A Comparison of Evaluation Methods in Coevolution 20070921
1. Final Presentation INF/SCR-06-54
Applied Computing Science, ICS
A Comparison of Evaluation
Methods in Coevolution
Ting-Shuo Yo
Supervisor: Edwin D. de Jong
Arno P.J.M. Siebes
2. Outline
● Introduction
● Evaluation methods in coevolution
● Performance measures
● Test problems
● Results and discussion
● Concluding remarks
3. Introduction
● Evolutionary computation
● Coevolution
● Coevolution for test-based problems
● Motivation of this study
4. Genetic Algorithm
Initialization
2. SELECTION Parents
1. EVALUATION
3. REPRODUCTION
Population (crossover, mutation,...)
4. REPLACEMENT
Offspring
While (not TERMINATE)
TERMINATE
End
6. Test-Based Problems
f(x)
original function
regression curve s1
s2
s3
x
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10
7. Coevolution for Test-Based Problems
Test 1. EVALUATION
population Interaction:
2. SELECTION ● Does the solution solve the
3. REPRODUCTION test?
4. REPLACEMENT ● How good does the solution
perform on the test?
Solution
population Solutions: the more tests it
solves the better.
2. SELECTION
3. REPRODUCTION Tests: the less solutions pass it
4. REPLACEMENT the better.
8. Motivation
● Coevolution provides a way to select tests
adaptively → stability and efficiency
● Solution concept → stability
● Efficiency depends on selection and
evaluation.
● Compared to evaluation based on all relevant
information, how do different coevolutionary
evaluation methods perform?
9. Concepts for Coevolutionary
Evaluation Methods
● Interaction
● Distinction and informativeness
● Dominance and multi-objective approach
10. Interaction
● A function that returns the outcome of interaction
between two individuals from different
subpopulations.
– Checkers players: which one wins
– Test / Solution: if the solution succeeds in solving the
test S 1 S 2 S 3 S 4 S 5 sum
T1 0 1 0 0 1 2
T2 0 0 1 1 0 2
● Interaction matrix T3 0 1 1 0 0 2
T4 1 0 0 0 0 1
T5 1 0 1 0 0 2
sum 2 2 3 1 1
11. Distinction
Solutions T3
S1 S2 S3 S4 S5 sum S1 S2 S3 S4 S5 sum
T1 0 1 0 0 1 2 S1 - 0 0 0 0
T2 0 0 1 1 0 2 S2 1 - 0 1 1
Test T3 0 1 1 0 0 2 S3 1 0 - 1 1
cases T4 1 0 0 0 0 1 S4 0 0 0 - 0
T5 1 0 1 0 0 2 S5 0 0 0 0 -
sum 2 2 3 1 1 sum 2 0 0 2 2 6
● Ability to keep diversity on the other subpopulation.
● Informativeness
12. Dominance and MO approach
f2
non-dominated
S1 is dominated by S2 iff:
dominated
f1
● Keep the best for each objective.
● MO: number of individuals that dominate it
14. AS and WS
● AS : (# positive interaction) / (# all interaction)
Solutions
S1 S2 S3 S4 S5 sum
T1 0 1 0 0 1 2 0.4
T2 0 0 1 1 0 2 0.4
Test T3 0 1 1 0 0 2 0.4
cases T4 1 0 0 0 0 1 0.2
T5 1 0 1 0 0 2 0.4
sum 2 2 3 1 1
0.4 0.4 0.6 0.2 0.2
● WS : each interaction is weighted differently.
15. AI and WI
● AI : # of distinctions it makes
● WI : each distinction is weighted differently.
S1>S2 S1>S3 S1>S4 S1>S5 .............
T1 1 1 0 1 .... 5
T2 0 0 0 1 .... 2
T3 1 1 0 0 .... 6
T4 0 1 0 1 .... 2
T5 0 0 0 0 .... 1
In the algorithm actually a weighted summation of AS and informativeness is used.
0.3 x informativeness + 0.7 x AS
16. MO
● Objectives : each individual in
the other subpopulation.
● MO: number of individuals that
dominate it. f2
non-dominated
● Non-dominated individuals dominated
have the highest fitness value.
f1
17. Performance Measures
● Objective Fitness (OF)
– Evaluation against a fix set of test cases
– Here we use "all possible test cases" since we have
picked problems with small sizes.
● Objective Fitness Correlation (OFC)
– Correlation between OFs and fitness values in the
coevolution (subjective fitness, SF).
18. Experimental Setup
● Controlled experiments: GAAS
– GA with AS from exhaustive evaluation.
● Compare the OF based on the same number of
interactions.
19. Test Problems
● Majority Function Problem (MFP)
– 1D cellular automata problem
– Two parameters: radius (r) and problem size (n)
A sample IC with n = 9 0 1 0 1 0 0 1 1 1
neighbor bits
target bit
Input 000 001 010 011 100 101 110 111
A sample rule with r = 1
Output 0 0 0 1 0 1 1 1
boolean-vector representation of this rule
21. Test Problems
● Symbolic Regression Problem (SRP)
– Curve fitting with Genetic Programming trees
– Two measures: sum of error and hit
+ f(x)
original function
GP Tree
regression curve
hit
* +
- x x x
x x
2x
x
22. Test Problems
● Parity Problem (PP)
– Determine odd/even for the number of 1's in a bit
string
– Two parameter: odd/even and bit string length (n)
A problem with n = 10
0 1 0 1 0 0 1 1 11
A solution tree
23. Test Problems: PP
5-even Parity
Boolean-vector 0 0 0 1 0 false (0)
D0 D1 D2 D3 D4
0
AND false
GP Tree
1 0
OR AND
1 1 0
NOT AND D2 NOT OR AND
0
D0 D3 D0 D1 D1 D2
0 1 0 0 0 0
35. Conclusions
● MO2 approach with weighted informativeness
(MO-AS-WI and MO-WS-WI) outperforms other
evaluation methods in coevolution.
● MO1 approach does not work well because
there are usually too many objectives. This can
be represented by a high NDR and results in a
random search.
● Coevolution is efficient for the MFP and SRP.
36. Issues
● Test problems used are small, and there is not
proof of generalizability to larger problems.
● Implication to statistical learning: select not only
difficult but also informative data for training.