Local Search

Search through neighboring configurations until some objective function is improved

Iterative improvement to a single saved state

Hill Climbing

Start from random configuration

Move to neighboring configuration using a small change

If objective improves, keep change; else discard

Local Search

Pros and Cons?

• Constant space
• Can be used online
• Can get stuck in local optima
• Can get stuck in plateaus

What do we do about local optima or plateaus?

Random Restarts

Random Downhill Steps

Random Restarts

If stuck in local optima, restart from initial solution

Keep track of best solution

Repeat as necessary

Random Downhill Steps

Allow moving to a worse state with a small probability

Keep track of best solution

Repeat as necessary

Simulated Annealing

Inspired by metallurgical processes

Metal is heated, then cooled to resolve internal structural defects

Simulated Annealing

Allow moving to a worse state with a small probability

Probability of moving to a worse state decreases over time

Simulated Annealing

Initialize a temperature, $T$ and a decay multiplier $d$

Allow moving to a worse state with probability
$\mathrm{e}^{(e(n) - e(n'))/T}$

Probability decays exponentially with lower temperature

Local Beam Search

Maintain $k$ states at each iteration

Keep $k$ best successors from all states combined

Note that these are $k$ separate searches that talk to each other!

Genetic Algorithms

Inspired by biological evolution

Maintain a population of candidate solutions

Generate new solutions by mutating
or combining existing ones

Genetic Algorithms

Fitness: how good the solution is for a given objective

Mutation: changing a solution into a neighbor configuration at random

Crossover: two parent solutions combine to produce a new
solution that retains some elements from both