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11 Human Competitive Results of Evolutionary Computation Presenter: Mati Bot Course: Advance Seminar in Algorithms (Prof. Yefim Dinitz)

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22 Human-Competitiveness Definition Evolving Hyper-Heuristics using Genetic Programming Rush-Hour (bronze Humies prize in 2009 by Ami Hauptman) Freecell(gold Humies prize in 2011 by Achiya Elyasaf) Other Examples Human Competitive Results of Evolutionary Computation Outline

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33 What is Human competitive? John Koza defined “Human-Competitiveness” in his book: Genetic Algorithms IV (2003). There are 8 criteria by which a result can be considered Human-Competitive.(will be explained in next slide) Our mission: Creation of Human-Competitive innovative solutions by means of Evolution.

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44 The 8 Criteria of Koza for Human Competitivenes. (A) result is a Patent from the past, improvement of a patent. A New patent.

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55 (B) result is equal to or better than another result that was published in a journal. The 8 Criteria of Koza for Human Competitivenes.

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66 (C) result is equal to or better than a result in a known DB of results. The 8 Criteria of Koza for Human Competitivenes.

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77 (D) publishable in its own right as a new scientific result. independent of the fact that the result was mechanically created. The 8 Criteria of Koza for Human Competitivenes.

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88 (E) The result is equal to or better than the best human-created solution. The 8 Criteria of Koza for Human Competitivenes.

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99 (F) equal to or better than an human achievement in its field at the time it was first discovered. The 8 Criteria of Koza for Human Competitivenes.

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10 (G) The result solves a problem of indisputable difficulty in its field. The 8 Criteria of Koza for Human Competitivenes.

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11 (H) The result holds its own or wins a regulated competition involving human contestants (in the form of either live human players or human-written computer programs). The 8 Criteria of Koza for Human Competitivenes.

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12 Humies Competition “Humies annual Competition” gives $$$ for the best HC results. (in GECCO conference) Awarding a gold, silver and bronze prizes to the best entries. (money $$$) BGU won 1 gold, 1 silver and 6 bronze prizes since 2005. I counted more than 75 Human-Competitive results on the Humies competition site. http://www.sigevo.org/gecco-2012/ http://www.sigevo.org/gecco-2012/ http://www.genetic-programming.org/hc2011/combined.html http://www.genetic-programming.org/hc2011/combined.html

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13 Evolving Hyper-Heuristics using Genetic Programming Ami Hauptman and Achiya Elyasaf

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14 Overview Introduction Searching Games State-Graphs Uninformed Search Heuristics Informed Search Evolving Heuristics Test Cases Rush Hour FreeCell

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15 Representing Games as State-Graphs Every puzzle/game can be represented as a state graph: In puzzles, board games etc., every piece move can be counted as an edge/transition between states In computer war games etc. – the place of the player / the enemy, all the parameters (health, shield…) define a state

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16 Rush-Hour as a state-graph Move blue Move purple

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17 Searching Games State-Graphs Uninformed/naïve Search BFS – Breadth First Search Optimal solution Exponential space in the search depth DFS – Depth First Search(without node coloring). We might “never” track down the right path. Usually games contain cycles Linear Space Iterative Deepening: Combination of BFS & DFS Iterative Deepening Each iteration DFS with a depth limit is performed. Limit grows from one iteration to another Worst case - traverse the entire graph

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18 Iterative Deepening

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19 Searching Games State-Graphs Uninformed Search Most of the game domains are PSPACE- Complete! Worst case - traverse the entire graph We need an informed-search! (or an intelligent approach to traversing the graph)

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20 Searching Games State-Graphs Heuristics Heuristic function h:states -> Real. For every state s, h(s) is an estimation of the minimal distance/cost from s to a solution In case h is perfect: an informed search that tries states with the lowest h-value first – will simply stroll to a solution For hard problems, finding a good h is hard Bad heuristic means the search might never track down the solution We need a good heuristic function to guide the informed search

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21 Searching Games State-Graphs Informed Search Best-First search: Like DFS but select nodes with higher heuristic value first Best-First search Not necessarily optimal

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22 Best-First Search 12 3 4

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23 Searching Games State-Graphs Informed Search A*: A* G(s)=cost from root till s H(s)=Heuristic estimation F(s)=G(s)+H(s) Holds closed and sorted open lists(the list of states needs to be checked out). Best (=lowest F(s)) node of all open nodes is selected.

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24 A* 4 12 3

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25 Searching Games State-Graphs Informed Search (Cont.) IDA*: Iterative-Deepening with A* IDA* The expanded nodes are pushed to the DFS stack by descending heuristic values Let g(s) be the cost to reach state s from root: Only nodes with f(s)=g(s)+h(s)

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26 Overview Introduction Searching Games State-Graphs Uninformed Search Heuristics Informed Search Evolving Heuristics Previous Work Rush Hour FreeCell

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27 For H 1, …,H n – heuristics building blocks. How should we choose the fittest heuristic? Minimum? Maximum? Linear combination? GA/GP may be used for: Building new heuristics from existing building blocks Finding weights for each heuristic (for applying linear combination) Finding conditions for applying each heuristic Evolving Heuristics

