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A Comparison of Evaluation Methods in Coevolution 20070921

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Presentation for GECCO 2007 conference

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A Comparison of Evaluation Methods in Coevolution 20070921

  1. 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. 2. Outline● Introduction● Evaluation methods in coevolution● Performance measures● Test problems● Results and discussion● Concluding remarks
  3. 3. Introduction● Evolutionary computation● Coevolution● Coevolution for test-based problems● Motivation of this study
  4. 4. Genetic AlgorithmInitialization 2. SELECTION Parents 1. EVALUATION 3. REPRODUCTION Population (crossover, mutation,...) 4. REPLACEMENT Offspring While (not TERMINATE) TERMINATE End
  5. 5. CoevolutionInitialization 1. EVALUATION ................ Subpopulation Subpopulation 2. SELECTION 2. SELECTION 3. REPRODUCTION 3. REPRODUCTION 4. REPLACEMENT 4. REPLACEMENT While (not TERMINATE) TERMINATE End
  6. 6. Test-Based Problemsf(x) original function regression curve s1 s2 s3 x t1 t2 t3 t4 t5 t6 t7 t8 t9 t10
  7. 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. 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. 9. Concepts for Coevolutionary Evaluation Methods● Interaction● Distinction and informativeness● Dominance and multi-objective approach
  10. 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. 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 1Test T3 0 1 1 0 0 2 S3 1 0 - 1 1cases 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. 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
  13. 13. Evaluation Methods● AS: Averaged Score● WS: Weighted Score● AI: Averaged Informativeness● WI: Weighted Informativeness● MO
  14. 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. 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. 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. 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. 18. Experimental Setup● Controlled experiments: GAAS – GA with AS from exhaustive evaluation.● Compare the OF based on the same number of interactions.
  19. 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 111A sample rule with r = 1 Output 0 0 0 1 0 1 1 1 boolean-vector representation of this rule
  20. 20. Test Problems● Majority Function Problem (MFP)
  21. 21. Test Problems● Symbolic Regression Problem (SRP) – Curve fitting with Genetic Programming trees – Two measures: sum of error and hit + f(x) original functionGP Tree regression curve hit * + - x x x x x 2x x
  22. 22. Test Problems● Parity Problem (PP) – Determine odd/even for the number of 1s 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. 23. Test Problems: PP 5-even ParityBoolean-vector 0 0 0 1 0 false (0) D0 D1 D2 D3 D4 0 AND falseGP 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
  24. 24. Results of MFP (r=2, n=9)
  25. 25. Results of MFP (r=2, n=9)
  26. 26. Results of SRP 6 4 x −2x x 2
  27. 27. Results of SRP 6 4 x −2x x 2
  28. 28. Results of PP (odd, n=10)
  29. 29. Results of PP (odd, n=10)
  30. 30. Summary of Results
  31. 31. Multi-objective Approach ● One run for COMO in MFP. ● OF drops when NDR rises. ● Why high NDR? – Duplicate solutions – Too many objectives
  32. 32. MO approach to improve WIMFP MO-WS-WI
  33. 33. MO approach to improve WISRP MO-AS-WI MO-WS-WI WeiSum-AS-WI MO-AS-AI MO-WS-AI
  34. 34. MO approach to improve WIPP MO-AS-WI
  35. 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. 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.
  37. 37. Question?
  38. 38. Thank you!
  39. 39. Average Score Solutions S1 S2 S3 S4 S5 T1 0 1 0 0 1 2 0.4 T2 0 0 1 1 0 2 0.4Test T3 0 1 1 0 0 2 0.4cases T4 1 0 0 0 0 2 0.4 T5 1 0 1 0 0 2 0.4 2 2 3 1 1 0.4 0.4 0.6 0.2 0.2 Max(O(m),O(n))
  40. 40. Weighted Score Solutions S1 S2 S3 S4 S5 T1 0 1 0 0 1 2 T2 0 0 1 1 0 2Test T3 0 1 1 0 0 2cases T4 1 0 0 0 0 2 T5 1 0 1 0 0 2 2 2 3 1 1 Max(O(m),O(n))
  41. 41. Average Informativeness Max(O(mn2),O(nm2))
  42. 42. Weighted Informativeness Max(O(mn2),O(nm2))
  43. 43. MO Max(O(mn2),O(nm2))

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