Second Order Heuristics in ACGP
- 1. Second Order Heuristics in ACGPJohn AleshunasUniversity of Missouri – Saint [email protected] JanikowUniversity of Missouri – Saint [email protected] W HauschildUniversity of Missouri – Saint [email protected]
- 2. OutlineThe Genetic Programming (GP) ModelIssues with the GP ModelConstrained Genetic Programming (CGP)Adaptable Constrained GP (ACGP)Adaptable Constrained GP (ACGP) HeuristicsACGP Learning ResultsConclusions 2
- 3. The Genetic Programming (GP) ModelEvolve a solution program from a population of candidatesRepresents individual solutions as variable size treesEmploys standard genetic operators SelectionCrossoverMutation 3
- 4. Issues with the GP ModelThe Function set and Terminal set (labels) define the representation space of a GP implementationOften the Function set and Terminal set are over specified to ensure that they cover the solution spaceClosureSufficiencyThis over specification increases the representation space and increases search time4
- 5. Issues with the GP ModelSearch is not completely biasedMutation is always randomCrossover 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 crossoverHow to improve the bias?Building “models” and using them to drive the search5
- 6. Constrained Genetic Programming (CGP)An Option to Reduce ComplexityDeveloped by Dr. Cezary Janikow in 1996It uses user-specified “model”1st order heuristics parent-childGlobal at the rootLocal anywhere Demonstrated to dramatically improve search time and complexity for problems such as SantaFe and 11-multiplexerBut the user has to give the “right” heuristics – discovery of the right heuristics can be a long process6
- 7. Adaptable Constrained GP (ACGP)Automating the CGP MethodologyDeveloped by Dr. Cezary Janikow in 2003ACGP discovers 1st order heuristicsAssumes that best trees are the “correct” heuristicsAdjusts the heuristics at generational intervals Regrows the population using the new heuristicsMutation and crossover are now biased using the heuristicsUses gradual adjustments of the heuristics to control convergence7
- 8. GP Building BlocksA Digression8The building block hypothesis states: Genetic processes work by combining relatively fit, short schema to form complete solutions.ab
- 9. Adaptable Constrained GP (ACGP)1st Order HeuristicsControls one argument to a functionDevelops a set of heuristicsLooks at parent node (function) and one child node (function or terminal)Treats those schema that are frequent in the fittest population members as desirableGradual heuristic adjustment prevents premature convergence9
- 10. Adaptable Constrained GP (ACGP)2nd Order HeuristicsControls all arguments to a functionDevelops a set of heuristicsLooks at parent node (function) and all child nodes (function or terminal)Treats those schema that are frequent in the fittest population members as desirableGradual heuristic adjustment prevents premature convergence10
- 11. Adaptable Constrained GP (ACGP)2nd Order HeuristicsConsider x*x1st order can only speak of * and one argument at a timeSuppose 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 needMechanism to discover 1st and 2nd order structuresValidate performance gains of 2nd order vs. 1st order11
- 12. Where is the Advantage in ACGP?Discovery of fit building blocksPromotes the use of fit building blocks in crossover, mutation and regrowCreates a population of highly fit compact solutionsACGP discovers heuristics that improve fitness primarily but also reduce tree sizes12
- 13. How ACGP Develops Its HeuristicsTabulate the frequency of building blocks in the population Tabulate the frequency of building blocks in the fittest individuals in the populationIncrease the probability of fit heuristicsSuppress the probability of less fit heuristicsAccess to heuristics is constant because of the tabulationDisregarding paging13
- 14. Representation of Heuristics in ACGP1st Order HeuristicsThe general form of the 1st order combinations isUsing 4 binary functions, 14 terminals, this creates 162 combinations14
- 15. Representation of Heuristics in ACGP2nd Order HeuristicsThe general form of the 2nd order combinations isUsing 4 binary functions, 14 terminals, this creates 2592 combinations15
- 16. Representation of Heuristics in ACGPHigher Order HeuristicsThe general form of the 3rd order combinations isUsing 4 binary functions, 14 terminals, this creates 13,728,800 combinations4th OH 3.76 * 1014 combinations 5th OH 2.84 * 1029 combinations 6th OH 1.62 * 1059 combinations 16
- 17. ACGP 2nd orderImplementation was painfully validated But experiments with Santafe and 11-multiplexer using 1st order and 2nd order gave the same resultsMeans that these problems do not have 2nd order structure not implied by joint probabilitiesFor validation, needed a function with obvious difference between 1st and 2nd order probabilities17
- 18. Experimental SetupTarget Equation: x*x + y*y + z*zHas very explicit 2nd order structure different from that implied by 1st orderFunction set: {+, -, *, /} (protected divide)Terminal set: {x, y, z, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}Population size: 500 Generations: 500Operators: crossover 85%, mutation 10%, selection 5%, regrow 100% at each iterationNumber of independent runs: 30 Fitness: sum of square errors on 100 random data points in the range -10 to 10Iteration length: 20 generations 18
- 19. ACGP Learning Results19Find the equationComparison of GP-Base, ACGP with 1st order and 2nd order heuristics. Training slope-off with 50% update
- 20. ACGP Learning Results20Find the equationComparison of GP-Base, ACGP with 1st order and 2nd order heuristics. Training slope-on
- 21. ACGP Learning Results21Find the equationComparison of GP-Base, ACGP with 1st order and 2nd order heuristics. Training slope-on, first five iterations
- 22. ACGP Learning Results22Find the equationComparison of GP-Base, Strong 1st Order and Strong 2nd Order Heuristics on 200 generation, no iterations
- 23. ACGP Learning Results23Find the equationComparison of Base, 1st Order and 2nd Order Heuristics on a Time Scale
- 24. ACGP Learning Results24Find the equationAverage tree structure for Base, 1st Order and 2nd Order Heuristics
- 25. ACGP Learning Limits25Find the equationComparison of Base, 1st Order and 2nd Order Heuristics with Training Slope on for an extended Bowl3 equation
- 26. ACGP Learning Results26Desirable 1st order heuristicsImplied 2nd order heuristicsDesirable 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 Results271st order heuristics{*1 , x}{*2 , x}{*1 , z}{*2 , z}{*2 , y}{*1 , y}0.22890.24260.24030.23230.24890.2087ACGP 12nd order heuristicsImpliedACGP 10.05320.05700.04780.06040.05060.05020.25450.00010.00010.23680.00010.2436{*, x, x}{*, x, z}{*, y, y}{*, z, z}{*, x, y}{*, y, z}ActualACGP 2
- 28. ACGP Learning Results28First-order heuristics discovered. Root’s heuristics are zero-order for Bowl3 equation
- 29. ACGP Learning Results29Second-order heuristics summary for ‘*’ for Bowl3 equation
- 30. ACGP Learning Results30Second-order heuristics summary for ‘+’ for Bowl3 equation
- 31. Conclusions and Further Work31The 1st and 2nd order heuristics of ACGP provide a significant performance improvement over the base GPIf very strong second-order heuristics are present, ACGP is able to process them and also to discover themRunning 2nd order doesn’t hurt if there is no explicit 2nd order not implied by 1stOverhead is minimalIf a problem does not have explicit second-order structure, ACGP running in first or second-order mode is the sameGoing higher than 2nd order has drawbacks.The next step will be to move on to standard test or real world problems
- 32. SummaryThe Genetic Programming (GP) ModelIssues with the GP ModelConstrained Genetic Programming (CGP)Adaptable Constrained GP (ACGP)Adaptable Constrained GP (ACGP) HeuristicsACGP Learning ResultsConclusions 32
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