Problem Solving:
Problem-solving in AI refers to the capability of Artificial Intelligence systems to find solutions to complex problems using various computational techniques. It involves breaking down a problem into smaller parts, analyzing possible solutions, and selecting the best one based on certain criteria.
Problem solving in Artificial Intelligence is the ability of AI systems to analyze data, identify patterns, and develop solutions to complex problems. AI-driven problem solving can tackle complex problems and offer solutions beyond what traditional methods can achieve.
Formulating Problems in AI:
In artificial intelligence, problem formulation is the process of defining a problem in a way that an AI system can understand and solve it efficiently. Formulating a problem in AI is the process of defining a real-world problem as a computational problem that an AI system can solve.
Formulating problems in AI is a critical step in developing effective solutions. It involves translating real-world challenges into a structured format that can be understood and processed by AI systems.
Effective problem formulation in AI is essential for developing successful solutions. Before an AI system can solve a problem, it must first be formulated in a way that an algorithm can process. This involves defining the problem, identifying constraints, and determining how the AI should search for a solution.
Elements of Problem Formulation in AI (Components of Problem Formulation in AI):
A problem in AI is typically defined by the following elements:
Initial State: The starting point of the problem-solving process.
Example: In a maze-solving problem, the initial state is the agent’s starting position.
Goal State: The desired outcome or objective the AI must achieve.
Example: Reaching the exit of a maze.
State Space: The set of all possible states the problem can have.
Example: All possible positions in a chess game.
Actions (Operators): The set of possible actions, an AI can take to move from one state to another.
Example: In a robot navigation problem, actions could be “move left,” “move right,” “move forward,” etc.
Transition Model: A description of how actions change the current state into a new state.
Example: If the AI moves right in a maze, the new position updates accordingly.
Path Cost: The cost associated with moving between states (e.g., distance, time).
Example: In GPS navigation, path cost could be the distance or time required to reach the destination.
Constraints: Conditions that must be satisfied for a solution to be valid.
Example: In scheduling problems, constraints may include “no two tasks can be scheduled at the same time.”
Types Of Problems in AI:
In Artificial Intelligence (A), problems can be categorized as ignorable, recoverable, or irrecoverable. AI systems are designed to solve problems by mimicking human intelligence.
Ignorable Problems: These are problems where certain solution steps can be skipped or ignored without affecting the overall outcome.
Recoverable Problems: Problems where mistakes can be corrected or undone, allowing flexibility in the problem-solving process.
Irrecoverable Problems: Problems where actions are permanent (irreversible) and require careful planning.
States and Operators:
In Artificial Intelligence, “states” represent different configurations or situations within a problem, while “operators” are the actions that can be taken to transition between these states.
In short, we can say, a state describes the current situations, and an operator is a function that allows us to move from one state to another.
State Space:
A state space is a set of all possible states that it can reach from the current state. In Artificial Intelligence, a state space is a model of all possible configurations of a problem.
Search Strategies:
Search strategies or Search Algorithms in Artificial Intelligence, are algorithms that help to solve search problems. They are used to find solutions in a search space.
Search in AI:
Search is a fundamental concept in AI that involves exploring possible solutions to find the best or optimal one. Search in AI refers to the process of navigating through a problem space to find a solution. The AI agent explores possible states and actions using a search strategy.
Example: Finding the shortest route on Google Maps involves searching through multiple paths to find the best one.
Search Algorithms (Search Strategies):
In Artificial Intelligence (AI), search algorithms are used to find solutions or paths in a problem space. These algorithms are generally categorized as informed or uninformed based on whether they use additional information about the problem domain.
Types of Search Algorithm or Search Strategies :
Based on the search problems, we can classify the search algorithm as
- Uninformed Search
- Informed Search
Uninformed Search:
Uninformed Search, also known as Blind Search refers to a search strategy that does not have any additional information about the goal’s location—except the information available in the problem definition itself. It explores the search space blindly without any guidance on which direction to proceed efficiently. Uninformed search doesn’t know anything beyond the structure of the problem. It lacks any additional information, exploring the search space systematically without guidance.
