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

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

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

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

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

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

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”

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…

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

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

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…

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

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

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.

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

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

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

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

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?

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?

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