Artificial Intelligence: Key Search Algorithms and Their Applications

The Role of Search Algorithms in AI

Search algorithms are essential tools in AI, helping solve complex problems, especially in single-agent games like puzzles and pathfinding. These algorithms systematically explore possibilities, seeking the most efficient path to a goal.

Single-Agent Pathfinding Problems

Examples of single-agent pathfinding problems include:

• Tile Games (3x3, 4x4, 5x5 puzzles): The player arranges tiles in a grid by moving a blank space.
• Travelling Salesman Problem (TSP): Finding the shortest path through a series of cities.
• Rubik’s Cube, Theorem Proving: Solving complex, structured problems by exploring state configurations.

Core Terminology in Search

• Problem Space: The environment where the search happens, comprising states and operators.
• Problem Instance: Defined by an initial state and a goal state.
• Problem Space Graph: A visual of states (nodes) and possible moves (edges).
• Depth of Problem: The shortest path from the initial to the goal state.
• Space & Time Complexity: Space complexity is the maximum memory usage, while time complexity is the total number of nodes created.
• Admissibility: An algorithm’s ability to always find the best solution.
• Branching Factor: Average number of child nodes in the search space.
• Depth: The shortest path length to the goal.

Brute-Force Search Strategies

Brute-force search methods are straightforward, requiring no problem-specific knowledge. They work well in problems with limited states.

1. Breadth-First Search (BFS)

   • Starts at the root, exploring all neighboring nodes before moving deeper.
   • Advantages: Finds the shortest path in graphs with equal weights.
   • Disadvantages: High memory usage due to storing multiple node levels. Complexity increases exponentially with depth.

2. Depth-First Search (DFS)

   • Uses recursion and a stack (LIFO structure), exploring as deep as possible along each path before backtracking.
   • Advantages: Requires less memory (linear space complexity).
   • Disadvantages: Risk of infinite loops without a cut-off depth. Performance depends on choosing an appropriate cut-off depth.

3. Bidirectional Search

   • Searches simultaneously from the initial and goal states, meeting in the middle.
   • Advantage: Faster as each search covers half the total path length.

4. Uniform Cost Search

   • Expands the least-cost path to nodes, optimal for variable path costs.
   • Disadvantage: Explores all paths with cost ≤ optimal path cost, increasing processing time.

5. Iterative Deepening Depth-First Search (IDDFS)

   • Combines depth-first exploration with iterative deepening, exploring progressively deeper levels.
   • Advantage: Saves memory by storing only nodes on the path and offers completeness and optimality.

Comparison of Algorithm Complexities

Criterion	Breadth First	Depth First	Bidirectional	Uniform Cost	Iterative Deepening
Time Complexity	$b^d$	$b^m$	$b^{d/2}$	$b^d$	$b^d$
Space Complexity	$b^d$	$b^m$	$b^{d/2}$	$b^d$	$b^d$
Optimality	Yes	No	Yes	Yes	Yes
Completeness	Yes	No	Yes	Yes	Yes

Informed (Heuristic) Search Strategies

Heuristic strategies use problem-specific knowledge to enhance search efficiency, making them ideal for complex problems with vast states.

1. Heuristic Evaluation Functions

   • Assess the cost of the optimal path between two states. For instance, in sliding tile puzzles, this may involve counting moves from the current to the goal state.

2. Pure Heuristic Search

   • Expands nodes based on heuristic values, using open and closed lists to manage expanded and unexplored nodes.

3. A Search*

   • Expands nodes that minimize $f(n) = g(n) + h(n)$, where:
     • $g(n)$ is the cost to reach the node.
     • $h(n)$ estimates the remaining cost to reach the goal.
   • Implemented with a priority queue, it is optimal for certain types of problems.

4. Greedy Best-First Search

   • Expands the node estimated to be closest to the goal based on $h(n)$ alone. It’s fast but not guaranteed to be optimal.

5. Local Search Algorithms

   • Begin with a potential solution and iteratively move to neighboring solutions. They can stop anytime and still produce a solution.

Local Search Strategies

1. Hill-Climbing Search

   • Starts with an arbitrary solution, making incremental changes to improve the outcome. If no improvement is possible, it stops.
   • Disadvantage: Risk of getting stuck in local optima.

2. Local Beam Search

   • Maintains a set of $k$ states, selecting the best successors in each iteration.
   • Advantage: Avoids local optima by keeping multiple possible paths.

3. Simulated Annealing

   • Modeled after the annealing process in metallurgy, this technique begins with high "temperature" to allow exploration, then cools to reduce randomness.
   • Advantage: Can escape local optima.

4. Traveling Salesman Problem (TSP)

   • The goal is to find the shortest route that visits every city once and returns to the starting point.
   • Evaluates all possible solutions, comparing the total cost to identify the shortest route.

Conclusion

AI search algorithms vary in approach, balancing exploration depth, memory use, and problem complexity. Understanding these techniques offers insight into solving diverse challenges, from games and puzzles to logistical and operational planning in the real world.