Uninformed search algorithm explores the search space without prior knowledge about the goal location. They rely solely on the structure of the search space. The uninformed search algorithm does not have any domain specific knowledge, such as closeness, location of the goal state, etc. These algorithms do not use problem-specific knowledge and explore the state space blindly. Uninformed search methods are foundational in AI and serve as a basis for more advanced search techniques that incorporate heuristics and domain knowledge.
Working: They generate and explore nodes systematically until a solution is found.
Characteristics of Uninformed Search:
- No heuristic guidance: These algorithms do not use any estimates of how far a given state is from the goal. We have no heuristic or domain knowledge to guide the search.
- Only uses problem structure: Such as initial state, operators, and goal test.
- Completeness: Many uninformed search algorithms are complete, meaning they will find a solution if one exists.
- Optimality: Some algorithms, like Uniform Cost Search, are optimal, while others, like DFS, are not.
Advantages:
- Simple to implement
- Does not require additional domain knowledge.
Disadvantages:
- Inefficient in large search space
- May explore unnecessary paths.
Applications:
- Solving puzzles like the 8-puzzle problem using BFS.
- Finding paths in small or well-structured Graphs.
- Network routing when no heuristic is available.
Types of Uninformed Search Algorithm:
Breadth-First Search (BFS)
It is one of the most common search strategies. It explores all nodes at the current depth before going deeper. A breadth-first search generally starts from the root node, examines the neighbour nodes, and then moves to the next level. Breadth-first search explores all the nodes at the present depth level before moving on to nodes at the next depth level. It uses the First-in, First-out (FIFO) strategy as it gives the shortest path to achieving the solution. The BFS algorithm starts with the start state, moves to the next level, and visits each node until it reaches the goal state. It explores all nodes level by level and guarantees finding the shortest path in terms of number of steps (if all steps have equal cost). It uses a queue to keep track of the nodes to be explored.
Example: Used in shortest path problems where all moves have equal cost.
Advantages:
- BFS will never be trapped in any unwanted nodes.
- If the graph has more than one solution, then BFS will return the optimal solution with the shortest path.
Disadvantages:
- BFS stores all the nodes in the current level and then moves them to the next level. This requires a lot of memory.
- BFS takes more time to reach the goal state, which is far away.
Depth-First Search (DFS)
Depth-First Searchexplores as far down a branch as possible before backtracking. It uses Last-in, First-out (LIFO) strategy and hence it can be implemented by using stack. DFS uses backtracking. It starts from the initial state and explores each path to its greatest depth before it moves to the next path. It explores as deep as possible along one path before backtracking. It is memory efficient, but may get stuck in infinite paths or miss optimal solutions. DFS is not guaranteed to find the optimal solution and can get stuck in deep branches. It uses a stack (or recursion) to keep track of the nodes.
Example: Solving mazes by going deep into one path before trying alternatives.
Advantages:
- It takes lesser memory as compared to BFS.
- The time complexity is lesser when compared to BFS.
- DFS does not require much more search.
Disadvantages:
- DFS does not always guarantee to give a solution.
- As DFS goes deep down, it may get trapped in an infinite loop.
Depth Limited Search (DLS):
Depth-Limited Search (DLS) is a depth-first search strategy with a predetermined depth limit. It is a variant of the Depth-First Search (DFS) used in Artificial Intelligence (AI), particularly in problem-solving and search algorithms. It’s designed to overcome some of the limitations of standard DFS, such as infinite paths in graphs or trees. In problems where the search tree is very deep or infinite, like in some game trees or planning problems DLS is used. It is particularly useful in scenarios where the search space is large, and there is a need to limit the depth of the search to avoid excessive resource consumption.
Depth-Limited search explores paths only up to a specified depth, preventing the search from going infinitely deep. It is a variation of DFS that imposes a limit on the depth of the search. It prevents the algorithm from going too deep into the search space, which can be useful in infinite or very large spaces.
Features of Depth Limited Search:
Depth Limitation: DLS imposes a limit on the depth of the search. This means that the algorithm will only explore nodes up to a specified depth (L). If the goal node is deeper than (L), it will not be found.
