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Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
Second Order Heuristics in ACGP
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Second Order Heuristics in ACGP

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  • 1. Second Order Heuristics in ACGP
    John Aleshunas
    University of Missouri – Saint Louis
    jja7w2@umsl.edu
    Cezary Janikow
    University of Missouri – Saint Louis
    janikow@umsl.edu
    Mark W Hauschild
    University of Missouri – Saint Louis
    mwh308@umsl.edu
  • 2. Outline
    The Genetic Programming (GP) Model
    Issues with the GP Model
    Constrained Genetic Programming (CGP)
    Adaptable Constrained GP (ACGP)
    Adaptable Constrained GP (ACGP) Heuristics
    ACGP Learning Results
    Conclusions
    2
  • 3. The Genetic Programming (GP) Model
    Evolve a solution program from a population of candidates
    Represents individual solutions as variable size trees
    Employs standard genetic operators
    Selection
    Crossover
    Mutation
    3
  • 4. Issues with the GP Model
    The Function set and Terminal set (labels) define the representation space of a GP implementation
    Often the Function set and Terminal set are over specified to ensure that they cover the solution space
    Closure
    Sufficiency
    This over specification increases the representation space and increases search time
    4
  • 5. Issues with the GP Model
    Search is not completely biased
    Mutation is always random
    Crossover is random given the current population (driven by the current population but random there)
    Selection is the only bias
    Selection drives the population and thus affects crossover
    How to improve the bias?
    Building “models” and using them to drive the search
    5
  • 6. Constrained Genetic Programming (CGP)An Option to Reduce Complexity
    Developed by Dr. Cezary Janikow in 1996
    It uses user-specified “model”
    1st order heuristics parent-child
    Global at the root
    Local anywhere
    Demonstrated to dramatically improve search time and complexity for problems such as SantaFe and 11-multiplexer
    But the user has to give the “right” heuristics – discovery of the right heuristics can be a long process
    6
  • 7. Adaptable Constrained GP (ACGP)Automating the CGP Methodology
    Developed by Dr. Cezary Janikow in 2003
    ACGP discovers 1st order heuristics
    Assumes that best trees are the “correct” heuristics
    Adjusts the heuristics at generational intervals
    Regrows the population using the new heuristics
    Mutation and crossover are now biased using the heuristics
    Uses gradual adjustments of the heuristics to control convergence
    7
  • 8. GP Building BlocksA Digression
    8
    The building block hypothesis states:
    Genetic processes work by combining relatively fit, short
    schema to form complete solutions.
    a
    b
  • 9. Adaptable Constrained GP (ACGP)1st Order Heuristics
    Controls one argument to a function
    Develops a set of heuristics
    Looks at parent node (function) and one child node (function or terminal)
    Treats those schema that are frequent in the fittest population members as desirable
    Gradual heuristic adjustment prevents premature convergence
    9
  • 10. Adaptable Constrained GP (ACGP)2nd Order Heuristics
    Controls all arguments to a function
    Develops a set of heuristics
    Looks at parent node (function) and all child nodes (function or terminal)
    Treats those schema that are frequent in the fittest population members as desirable
    Gradual heuristic adjustment prevents premature convergence
    10
  • 11. Adaptable Constrained GP (ACGP)2nd Order Heuristics
    Consider x*x
    1st order can only speak of * and one argument at a time
    Suppose that x* is 10% and that *x is 10%
    In the absence of heuristics about the entire subtree x*x, the probability of x*x will be joint as 1%
    But the true probability of x*x in the problem can be up to 10%
    Processing 1st order will always process it as 1%
    We need 2nd order (subtree) to process this as 10%
    We need
    Mechanism to discover 1st and 2nd order structures
    Validate performance gains of 2nd order vs. 1st order
    11
  • 12. Where is the Advantage in ACGP?
