AI - Popular Search Algorithms

AI Search Algorithms, Brute-Force Search, Heuristic Search, Local Search, Pathfinding Problems, Artificial Intelligence

Understanding AI Search Algorithms for Problem Solving

In the field of Artificial Intelligence (AI), searching is a fundamental technique used for problem-solving. Whether it’s a game of Sudoku, a crossword puzzle, or other single-player games, search algorithms are crucial in finding solutions by identifying particular positions or paths within these games.

Single-Agent Pathfinding Problems

Single-agent pathfinding problems involve challenges where a single player needs to navigate through a space to reach a goal. Examples of these problems include:

• Tile Puzzles: Games like the 3x3 eight-tile puzzle, 4x4 fifteen-tile puzzle, and 5x5 twenty-four tile puzzle. The player must arrange tiles in a specific order by sliding them horizontally or vertically into a blank space.
• Other Examples: Challenges such as the Travelling Salesman Problem, solving a Rubik’s Cube, and Theorem Proving.

Key Search Terminology in AI

Understanding search algorithms requires familiarity with some key terms:

• Problem Space: This refers to the environment where the search takes place, consisting of a set of states and operators that can change those states.
• Problem Instance: This is the combination of the initial state and the goal state.
• Problem Space Graph: A graphical representation of the problem states, where nodes represent states, and edges represent operators.
• Depth of a Problem: This is the length of the shortest path or sequence of operators from the initial state to the goal state.
• Space Complexity: The maximum number of nodes stored in memory during the search.
• Time Complexity: The maximum number of nodes created during the search process.
• Admissibility: A property of an algorithm that guarantees finding an optimal solution.
• Branching Factor: The average number of child nodes generated from any given node in the problem space graph.
• Depth: The length of the shortest path from the initial state to the goal state.

Brute-Force Search Strategies in AI

Brute-force search strategies are simple and do not require any domain-specific knowledge. They are effective for problems with a small number of possible states.

Requirements for Brute-Force Search

• A description of the state.
• A set of valid operators.
• The initial state.
• A description of the goal state.

Breadth-First Search

Breadth-First Search (BFS) begins at the root node and explores neighboring nodes first before moving to the next level of neighbors. It continues generating trees until the solution is found and can be implemented using a First-In-First-Out (FIFO) queue data structure. BFS guarantees the shortest path to the solution.

If the branching factor (the average number of child nodes per node) is b, and the depth of the tree is d, the number of nodes at level d is b^d.

Disadvantage: BFS can consume a significant amount of memory since it saves each level of nodes to create the next one. The space requirement grows exponentially, and the complexity depends on the number of nodes. BFS can check for duplicate nodes.

Depth-First Search

Depth-First Search (DFS) is implemented using recursion with a Last-In-First-Out (LIFO) stack data structure. It creates the same set of nodes as BFS but in a different order. In each iteration, nodes on a single path from the root to the leaf are stored, so the space requirement is linear.

If the branching factor is b and the depth is m, the storage space required is b^m.

Disadvantage: DFS may not terminate and can continue infinitely on one path. To avoid this, a cut-off depth is chosen. If the cut-off is less than the ideal depth d, the algorithm may fail. If the cut-off is greater than d, execution time increases. DFS cannot check for duplicate nodes.

Bidirectional Search

Bidirectional Search works by simultaneously searching forward from the initial state and backward from the goal state until both searches meet at a common state. The path from the initial state is concatenated with the inverse path from the goal state. This search reduces the amount of work by searching only up to half of the total path length.

Uniform Cost Search

In Uniform Cost Search, nodes are sorted by the increasing cost of the path to reach them. The algorithm always expands the node with the least cost, making it identical to BFS when all transitions have the same cost. It explores paths in increasing order of cost.

Disadvantage: There can be multiple long paths with costs less than or equal to the optimal cost C*, and the algorithm must explore all of them.

Iterative Deepening Depth-First Search

Iterative Deepening Depth-First Search combines the benefits of BFS and DFS. It performs DFS to a certain depth, then starts over, increasing the depth level each time until the solution is found. The algorithm only saves a stack of nodes and continues until it finds a solution at the desired depth d.

The number of nodes created at depth d is b^d, and at depth d-1 is b^{d-1}.

Comparing the Complexities of Various Algorithms

Here’s a comparison of different search algorithms based on time complexity, space complexity, optimality, and completeness:

Informed (Heuristic) Search Strategies in AI

For larger problems with numerous possible states, adding problem-specific knowledge can significantly enhance the efficiency of search algorithms. These are known as heuristic search strategies.

Heuristic Evaluation Functions

Heuristic evaluation functions estimate the cost of the optimal path between two states. For instance, in sliding-tile games, the heuristic function might count the number of moves each tile needs to reach its goal state, then sum these