Prevention of Infinite Loops: By limiting the depth, DLS helps prevent infinite loops that can occur in cyclic graphs, where the algorithm might otherwise keep revisiting the same nodes.
Memory Efficiency: DLS is more memory-efficient than breadth-first search (BFS) because it does not need to store all nodes at the current level. It only needs to keep track of the nodes along the current path.
Completeness: DLS is not complete; it may fail to find a solution if the solution is deeper than the specified depth limit (L).
Advantages
- Avoids the infinite recursion problem in DFS.
- Uses less memory than Breadth-First Search (BFS).
- More efficient when the solution is within a known depth.
Disadvantages
- Not complete if the solution is beyond the depth limit.
- Not optimal (might find a non-shortest solution).
- Choosing the right depth limit can be tricky.
Iterative Deepening Depth-First Search (IDDFS):
Iterative Deepening Depth-First Search (IDDFS) is a search algorithm that combines the benefits of Depth-First Search (DFS) and Breadth-First Search (BFS). It repeatedly applies Depth-Limited Searches with increasing depth limits. This algorithm is particularly useful in scenarios where the search space is large and the depth of the solution is unknown.
IDDFS performs a series of DLS with increasing depth limits. It starts with depth = 0 and increases the depth limit by 1 in each iteration until the goal is found. It’s particularly useful in scenarios where the depth of the solution is unknown and memory is limited.
Features of IDDFS:
Combination of DFS and BFS: IDDFS performs a series of depth-limited searches (DLS) with increasing depth limits. This allows it to explore the search space in a manner similar to BFS while using the memory efficiency of DFS.
Completeness: IDDFS is complete, meaning it will find a solution if one exists, regardless of the depth of the solution.
Optimality: In unweighted graphs, IDDFS is optimal, as it will find the shortest path to the goal node.
Advantages:
- IDDFS is complete, meaning it will always find a solution if one exists, regardless of the depth of the solution.
- Unlike Depth-Limited Search (DLS), which requires a predetermined depth limit, IDDFS dynamically increases the depth limit until a solution is found.
- IDDFS allows for incremental exploration of the search space.
- IDDFS is particularly effective in large search spaces where the depth of the solution is not known.
Disadvantages
- Not ideal if branching factor is extremely high or the state space has high cost of node generation.
- Not Suitable for High-Cost or Non-Uniform Cost Problems. IDDFS is not optimal if step costs vary.
- No Memory of Explored Paths. Like DFS, IDDFS doesn’t remember previously explored nodes.
- Not Efficient for Very Deep Solutions. If the solution is very deep, IDDFS may spend a lot of time redoing shallow-level searches before reaching useful depth.
Uniform Cost Search (UCS)
Uniform cost search is considered the best search algorithm for a weighted graph or graph with costs. It expands the node with the lowest path cost and guarantees finding the optimal solution. Uniform cost search can be implemented using a priority queue. It chooses the least-cost path first, based on the path cost function. It is equivalent to BFS if all costs are equal. It is optimal and complete, making it suitable for weighted graphs.
Example: Finding the shortest path in Google Maps.
Advantages:
- This algorithm is optimal as the selection of paths is based on the lowest cost.
Disadvantages:
- The algorithm does not consider how many steps it takes to reach the lowest path. This may result in an infinite loop also.
Bidirectional Search:
Bidirectional search is a search algorithm in artificial intelligence that simultaneously explores the search space from both the initial state and the goal state. The idea is to meet in the middle, which can significantly reduce the search time and space compared to unidirectional search methods.
It is an efficient uninformed search strategy in Artificial Intelligence that simultaneously searches forward from the initial state and backward from the goal state, with the goal of meeting in the middle.
Characteristics of Bidirectional Search:
- Completeness: Bidirectional search is complete, meaning it will find a solution if one exists, provided that the search spaces from both directions are finite and the search is conducted correctly.
- Optimality: If both search directions use the same cost function and the search space is uniform, the algorithm can be optimal. However, if the costs differ or if the search spaces are not symmetric, optimality may not be guaranteed.
Advantages:
- Much faster than BFS/DFS in large search spaces.
- Reduces time and space complexity significantly (if applicable).