    Discovery of fit building blocks
    Promotes the use of fit building blocks in crossover, mutation and regrow
    Creates a population of highly fit compact solutions
    ACGP discovers heuristics that improve fitness primarily but also reduce tree sizes
    12
  • 13. How ACGP Develops Its Heuristics
    Tabulate the frequency of building blocks in the population
    Tabulate the frequency of building blocks in the fittest individuals in the population
    Increase the probability of fit heuristics
    Suppress the probability of less fit heuristics
    Access to heuristics is constant because of the tabulation
    Disregarding paging
    13
  • 14. Representation of Heuristics in ACGP1st Order Heuristics
    The general form of the 1st order combinations is
    Using 4 binary functions, 14 terminals, this creates 162 combinations
    14
  • 15. Representation of Heuristics in ACGP2nd Order Heuristics
    The general form of the 2nd order combinations is
    Using 4 binary functions, 14 terminals, this creates 2592 combinations
    15
  • 16. Representation of Heuristics in ACGPHigher Order Heuristics
    The general form of the 3rd order combinations is
    Using 4 binary functions, 14 terminals, this creates 13,728,800 combinations
    4th OH 3.76 * 1014 combinations
    5th OH 2.84 * 1029 combinations
    6th OH 1.62 * 1059 combinations
    16
  • 17. ACGP 2nd order
    Implementation was painfully validated
    But experiments with Santafe and 11-multiplexer using 1st order and 2nd order gave the same results
    Means that these problems do not have 2nd order structure not implied by joint probabilities
    For validation, needed a function with obvious difference between 1st and 2nd order probabilities
    17
  • 18. Experimental Setup
    Target Equation: x*x + y*y + z*z
    Has very explicit 2nd order structure different from that implied by 1st order
    Function set: {+, -, *, /} (protected divide)
    Terminal set: {x, y, z, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}
    Population size: 500
    Generations: 500
    Operators: crossover 85%, mutation 10%, selection 5%, regrow 100% at each iteration
    Number of independent runs: 30
    Fitness: sum of square errors on 100 random data points in the range -10 to 10
    Iteration length: 20 generations
    18
  • 19. ACGP Learning Results
    19
    Find the equation
    Comparison of GP-Base, ACGP with 1st order and 2nd order heuristics.
    Training slope-off with 50% update
  • 20. ACGP Learning Results
    20
    Find the equation
    Comparison of GP-Base, ACGP with 1st order and 2nd order heuristics.
    Training slope-on
  • 21. ACGP Learning Results
    21
    Find the equation
    Comparison of GP-Base, ACGP with 1st order and 2nd order heuristics.
    Training slope-on, first five iterations
  • 22. ACGP Learning Results
    22
    Find the equation
    Comparison of GP-Base, Strong 1st Order and Strong 2nd Order Heuristics on 200 generation, no iterations
  • 23. ACGP Learning Results
    23
    Find the equation
    Comparison of Base, 1st Order and 2nd Order Heuristics on a Time Scale
  • 24. ACGP Learning Results
    24
    Find the equation
    Average tree structure for Base, 1st Order and 2nd Order Heuristics
  • 25. ACGP Learning Limits
    25
    Find the equation
    Comparison of Base, 1st Order and 2nd Order Heuristics with Training Slope on for an extended Bowl3 equation
  • 26. ACGP Learning Results
    26
    Desirable 1st order heuristics
    Implied 2nd order heuristics
    Desirable 2nd order heuristics
    {*1 , x}
    {*2 , x}
    {*1 , z}
    {*2 , z}
    {*2 , y}
    {*1 , y}
    {+1 , *}
    {+1 , +}
    {+2 , +}
    {+2 , *}
    {*, x, x}
    {*, x, z}
    {*, y, x}
    {*, y, z}
    {*, x, y}
    {*, y, y}
    {*, z, x}
    {*, z, z}
    {*, z, y}
    {+, *, +}
    {+, *, *}
    {+, +, *}
    {*, x, x}
    {*, y, y}
    {*, z, z}
    {+, +, +}
    {+, *, +}
    {+, *, *}
    {+, +, *}
  • 27. ACGP Learning Results
    27
    1st order heuristics
    {*1 , x}
    {*2 , x}
    {*1 , z}
    {*2 , z}
    {*2 , y}
    {*1 , y}
    0.2289
    0.2426
    0.2403
    0.2323
    0.2489
    0.2087
    ACGP 1
    2nd order heuristics
    Implied
    ACGP 1
    0.0532
    0.0570
    0.0478
    0.0604
    0.0506
    0.0502
    0.2545
    0.0001
    0.0001
    0.2368
    0.0001
    0.2436
    {*, x, x}
    {*, x, z}
    {*, y, y}
    {*, z, z}
    {*, x, y}
    {*, y, z}
    Actual
    ACGP 2
  • 28. ACGP Learning Results
    28
    First-order heuristics discovered. Root’s heuristics are zero-order for
    Bowl3 equation
  • 29. ACGP Learning Results
    29
    Second-order heuristics summary for ‘*’ for Bowl3 equation
  • 30. ACGP Learning Results
    30
    Second-order heuristics summary for ‘+’ for Bowl3 equation
  • 31. Conclusions and Further Work
    31
    The 1st and 2nd order heuristics of ACGP provide a significant performance improvement over the base GP
    If very strong second-order heuristics are present, ACGP is able to process them and also to discover them
    Running 2nd order doesn’t hurt if there is no explicit 2nd order not implied by 1st
    Overhead is minimal
    If a problem does not have explicit second-order structure, ACGP running in first or second-order mode is the same
    Going higher than 2nd order has drawbacks.
