DDP
 Input = Set of enabled mitigations.
 Output = Two values: (Cost, Attainment)
 Those values are normalized and combined into a
single score [Jalali ‘08]:

14. 14
Roadmap
 Model
 Algorithms
 Experiments
 Future Work
 Conclusions

15. 15
Search-Based Software Engineering
No single solution, so reformulate as a search problem and find several!
 Four factors must be met: [Harman ’01, Harman ‘04]
 1. A large search space.
 2. Low computational complexity.
 3. Approximate continuity (in the score space).
 4. No known optimal solutions.
 DDP Problem fits all:
 1. Some models have up to (299 = 6.33*1029) possible settings.
 2. Calculating the score is fast, algorithms run in O(N2)
 3. Discrete variables, but continuous score space.
 4. Solutions depend on project settings, optimal not known.

16. 16
Theory of KEYS
 Theory: A minority of variables control the majority
of the search space. [Menzies ‘07]
 If so, then a search that (a) finds those keys and (b)
explores their ranges will rapidly plateau to stable,
optimal solutions.
 This is not new: narrows, master-variables, back
doors, and feature subset selection all work on the
same theory.
 [Amarel ’86, Crawford ’94, Kohavi ’97, Menzies ’03, Williams ’03]
 Everyone reports them, but few exploit them!

17. 17
KEYS Algorithm
 Two components: greedy search and a Bayesian
ranking method (BORE = “Best or Rest”).
 Each round, a greedy search:
 Generate 100 configurations of mitigations 1…M.
 Score them.
 Sort top 10% of scores into “Best” grouping, bottom 90% into
“Rest.”
 Rank individual mitigations using BORE.
 The top ranking mitigation is fixed for all subsequent rounds.
 Stop when every mitigation has a value, return final
cost and attainment values.

18. 18
BORE Ranking Heuristic
 We don’t have to actually search for the keys, just
keep frequency counts for “best” and “rest” scores.
 BORE [Clark ‘05] based on Bayes’ theorem. Use
those frequency counts to calculate:
 To avoid low-frequency evidence, add support term:

19. 19
KEYS vs KEYS2
 KEYS fixes a single top-
ranked mitigation each
round.
 KEYS2 [Gay ‘10]
incrementally sets more
(1 in round 1, 2 in round
2… M in round M)
 Slightly less tame, much
faster.

20. 20
Discovering KEYS2
 KEYS2 is simple, developing it was not!
 Many different heuristics tried:
 Simple: Complex:
 Set more in powers of 2 Shift best/rest slope
 ln(round) Neighborhood exploration
 top N% KEYS-R
 Lesson in simplicity.

21. 21
Benchmarked Algorithms
 KEYS much be benchmarked against standard SBSE
techniques.
 Simulated Annealing, MaxWalkSat, A* Search
 Chosen techniques are discrete, sequential,
unconstrained algorithms. [Gu ‘97]
 Constrained searches work towards a pre-determined number
of solutions, unconstrained adjust to their goal space.

22. 22
Simulated Annealing
 Classic, yet common, approach. [Kirkpatrick ’83]
 Choose a random starting position.
 Look at a “neighboring” configuration.
 If it is better, go to it.
 If not, move based on guidance from probability function
(biased by the current temperature).
 Over time, temperature lowers. Wild jumps stabilize
to small wiggles.

23. 23
MaxWalkSat
 Hybridized local/random search. [Kautz ‘96, Selman ‘93]
 Start with random configuration.
 Either perform
 Local Search: Move to a neighboring configuration with a
better score. (70%)
 Random Search: Change one random mitigation setting. (30%)
 Keeps working towards a score threshold. Allotted a
certain number of resets, which it will use if it fails to
pass the threshold within a certain number of
rounds.

24. 24
A* Search
 Best first path-finding heuristic. [Hart ‘68]
 Uses distance from origin (G) and estimated cost to
goal (H), and moves to the neighbor that minimizes
G+H.
 Moves to new location and adds the previous
location to a closed list to prevent backtracking.
 Optimal search because it always underestimates H.
 Stops after being stuck for 10 rounds.