Disadvantages:
- Hard to implement if:
- The goal state is not explicitly known.
- Actions are not easily reversible.
- Requires extra memory for managing two frontiers and checking for intersections.
Applications:
Bidirectional search is particularly useful in scenarios where the search space is large and the goal state is well-defined. It is commonly applied in:
- Pathfinding algorithms (e.g., in navigation systems).
- Puzzle-solving (e.g., the 8-puzzle problem).
- Game AI (e.g., chess or checkers).
Informed Search:
Informed search is a type of search strategy used in artificial intelligence (AI) that utilizes additional information to guide the search process more efficiently. Informed search algorithms use heuristics, which are problem-specific knowledge or rules of thumb or educated guesses, to estimate the cost or distance to the goal from a given state. This allows the algorithm to prioritize certain paths over others, potentially leading to faster solutions. Informed Search is also called Heuristic Search. These algorithms use heuristic functions to guide the search toward the goal, making them more efficient.
Informed search algorithm uses domain-specific knowledge to make better decisions about which path to explore, improving efficiency. In contrast to uninformed search algorithms, informed search algorithms require details such as distance to reach the goal, steps to reach the goal, and cost of the paths, which makes this algorithm more efficient.
Working: They evaluate nodes based on heuristic functions to optimize the search process.
Advantages
- More efficient than uninformed search
- Can find the optimal path faster
- Faster than uninformed search for large problems.
- More likely to find the optimal or near-optimal solution.
Disadvantages
- Requires a well-designed heuristic function. Poor heuristics can misguide the search. Designing a good heuristic can be challenging.
- Some heuristics may be expensive to compute. Computational cost depends on the heuristic quality.
Applications:
Informed search algorithms play a crucial role in various applications across multiple domains, providing efficient solutions to complex problems.
Pathfinding and Navigation
- Robot navigation: In robotics, informed search algorithms like A* are used for pathfinding, allowing robots to navigate through environments while avoiding obstacles and finding the shortest route to a target.
- Video Games: Game AI often employs informed search algorithms to control non-player characters (NPCs) for navigation and movement within game worlds, ensuring efficient and realistic behavior.
Robotics
- Motion planning for robotic arms or mobile robots. Heuristic-based planning helps a robot arm decide the most efficient path to grasp an object without collision.
- Autonomous vehicles (self-driving cars)
Route Planning
- GPS Navigation Systems: Informed search algorithms are used in GPS systems to calculate the shortest or fastest route from a starting point to a destination, taking into account real-time traffic data and road conditions.
- Logistics and Supply Chain: Companies use informed search algorithms to optimize delivery routes for vehicles, minimizing travel time and costs while ensuring timely deliveries.
Puzzle Solving
- Game Solvers: Informed search algorithms are applied to solve puzzles like the 8-puzzle or Rubik’s Cube, where the goal is to reach a specific configuration from a given starting state.
- Sudoku Solvers: Algorithms like A* can be used to solve Sudoku puzzles by exploring possible placements of numbers based on constraints.
Natural Language Processing
- Parsing and Understanding: Informed search algorithms can be used in natural language processing tasks, such as parsing sentences or understanding context, by exploring possible interpretations based on linguistic rules and heuristics.
Types of Informed Search Strategies:
Informed search algorithms can be categorized into several types based on their strategies and characteristics. Here are some of the most common types of informed search algorithms:
A* Search Algorithm:
A* Search is one of the most powerful and widely used informed search algorithms. It combines the benefits of Uniform Cost Search and Greedy Best-First Search by considering both the cost to reach a node and the estimated cost to the goal. It combines the advantages of both with better memory usage. It uses a heuristic function to find the shortest path. A* search algorithm guarantees the optimal solution if h(n) is admissible (never overestimates).
Example: AI in video games calculating the shortest route for a character.
Key Features of A* Search
Evaluation Function: A* uses an evaluation function f(n) that combines the cost to reach the current node n and the estimated cost from n to the goal. The function is defined as:
f(n)=g(n)+h(n)
where:
- g(n) is the cost from the start node to node n.
- h(n) is the heuristic estimate of the cost from node n to the goal.
