Business 1 Template

Evolving Hyper-Heuristics using Genetic ProgrammingSupervisor: Moshe Sipper

Achiya Elyasaf

#1OverviewIntroductionSearching Games State-GraphsUninformed SearchHeuristicsInformed SearchEvolving HeuristicsPrevious WorkRush HourFreeCell##Representing Games as State-GraphsEvery puzzle/game can be represented as a state graph:In puzzles, board games etc., every piece move can be counted as a different stateIn computer war games etc. the place of the player / the enemy, all the parameters (health, shield) define a state

##Rush-Hour as a state-graph

##Searching Games State-GraphsUninformed SearchBFS Exponential in the search depthDFS Linear in the length of the current search path. BUT:We might never track down the right path.Usually games contain cyclesIterative Deepening: Combination of BFS & DFSEach iteration DFS with a depth limit is performed.Limit grows from one iteration to anotherWorst case - traverse the entire graph##Searching Games State-GraphsUninformed SearchMost of the game domains are PSPACE-Complete!Worst case - traverse the entire graphWe need an informed-search!##Searching Games State-GraphsHeuristicsh:states -> Real. For every state s, h(s) is an estimation of the minimal distance/cost from s to a solutionh is perfect: an informed search that tries states with highest h-score first will simply stroll to solutionFor hard problems, finding h is hardBad heuristic means the search might never track down the solution

We need a good heuristic function to guide informed search##Searching Games State-Graphs Informed SearchBest-First search: Like DFS but select nodes with higher heuristic value firstNot necessarily optimalMight enter cycles (local extremum)A*: Holds closed and sorted (by h-value) open lists. Best node of all open nodes is selectedMaintenance and size of open and closed is not admissible##Searching Games State-Graphs Informed Search (Cont.)IDA*: Iterative-Deepening with A*The expanded nodes are pushed to the DFS stack by descending heuristic valuesLet g(si) be the min depth of state si: Only nodes with f(s)=g(s)+h(s)