Lecture 2 - searches Flashcards
Search
The process of looking for a sequence of actions that reaches the goal
- Input: problem
- Output: solution in the form of an action sequence
[Basic | uninformed | blind] search
when strategies have no additional information about states beyond that provided in the problem definition.
Basic search:
Depth-first search (DFS)
One way is to iteratively pick one of the children at every node visited and work forward
Other alternatives are ignored as long as there is a chance of reaching the goal.
When a dead end is reached, the algorithm backtracks to the previous choice point.
Breadth-first search* (BFS)
check all paths of a given length before moving on to the next level.
-> Depth-first search when …
If You are confident that complete paths or dead ends are found after a reasonable amount of steps
Breadth-first search when …
- example
If You are working with very deep trees
BUT not when you think that all paths reach the goal at about the same depth, because:
Using breadth-first search on very deep search trees with similar depths to the goal is inefficient, because it requires storing and exploring a large number of nodes at the shallow levels before reaching the goal,
-> leading to excessive memory usage;
Example:
for instance; in a chess game where each level represents a move, exploring all possible moves exhaustively before deeper levels may be impractical due to the vast number of initial moves and board configurations.
Non-deterministic search when…
If you don’t know much about the problem set
If you have more information and the problem set is heuristically informed (2)
-> Hill climbing*
-> Beam search*
Non-deterministic search algorithm
- definition
- Example
It explores different possibilities without knowing the exact outcome, allowing for a more flexible exploration of the search space.
Example:
imagine a robot trying to navigate through a maze. In a non-deterministic search, at each intersection, the robot may randomly choose one of the available paths without knowing which one is the correct route. This randomness allows the algorithm to explore multiple paths simultaneously, potentially finding a solution more efficiently, especially in scenarios with uncertain or changing environments.
Hill climbing algorithm
- definition
- example
it chooses the neighbor with the highest improvement, “climbing” up the metaphorical hill, until it reaches a peak where no better solution can be found locally.
Example:
imagine a traveller trying to reach the highest point on a mountain.
Starting from any location, the traveller takes steps in the steepest uphill direction.
At each step, they move to the adjacent point with the highest elevation.
The process continues until they reach a peak where no higher point can be reached with a single step, representing a locally optimal solution.
-> it is the same as DFS, but with a preference
-> it is a greedy algorithm*
Beam search algorithm
- Definition
- Example
Modification of BFS, in the same manner as DFS is modified in Hill climbing
Beam search performs breadth-first search,
-> moving downward only through the best w nodes.
Example:
in natural language processing, beam search is commonly employed in machine translation; if translating a sentence, the algorithm considers only a fixed number of best possible translations at each step, leading to a more efficient and practical search process.
Optimal search algorithm
Finding a path from start to goal is not always the goal.
For example, I do not want to plan any route from work to a bar, I want to find the shortest path possible.
But we don’t want to evaluate all possible paths.
-> Branch-and-Bound*
Branch-and-bound algorithm
- defintion
- example
It works by expanding nodes ordered by traveled distance.
-> Once it has found a solution
-> Ignores paths with distances that are equal to or greater than the distance for that solution
Example:
Consider a traveling salesperson trying to find the shortest route to visit a set of cities. The algorithm would start with an initial route, then systematically explore different routes by considering all possible combinations of cities. As it explores, it keeps track of the best route found so far and uses this information to eliminate paths that cannot lead to a better solution. This process continues until the optimal route is discovered.
informing branch-and-bound about the estimated distance left
-> heuristic branch-and-bound
Heuristic branch-and-bound algorithm
- definition
- Example
After all, e(total path length) = d(already traveled) + e(distance remaining)
-> use accumulated distances + estimates to expand nodes.
Example:
in the traveling salesman problem, it might use a heuristic to prioritize visiting cities based on proximity, gradually refining the tour for a more efficient solution.
