CSCI 4310

1. CSCI 4310 Lecture 10: Local Search Algorithms Adapted from Russell and Norvig & Coppin

2. Reading • Section 5.8 in Artificial Intelligence Illuminated by Ben Coppin • ISBN 0-7637-3230-3 • Chapter 4 in Artifical Intelligence, A Modern Approach by Russell and Norvig • ISBN 0-13-790395-2 • Chapters 4 and 25 in Winston

3. Techniques as Metaheuristics • wikipedia • Methods for solving problems by combining heuristics - hopefully efficiently. • Generally applied to problems for which there is no satisfactory problem-specific algorithm • Not a panacea

4. What is local search? • Local search algorithms operate using a single current state • Search involves moving to neighbors of the current state • We don’t care how we got to the current state • ie: No one cares how you arrived at the 8 queens solution • Don’t need intermediate steps • We do need a path for TSP • But not the discarded longer paths

5. Purpose • Local search strategies • Can often find ‘good’ solutions in large or infinite search spaces • Work well with optimization problems • An objective function • Like Genetic Algorithms • Nature has provided reproductive fitness as an objective function • No goal test or path cost as we saw with directed search

6. Local Search • State space landscape • State is current location on the curve • If height of state is cost, finding the global minimum is the goal

7. Local Search • Complete local search algorithm • Always finds a goal if one exists • Optimal local search algorithm • Always finds a global min / max Google image search for “Global Maxima”

8. Hill climbing • Greedy local search • If minimizing, this is ‘gradient descent’ • The algorithm will “never get worse” • Suffers from the same mountain climbing problems we have discussed • Sometimes worse must you get in order to find the better -Yoda • We can do better…

9. Stochastic Hill Climbing • Generate successors randomly until one is better than the current state • Good choice when each state has a very large number of successors • Still, this is an incomplete algorithm • We may get stuck in a local maxima

10. Random Restart Hill Climbing • Generate start states randomly • Then proceed with hill climbing • Will eventually generate a goal state as the initial state • we should have a complete algorithm by dumb luck (eventually) • Hard problems typically have an large number of local maxima • This may be a decent definition of “difficult” as related to search strategy

11. Simulated Annealing • Problems so far: • Never making downhill moves is guaranteed to be incomplete • A purely random walk (choosing a successor state randomly) is complete, but boring and inefficient • Let’s combine and see what happens…

12. Simulated Annealing • Uses the concept of ‘temperature’ which decreases as we proceed • Instead of picking the best next move, we choose randomly • If the move improves, we accept • If not, we accept with a probability that exponentially decreases with the ‘badness’ of the move • At high temperature, we are more likely to accept random ‘bad’ moves • As the system cools, ‘bad’ moves are less likely

13. Simulated Annealing • Temperature eventually goes to 0. • At Temperature = 0, this is the greedy algorithm

14. Simulated Annealing s := s0; e := E(s) // Initial state, energy. sb := s; eb := e // Initial "best" solution k := 0 // Energy evaluation count. while k < kmax and e > emax // While time left & not good enough: sn := neighbour(s) // Pick some neighbour. en := E(sn) // Compute its energy. if en < eb then // Is this a new best? sb := sn; eb := en // Yes, save it. if P(e, en, temp(k/kmax)) > random() then // Should we move to it? s := sn; e := en // Yes, change state. k := k + 1 // One more evaluation done return sb // Return the best solution found.

15. Simulated Annealing • Similar colors attract at short distances and repel at slightly larger distances. Each move swaps two pixels Pictures: wikipedia Fast cooling Slow cooling

16. Tabu Search • Keep a list of k states previously visited to avoid repeating paths • Combine this technique with other heuristics • Avoid local optima by rewarding exploration of new paths, even if they appear relatively poor • “a bad strategic choice can yield more information than a good random choice.” • The home of Tabu search

17. Ant Colony Optimization • Send artificial ‘ants’ along graph edges • Drop pheromone as you travel • Next generation of ants are attracted to pheromone • Applied to Traveling Salesman • Read this paper

18. Local Beam Search • Hill climbing and variants have one current state • Beam search keeps k states • For each of k states, generate all potential next states • If any next state is goal, terminate • Otherwise, select k best successors • Each search thread shares information • So, not just k parallel searches

19. Local Beam Search 2 • Quickly move resources to where the most progress is being made • But suffers a lack of diversity and can quickly devolve into parallel hill climbing • So, we can apply our same techniques • Randomize – choose k successors at random • At the point in any algorithm where we are getting stuck – just randomize to re-introduce diversity • What does this sound like in the genetic realm?

20. Stochastic Beam Search • Choose a pool of next states at random • Select k with probability increasing as a function of the value of the state • Successors (offspring) of a state (organism) populate the next generation according to a value (fitness) • Sound familiar?

21. Genetic Algorithms • Variant of stochastic beam search • Rather than modifying a single state… • Two parent states are combined to form a successor state • This state is embodied in the phenotype