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 dont care how we got to the current state
• ie No one cares how you arrived at the 8 queens
  solution
• Dont 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
• Lets 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 lt kmax and e gt emax // While
  time left not good enough
• sn neighbour(s) // Pick
  some neighbour.
• en E(sn) // Compute
  its energy.
• if en lt eb then // Is this
  a new best?
• sb sn eb en // Yes,
  save it.
• if P(e, en, temp(k/kmax)) gt random() then //
  Should we move to it?
• s sn e en // Yes,
  change state.

15
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

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