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
Chapter 4 in Artifical Intelligence, A Modern Approach by Russell and Norvig
ISBN
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 := // 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 // One more evaluation done
return sb // Return the best solution found.

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