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28 Evolving Heuristics: GA W 1 =0.3W 2 =0.01W 3 =0.2…W n =0. 1

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29 Evolving Heuristics: GP If And ≤ ≤ H1 0.4 ≥ ≥ H2 0.7 + + H2 * * H1 0.1 * * H5 / / H1 0.1 Condition True False

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30 Evolving Heuristics: Policies ConditionResult Condition 1Hyper Heuristics 1 Condition 2Hyper Heuristics 2 Condition nHyper Heuristics n Default Hyper Heuristics

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31 Evolving Heuristics: Fitness Function

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32 Overview Introduction Searching Games State-Graphs Uninformed Search Heuristics Informed Search Evolving Heuristics Test cases Rush Hour FreeCell

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33 Rush Hour GP-Rush [Hauptman et al, 2009] Bronze Humies award

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34 Domain-Specific Heuristics Hand-Crafted Heuristics / Guides: Blocker estimation – lower bound (admissible) Blocker estimation Goal distance – Manhattan distance Goal distance Hybrid blockers distance – combine the above two Hybrid blockers distance Is Move To Secluded – did the car enter a secluded area? (last move blocks all other cars) Is Move To Secluded Is a Releasing Move – if the last move increased the number of free cars.

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35 Blockers Estimation Lower bound for number of steps to goal By: Counting moves to free blocking cars Example: O is blocking RED Need at least: Move O Move C Move B Move A H = 4

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36 Goal Distance 16 Deduce goal Use “Manhattan Distance” from goal as h measure

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37 Hybrid 16+8=24 “Manhattan Distance” + Blockers Estimation

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38 Policy “Ingredients” Functions & Terminals: ConditionsResults TerminalsIsMoveToSecluded, isReleasingMove, g, PhaseByDistance, PhaseByBlockers, NumberOfSiblings, DifficultyLevel, BlockersLowerBound, GoalDistance, Hybrid, 0, 0.1, …, 0.9, 1 BlockersLowerBound, GoalDistance, Hybrid, 0, 0.1, …, 0.9, 1 SetsIf, AND, OR, ≤, ≥+, *

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39 Results Average reduction of nodes required to solve test problems, with respect to the number of nodes scanned by iterative deepening: H1: the heuristic function BlockersLowerBound. H2: GoalDistance. H3: Hybrid. Hc is our hand-crafted policy. GP is the best evolved policy, selected according to performance on the training set. Heuristic: Problem IDH1H2H3HcGP 6x6100%72%94%102%70%40% 8x8100%69%75%70%50%10%

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40 Results (cont’d) Time (in seconds) required to solve problems JAM01... JAM40: ID – iterative deepening, Hi – average of our three hand-crafted heuristics, Hc – our hand-crafted policy. GP – our best evolved policy. human players (average of top 5).

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41 FreeCell FreeCell remained relatively obscure until Windows 95 There are 32,000 solvable problems (known as Microsoft 32K), except for game #11982, which has been proven to be unsolvable Evolving hyper heuristic-based solvers for Rush-Hour and FreeCell [Hauptman et al, SOCS 2010] GA-FreeCell: Evolving Solvers for the Game of FreeCell [Elyasaf et al, GECCO 2011]

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42 FreeCell (cont’d) As opposed to Rush Hour, blind search failed miserably The best published solver to date solves 96% of Microsoft 32K Reasons: High branching factor Hard to generate a good heuristic

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43 Learning Methods: Random Deals Which deals (( חלוקות קלפים should we use for training? First method tested - random deals This is what we did in Rush Hour Here it yielded poor results Very hard domain

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44 Learning Methods: Gradual Difficulty Second method tested - gradual difficulty Sort the problems by difficulty Each generation tests solvers against 5 deals from the current difficulty level + 1 random deal easyhard

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45 A few words on Co-evolution Population 1Population 2 Test for fitness Solution, Solvers. Examples: Freecell Solver Rush Hour Solver Chess player Problems, adversaries, Examples: Freecell Deals Rush Hour Boards Another Chess Player Examples?

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46 Learning Methods: Hillis-Style Co-evolution Third method tested - Hillis-style co-evolution using “Hall-of-Fame”: A deal population is composed of 40 deals (=40 individuals) + 10 deals that represent a hall-of- fame Each hyper-heuristic is tested against 4 deal individuals and 2 hall-of-fame deals

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47 Learning Methods: Rosin-style Co-evolution Fourth method tested - Rosin-style co-evolution: Each deal individual consists of 6 deals Mutation and crossover: Crossover: Mutation 118973042238457364 2837118923983412 179875984 3001113498 p1 p2 118973042238457364 2837118923983412 179875984 3001113498 p1 118973042238457364179875984 2015

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48 Results Learning Method Run Node Reduction Time Reduction Length Reduction Solved -HSD100% 96% Gradual Difficulty GA-123%31%1%71% GA-227%30%103%70% GP---- Policy28%36%6%36% Rosin-style coevolution GA 87%93%41%98% Policy 89%90%40%99%

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49 Other Human Competitive results Antenna Design for the International Space Station Automatically finding patches using genetic programming Evolvable Malware And many more on Humies site.

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50 Thank you for listening any questions?

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