1. 1 Intro to AI Local Search

2. 2 Intro to AI Local search and optimization Local search: –use single current state & move to neighboring states Idea: –start with an initial guess at a solution, –incrementally improve it until it is one. Advantages: –use very little memory –often find reasonable solutions in large or infinite state spaces Also useful for pure optimization problems –find best state according to some objective function –e.g. survival of the fittest as a metaphor for optimization

3. 3 Intro to AI Hill climbing

4. 4 Intro to AI Hill climbing Terminates when a peak is reached. Does not look ahead of the immediate neighbors of the current state Chooses randomly among the set of best successors Doesn’t backtrack.

5. 5 Intro to AI Hill climbing Select the node with the best h and DO NOT backtrack. Local optima Plateau, Ridge Space & Time complexity? Optimality?

6. 6 Intro to AI Hill climbing - shape of a problem

7. 7 Intro to AI Simulated annealing search Idea: escape local maxima by allowing some "bad" moves but gradually decrease their frequency

8. 8 Intro to AI Properties of simulated annealing search One can prove: If T decreases slowly enough, then simulated annealing search will find a global optimum with probability approaching 1 Widely used in VLSI layout, airline scheduling, etc http://www.youtube.com/watch?v=VWtYLv-4oP0 http://www.youtube.com/watch?v=VWtYLv-4oP0

9. 9 Intro to AI Potential fields (by Oussama Khatib) –attractive potential: pulls toward the goal –repulsive potential: pushes away from the obstacles Greedy hill climbing search on an overall potential function, which is the sum of attractive & repulsive potentials. Hill Climbing in Motion Planning

10. 10 Intro to AI Hill Climbing in Motion Planning (a)configuration space (b)attractive potential (c)repulsive potential (d)overall potential (e)solution path the robot ends up following

11. 11 Intro to AI Potential field navigation with local minimum avoidance http://www.youtube.com/watch?v=Cr7PSr6SHTI Team of robots in flexible formation while avoiding obstacles; The leader robot is remotely controlled by human; The rest must keep close to all the mates, but avoid collision. http://www.youtube.com/watch?v=7PKCdu5u8LY&hl=ko Hill Climbing in Motion Planning

12. 12 Intro to AI Not interested in finding low-cost “path from start to the goal”. Instead, interested in “final state” we end up in. Usually, states are possible solutions to some problem (often associated with some cost function), and our goal is to find a state with the minimum possible cost (Example) 8-Queens problem Traveling Salesman Problem Automobile part assembly sequence (an engineer at GM found a way to save $20 per automobile.) Optimization Search

13. 13 Intro to AI TSP Classic NP-hard problem (no polynomial time algorithm exists) A salesperson starts at a given city, and has a list of cities to visit. His task is to visit all of these cities, and then return to the starting city. Furthermore, he is a dishonest salesperson, and therefore can’t return to the same city twice. The problem is to find the circuit of these cities that has minimum cost. Can be modeled as a path planning problem & solved using A* search. –State: partial tour –Operator: extend a tour by adding one city A*’s optimality vs. NP-hard of TSP

14. 14 Intro to AI TSP as Optimization Problem Model –State: complete tours (that visit all cities) –Operator: take two adjacent cities in the tour and flip their order in which they are visited. –Cost function: sum of the edge costs of the edges in the tour. Apply greedy hill climbing search to look for a local optimum.

15. 15 Intro to AI SAT problem Propositional satisfiability –Given a sentence in propositional logic, –Find a truth assignment that satisfies the given formula. (example) SAT solvers are general enough to be used to solve various problems –digital hardware verification. –planning in AI

16. 16 Intro to AI SAT problem CNF (Conjunctive Normal Form) –literal: propositional variable or its negation (example) –clause: disjunction (“or”) of literals (example) –CNF: conjunction (“and”) of clauses (example) Local search for SAT problem –State: complete truth assignments –Operator: flipping the truth value of a single variable –Cost: number of unsatisfied clauses GSAT: SAT solver with hill climbing search

17. 17 Intro to AI Genetic Algorithms individual: represents a possible solution population fitness function: evaluates how well a solution solves the problem. crossover mutation

18. 18 Intro to AI Genetic Algorithms http://www.youtube.com/watch?v=mec7fYHH5u0