Artificial Intelligence

Transcription

1 Artificial Intelligence Lesson 4 Local Search Local improvement, no paths Look around at states in the local neighborhood and choose the one with the best value Pros: Quick (usually linear) Sometimes enough Linear space complexity can often find reasonable solutions in large or infinite (continuous) state spaces for which systematic algorithms are unsuitable. Suitable for optimization problems Cons: Not optimal Can stuck on local maximum, plateau Local Search Cont. Hill Climbing In order to avoid local maximum and plateaus we permit moves to states with lower values in probability p. The different algorithms differ in p. Algorithm Hill Climbing,GSAT Random Walk Mixed Walk, Mixed GSAT Simulated Annealing p=0 p=1 p p=c (domain specific) p=acceptor(dh, T) Always choose the next best successor Stop when no improvement possible In order to avoid plateaus and local maximum: - Sideways move - Stochastic hill climbing - Random-restart algorithm

2 Simulated Annealing Permits moves to states with lower values Gradually decreases the frequency of such moves and their size. Schedule() Returns the current temperature Depends on start temperature and round number Acceptor() Returns the probability of choosing bad node. Depends on h(n)-h(n_son) and current temperature. Simulated Annealing Pseudo code Simulated Annealing(start node s, Temperature t, ) 1. Set starttemp=t //for schedule function 2. Set h= h(s) 3. Set round=0 4. while terminal condition not true 1. Set s_new = choose random son of s 2. Set h_new = h(s_new) 3. if (h_new < h) or (random() < acceptor(h_new-h,t)) 1. Set s=s_new 2. Set h=h_new 3. Set t=schedule(starttemp, round) 4. Set round=round Simulated Annealing Pseudo code Cont. Acceptor func. example: Schedule func. example: c round 0<c<1 h c t e 0 c 1 starttemp GSAT greedy local search procedure for satisfying logic formulas in a conjunctive normal form (CNF). An implementation of Hill Climbing for the CNF domain. Note: SAT is NP-Complete problem

3 GSAT Pseudo code GSAT(Integer tries, Integer flips ) 1. for i=1 to tries 1. Set T=a randomly generated truth assignment 2. for j= 1 to flips 1. if T satisfies C then return T 2. FLIP any variables in T that results in the greatest decrease in the number of unsatisfied clauses 3. Save the currently best T Genetic Algorithm Inspired by Darwin's theory of evolution: survival of the fittest. begins with a set of solutions chromosomes called population. Best solutions from generation n are taken and used to form a generation n+1 applying crossover and mutation operators Genetic Algorithm Pseudo code choose initial population evaluate each individual's fitness repeat until terminating condition select individuals to reproduce //better fitness better //chance to be selected mate pairs at random in crossover_prob. apply crossover operator in mutation_prob. apply mutation operator evaluate each individual's fitness Exercise Q: Is there a danger of Local maximum in GA? How does the algorithm tries to avoid it? A: The mutation operator, which inserts randomization to the algorithm. Q: If start temperature very close to 0 in SA how will the algorithm behave? What problem will it cause? How partially can we solve it? A: Greedy Search with no Closed list. It will stuck on the first local max. Restart the algorithm or use backtracking

4 Exercise Cont. Q: Solve the Traveling Salesman Problem using: Simulated annealing (SA) Genetic Algorithm (GA). A: For both algorithms a state is a vector which represents the order in which the salesman travels. State value/fitness is the distance the agent traveled. State expand/mutation is to swap order of two cities in path. Exercise Cont. GA: crossover: greedy crossover [greffenstette,1985]: GreedyCrossover(vector v1, vector v2) 1. Set vector res=v1[0] //v1 and v2 are chosen randomly 2. Repeat until res =number of cities 1. Select the closest city to res[i] from v1[i+1],v2[i+1] which is not already in res. 2. If not possible select randomly a city which is not in res Artificial Intelligence Search Algorithms Hierarchy Global Informed Uninformed A* IDA* Greedy DFS IDS BFS Uniform Cost Local 65 Lesson 5 66 GSAT Hill Climbing Random Walk Mixed Walk Mixed GSAT Simulated Annealing 4

5 Exercise Exercise Cont. What are the different data structures used to implement the open list in BFS,DFS,BeFS: BFS DFS Best-FS (Greedy,A*,Unifo rm-cost Alg). Queue Stack Priority Queue If there is no solution a* will explore the whole graph [yes] An admissible heuristic function h(n) will always return smaller values than the real distance to the goal [no. h(n)<=h*(n) ] h,h admissible A* will expand the same number of nodes with both func. [no]