25. 25
Other Methods
 [Gu ‘97]’s survey lists hundreds of methods!
 Gradient descent methods and sensitivity analysis
assume a continuous range for model variables.
 DDP models are discrete!
 Integer programming could still be used (CPLEX
[Mittelmann ‘07])
 Too slow! [Coarfa ‘00]
 SE problems are over-constrained, so a solution over all
constraints is not possible. [Harman ’07]
 Parallel algorithms
 Communications overhead overwhelms benefits.

26. 26
Roadmap
 Model
 Algorithms
 Experiments
 Future Work
 Conclusions

27. 27
Experiment 1: Costs and Attainments
 We use real-world models 2,4,5 (1,3 are too small
and were only used for debugging).
 Models discussed in [Feather ‘02, Jalali ‘08, Menzies ‘03]
 Run each algorithm 1000 times per model.
 Removed outlier problems by generating a lot of data points.
 Still a small enough number to collect results in a short time
span.
 Graph cost and attainment values.
 Values towards bottom-right better.

28. 28
Experiment 1 Results
Model
Cost
(Y-Axis)
Algorithm
Attainment
(X-Axis)

29. 29
Experiment 1 Results
Bad
Good

30. 30
Experiment 1 Results

31. 31
Summing it Up…
Feature Simulated MaxWalkSat A* KEYS KEYS2
Annealing
High-Quality Results No No Yes Yes Yes
Low Result Variance No No No Yes Yes
(Tame)
Scores Plateau to Stability ? ? ? ? ?
(Well-behaved)
Real-Time Results ? ? ? ? ?
Scalability ? ? ? ? ?

32. 32
Experiment 2: Runtimes
 For each model:
 Run each algorithm 100
times.
 Record runtime using
Unix “time” command.
 Divide runtime/100 to get
average.

33. 33
Experiment 2 Results
Model 2 Model 4 Model 5
(31 mitigations) (58 mitigations) (99 mitigations)
Simulated 0.577 1.258 0.854
Annealing
MaxWalkSat 0.122 0.429 0.398
A* Search 0.003 0.017 0.048
KEYS 0.011 0.053 0.115
KEYS2 0.006 0.018 0.038

34. 34
Summing it Up…
Feature Simulated MaxWalkSat A* KEYS KEYS2
Annealing
High-Quality Results No No Yes Yes Yes
Low Result Variance No No No Yes Yes
(Tame)
Scores Plateau to Stability ? ? ? ? ?
(Well-behaved)
Real-Time Results No No Yes Yes Yes
Scalability ? ? ? ? ?

35. 35
Experiment 3: Scale-Up Study
 By 2013, we expect DDP
models 8x larger than
those used in this thesis
(from 2008) Year Num. Variables
2004 30
 KEYS and KEYS2 are 2008 100
“real time” now, but will 2010 300
they scale? 2013 800

36. 36
Artificial Model Generation
 To test scalability, a generator builds synthesized
models by:
 Studying the existing real-world models and collecting
statistics on its internal structure.
 Mutating them into larger models based on user-input size,
density, and distribution altering parameters
 Models built that were 2,4, and 8 times larger than
existing models.

37. 37
Scale-Up Results (1)

38. 38
Scale-Up Results (2)

39. 39
Scale-Up Results (3)
KEYS KEYS2
Runtimes Model Calls Runtimes Model Calls
Exponential 0.82 0.83 0.88 0.93
Polynomial 0.99 0.99 0.99 0.98
(of degree 2)
 KEYS and KEYS2 fit to O(N2)
 Both scale to larger models, but KEYS requires
exponentially more model calls (thus, large jump in
execution time)
 Thus, we recommend KEYS2

40. 40
Summing it Up…
Feature Simulated MaxWalkSat A* KEYS KEYS2
Annealing
High-Quality Results No No Yes Yes Yes
Low Result Variance No No No Yes Yes
(Tame)
Scores Plateau to Stability ? ? ? ? ?
(Well-behaved)
Real-Time Results No No Yes Yes Yes
Scalability No No Maybe No Yes

41. 41
Decision Ordering Diagrams
 Design of KEYS2 automatically provides a way to
explore the decision neighborhood.
 Decision ordering diagrams – Visual format that
ranks decisions from most to least important . [Gay ‘10]

42. 42
Decision Ordering Diagrams (2)
 These diagrams can be used to assess solution
robustness in linear time by
 (A) Considering the variance in performance after applying X
decisions.
 Spread = measure of variance (75th-25th quartile)

43. 43
Decision Ordering Diagrams (3)
 These diagrams can be used to assess solution
robustness in linear time by
 (B) Comparing the results of using the first X decisions to that
of X-1 or X+1.

