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Second Order Heuristics in ACGP
 

Second Order Heuristics in ACGP

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    Second Order Heuristics in ACGP Second Order Heuristics in ACGP Presentation Transcript

    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • 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
    • ACGP Learning Results
      20
      Find the equation
      Comparison of GP-Base, ACGP with 1st order and 2nd order heuristics.
      Training slope-on
    • 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
    • ACGP Learning Results
      22
      Find the equation
      Comparison of GP-Base, Strong 1st Order and Strong 2nd Order Heuristics on 200 generation, no iterations
    • ACGP Learning Results
      23
      Find the equation
      Comparison of Base, 1st Order and 2nd Order Heuristics on a Time Scale
    • ACGP Learning Results
      24
      Find the equation
      Average tree structure for Base, 1st Order and 2nd Order Heuristics
    • 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
    • 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}
      {+, +, +}
      {+, *, +}
      {+, *, *}
      {+, +, *}
    • 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
    • ACGP Learning Results
      28
      First-order heuristics discovered. Root’s heuristics are zero-order for
      Bowl3 equation
    • ACGP Learning Results
      29
      Second-order heuristics summary for ‘*’ for Bowl3 equation
    • ACGP Learning Results
      30
      Second-order heuristics summary for ‘+’ for Bowl3 equation
    • 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
    • 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
    • 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
    • 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
    • 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