    The next step will be to move on to standard test or real world problems
  • 32. Summary
    The Genetic Programming (GP) Model
    Issues with the GP Model
    Constrained Genetic Programming (CGP)
    Adaptable Constrained GP (ACGP)
    Adaptable Constrained GP (ACGP) Heuristics
    ACGP Learning Results
    Conclusions
    32
  • 33. References
    Banzhaf, W., Nordin, P., Keller, R., Francone, F., Genetic Programming – An Introduction, Morgan Kaufmann, 1998
    Janikow, Cezary Z. A Methodology for Processing Problem Constraints in Genetic Programming, Computers and Mathematics with Applications. 32(8):97-113, 1996.
    Janikow, Cezary Z., Deshpande, Rahul, Adaptation of Representation in GP. AMS 20032
    Janikow, Cezary Z. ACGP: Adaptable Constrained Genetic Programming. In O’Reilly, Una-May, Yu, Tina, and Riolo, Rick L., editors. Genetic Programming Theory and Practice (II). Springer,
    New York, NY, 2005, 191-206
    Janikow, Cezary Z., and Mann, Christopher J. CGP Visits the Santa Fe Trail – Effects of Heuristics on GP. GECCO’05, June 25-29, 2005
    Koza, John R. Genetic Programming. The MIT Press. 1992.
    Koza, John R. Genetic Programming II. The MIT Press. 1994.
    Looks, Moshe, Competent Program Evolution, Sever Institute of Washington University, December 2006
    33
  • 34. References
    Looks, Moshe, Competent Program Evolution, Sever Institute of Washington University, December 2006
    McKay, Robert I., Hoai, Nguyen X., Whigham, Peter A., Shan, Yin, O’Neill, Michael, Grammar-based Genetic Programming: a survey, Genetic Programming and Evolvable Machines, Springer Science + Business Media, September 2010
    Poli, Riccardo, Langdon, William, B., Schema Theory for Genetic Programming with One-point Crossover and Point Mutation, Evolutionary Computation, MIT Press, Fall 1998
    Sastry, Kumara, O’Reilly, Una-May, Goldberg, David, Hill, David, Building-Block Supply in Genetic Programming, IlliGAL Report No. 2003012, April 2003
    Shan, Yin, McKay, Robert, Essam, Daryl, Abbass, Hussein, A Survey of Probabilistic Model Building Genetic Programming, The Artificial Life and Adaptive Robotics Laboratory, School of Information Technology and Electrical Engineering, University of New South Wales, Australia, 2005
    Burke, Edmund, Gustafson, Steven, and Kendall, Graham. A survey and analysis of diversity measures in genetic programming. In Langdon, W., Cantu-Paz, E. Mathias, K., Roy, R., Davis, D., Poli, R., Balakrishnan, K., Honavar, V., Rudolph, G., Wegener, J., Bull, L., Potter, M., Schultz, A., Miller, J., Burke, E. and Jonoska, N., editors. GECCO2002: Proceedings of the Genetic and Evolutionary Computation Conference, 716-723, New York. Morgan Kaufmann.
    34
  • 35. References
    Daida, Jason, Hills, Adam, Ward, David, and Long, Stephen. Visualizing tree structures in genetic programming. In Cantu-Paz, E., Foster, J., Deb, K., Davis, D., Roy, R., O’Reilly, U., Beyer, H., Standish, R., Kendall, G., Wilson, S., Harman, M., Wegener, J., Dasgupta, D., Potter, M., Schultz, A., Dowsland, K., Jonoska, N., and Miller, J., editors, Genetic and Evolutionary Computation – GECCO-2003, volume 2724 of LNCS, 1652-1664, Chicago. Springer Verlag.
    Hall, John M. and Soule, Terence. Does Genetic Programming Inherently Adopt Structured Design Techniques? In O’Reilly, Una-May, Yu, Tina, and Riolo, Rick L., editors. Genetic Programming Theory and Practice (II). Springer, New York, NY, 2005, 159-174.
    Langon, William. Quadratic bloat in genetic programming. In Whitley, D., Goldberg, D., Cantu-Paz, E., Spector, L., Parmee, I., and Beyer, H-G., editors, Proceedings of the Genetic and Evolutionary Conference GECCO 2000, 451-458, Las Vegas. Morgan Kaufmann.
    McPhee, Nicholas F. and Hopper, Nicholas J. Analysis of genetic diversity through population history. In Banzhaf, W., Daida, J., Eiben, A. Garzon, M. Honavar, V., Jakiela, M. and Smith, R., editors Proceedings of the Genetic and Evolutionary Computation Conference, volume 2, pages 1112-1120, Orlando, Florida, USA. Morgan Kaufmann.
    Franz Rothlauf. Representations for Genetic and Evolutionary Algorithm. Springer, 2010.
    35

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