44. 44
Decision Ordering Diagrams (4)
 Useful under three conditions:
 (a) scores output are well-behaved
 (b) variance is tamed
 (c) they are generated in a timely manner.

45. 45
Summing it Up…
Feature Simulated MaxWalkSat A* KEYS KEYS2
Annealing
High-Quality Results No No Yes Yes Yes
Low Result Variance No No No Yes Yes
(Tame)
Scores Plateau to Stability No No No Yes Yes
(Well-behaved)
Real-Time Results No No Yes Yes Yes
Scalability No No Maybe Yes Yes

46. 46
Roadmap
 Model
 Algorithms
 Experiments
 Future Work
 Conclusions

47. 47
Future Work
 Weakness in KEYS2 – it
must call the model 100x
per round.
 70% of execution time is
spent calling the model.
 To improve –call the
model less.
 Problem: do this without
losing support!

48. 48
Future Directions
 Two main parts – cache and active learning.
 Don’t call the model, just look up scores.
 Clustering must be efficient [Jiang ’08, Poshyvanyk ‘08]
 First round – generate 100 random configurations.
 Greedily cluster them, assign identifiers to each, build a
hierarchical distance tree.
 After this, can simply drop new instances into the tree (as the
number of clusters will remain fixed).
 The model only needs to be called for new instances.

49. 49
Future Directions (2)
 Most learners passive – blindly generating or
reading data.
 Active learners exercise control over what data they
learn on [Cohn ‘94].
 Many clusters are linear – their members form a
smooth area of the search space with similar scores
[Shepperd ‘97].
 If a new configuration falls into a linear region, don’t
poll the model, just interpolate its score.
 Train KEYS2 to outright ignore linear regions with
poor scores.

50. 50
KEYS as a Component
Treatment Learning Bayesian Nets
(NASA Ames) (Tsinghua University)
 Work with Misty Davies, Karen  Work with Hongyu Zhang.
Gundy-Burlet.
 Bayes Net = directed graph of
 Design process: Run variables and their influences.
simulations, then apply  Variable ordering problem
Treatment Learning via [Hsu ‘04]
TAR3 or TAR4.1  Order of variables examined by
[Menzies ‘03b] learning process is crucial to
performance!
 KEYS is a multi-stage  Need a ranking from best -> worst
version of TAR4.1  Genetic algorithms sometimes used,
but they are slow.
 Future – KEYS as part of  KEYS offers a potential solution
the simulator. to the VOP.

51. 51
Roadmap
 Model
 Algorithms
 Experiments
 Future Work
 Conclusions

52. 52
Conclusions
 Optimization tools can study the space of
requirements, risks, and mitigations.
 Finding a balance between costs and attainment is
hard!
 Such solutions can be brittle, so we must comment on
solution robustness. [Harman ‘01]

53. 53
Conclusions (2)
 Pre-experimental concerns:
 An algorithm would need to trade solution quality for
robustness (variance vs score).
 Demonstrating solution robustness is time-consuming and
requires multiple procedure calls.
 KEYS2 defies both concerns.
 Generates higher quality solutions than standard methods, and
generates results that are tame and well-behaved (thus, we can
generate decision ordering graphs to assess robustness).
 Is faster than other techniques, and can generate decision
ordering graphs in O(N2)

54. 54
We Recommend KEYS2
Feature Simulated MaxWalkSat A* KEYS KEYS2
Annealing
High-Quality Results No No Yes Yes Yes
Low Result Variance No No No Yes Yes
(Tame)
Scores Plateau to Stability No No No Yes Yes
(Well-behaved)
Real-Time Results No No Yes Yes Yes
Scalability No No Maybe No Yes

55. 55
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