Introduction to Artificial Intelligence 2 nd semester 2016/2017. Chapter 4: Beyond Classical Search

Transcription

1 Introduction to Artificial Intelligence 2 nd semester 2016/2017 Chapter 4: Beyond Classical Search Mohamed B. Abubaker Palestine Technical College Deir El-Balah 1

2 Outlines local search algorithms and optimization problems Hill climbing search Simulated annealing Local beam search Genetic algorithms 2

3 Introduction In Chapter 3, we covered problems that considered the whole search space and produced a sequence of actions leading to a goal. explore the search space systematically. keep one or more paths in memory. record which alternatives have been explored at each point along the path When a goal is found, the path to that goal also constitutes a solution to the problem In many problems, path is irrelevant; the goal state itself is the solution; for example: N-queen problem, VLSI layout, Factory floor layout, Flight scheduling, etc 3

4 Local search Informed search If the path to the goal does not matter, we might consider a local search algorithms. Local search algorithms: Operate using a single current node (rather than multiple paths) Move only to the neighbors of that node. The paths followed by the local search are not retained. Two key advantages: use little memory. find reasonable solutions in large or infinite state spaces for which systematic algorithms are unsuitable. Local search algorithms are useful for solving optimization problems the aim is to find the best state according to an objective function. 4

5 State-space Landscape Defined by: Location defined by the state. Elevation defined by the value of the heuristic cost function (or) objective function. A local search algorithm is called complete if it always finds a goal if one exists and is called optimal if the found goal is the global minimum/maximum sideways move 5

6 Hill climbing steepest-ascent or steepest-descent algorithm it is a loop that continuously moves in the direction of increasing value (uphill) It terminates when a peak is reached. The algorithm does not maintain a search tree, so the data structure for the current node need only record the state and the value of the objective function. Hill climbing does not look ahead of the immediate neighbors of the current state. Basic Hill-climbing Like climbing Everest in a thick fog with amnesia Hill climbing is sometimes called greedy local search because it grabs a good neighbor state without thinking ahead about where to go next. 6

7 Hill climbing (cont.) 7

8 Hill climbing (cont.) hill climbing often gets stuck for the following reasons: Local maxima: a local maximum is a peak that is higher than each of its neighboring states but lower than the global maximum. Ridges: result in a sequence of local maxima Plateau: a plateau is a flat area of the state-space landscape. It can be a flat local maximum, from which no uphill exit exists, or a shoulder, from which progress is possible. Ridges 8

9 Hill climbing : 8-queens problem 9

10 Hill-climbing variations Stochastic hill-climbing Random selection among the uphill moves. The selection probability can vary with the steepness of the uphill move. First-choice hill-climbing Generating successors randomly one-by-one until one is generated that is better than the current state. Random-restart hill-climbing If at first you don t succeed, try, try again. by generated initial state.

11 Simulated Annealing Simulated annealing (SA) works similar to hill climbing but also allows downhill moves. Mimics the annealing process in metallurgy, which starts at high temperature T and allows to reach a low energy state by gradual cooling. A random move is generated at each iteration. If it improves the objective function the move is always accepted. If the objective function is worsened the move is accepted with probability p p is exponentially reduced with the badness of the move and also decreases with the temperature T Simulated annealing starts with high T which is reduced over time; bad moves are more likely to be allowed at the start and become more unlikely. 11

12 Simulated Annealing (cont.) 12

13 Local beam search keeps track of k states rather than just one. It begins with k randomly generated states. At each step, all the successors of all k states are generated. If any one is a goal, the algorithm halts. Otherwise, it selects the k best successors from the complete list and repeats. In a random-restart search, each search process runs independently of the others. In a local beam search, useful information is passed among the parallel search threads. Can suffer from lack of diversity, since the k states quickly become concentrated at a small region turning local beam search into a form of hill-climbing Stochastic beam search alleviates this by randomly selecting the k successors with a probability corresponding to their objective function values 13

14 Genetic algorithms A successor state is generated by combining two parent states. Start with k randomly generated states (population) Each state, or individual (Chromosome), is represented as a string over a finite alphabet most commonly, a string of 0s and 1s. Evaluation function (fitness function). Higher values for better states. Produce the next generation of states by selection, crossover, and mutation. 14

15 Genetic algorithms (cont.) Representing 8-queens states. Fitness function: number of non-attacking pairs of queens (min = 0, max = 8 7/2 = 28) 15

16 Genetic algorithms (cont.) Crossover 16

17 Genetic algorithms (cont.) 17