Heuristic Function: The heuristic h(n) should be admissible, meaning it never overestimates the true cost to reach the goal. This property ensures that A* is both complete and optimal.
Open and Closed Lists: A* maintains two lists:
- Open List: Contains nodes that need to be evaluated.
- Closed List: Contains nodes that have already been evaluated.
Advantages:
- Optimality: A* is guaranteed to find the optimal solution if the heuristic is admissible.
- Completeness: A* will find a solution if one exists, provided the search space is finite.
- Flexibility: The performance of A* can be adjusted by modifying the heuristic function, allowing it to be tailored to specific problems.
Disadvantages:
- Memory Usage: A* can consume a significant amount of memory, as it stores all generated nodes in the open and closed lists, which can be problematic for large search spaces.
- Heuristic Design: The effectiveness of A* heavily relies on the quality of the heuristic. A poorly designed heuristic can lead to inefficient searches.
Greedy Best-First Search
Greedy Best-First Search (GBFS) is an informed search algorithm that uses a heuristic to guide its search process. The primary goal of GBFS is to expand the most promising node based on the heuristic estimate of the cost to reach the goal. This approach can lead to faster solutions in some cases, but it does not guarantee optimality.
Greedy best-first search uses the properties of both depth-first search and breadth-first search. It traverses the node by selecting the path that appears best at the moment. Greedy Best-First Search uses a heuristic function, h(n) to expand the node that appears closest to the goal. It uses a priority queue based on h(n).
Example: Navigating a maze by always moving toward the goal.
Key Features of Greedy Best-First Search
Heuristic Function: GBFS uses a heuristic function h(n) that estimates the cost from the current node n to the goal. The algorithm selects the node with the lowest heuristic value for expansion.
Evaluation Function: The evaluation function in GBFS is simply the heuristic: f(n)=h(n)
Unlike A* search, GBFS does not consider the cost to reach the current node g(n).
Node Expansion: The algorithm expands the node with the lowest h(n) value, which is assumed to be the most promising path toward the goal.
Advantages
- Efficiency: GBFS can be faster than uninformed search methods because it uses heuristics to prioritize nodes that are likely to lead to the goal.
- Simplicity: The algorithm is straightforward to implement and understand.
Disadvantages
- Non-optimality: GBFS does not guarantee that the solution found is optimal. It may choose paths that seem promising based on the heuristic but lead to suboptimal solutions.
- Completeness: The algorithm may get stuck in loops or fail to find a solution in certain cases, especially in infinite state spaces or poorly designed heuristics.
- Greediness: The focus on immediate gains can lead to poor overall performance, as it may overlook longer paths that could lead to a better solution.
Recursive Best-First Search (RBFS):
RBFS is a recursive version of Best-First Search that uses limited memory. It keeps track of the best node to expand and can backtrack when necessary. RBFS is complete and optimal if the heuristic is admissible.
Iterative Deepening A* (IDA*):
IDA* combines the space efficiency of depth-first search with the optimality of A*. It performs a series of depth-limited searches, gradually increasing the cost threshold based on the evaluation function f(n). IDA* is complete and optimal if the heuristic is admissible.
Beam Search:
Beam Search is a variation of Best-First Search that limits the number of nodes expanded at each level to a fixed number (the “beam width”). It retains only the best nodes based on the heuristic. Beam Search is not guaranteed to find the optimal solution, as it may discard potentially better paths due to its limited beam width.
Comparison of Uninformed and Informed Search Algorithms
Uninformed search is also known as blind search, whereas informed search is also called Heuristics Search. Uniformed search does not require much information, whereas informed search requires domain-specific details. Compared to uninformed search, informed search strategies are more efficient, and the time complexity of uninformed search strategies is greater. Informed search handles the problem better than blind search.
Differences Between Informed and Uninformed Search:
Informed search algorithms utilize additional knowledge or heuristics to efficiently guide the search process towards a goal, while uninformed search algorithms operate without such information, exploring the search space blindly. This often makes informed searches more optimized and faster compared to their uninformed counterparts.
Key Differences:
| Feature | Informed Search | Uninformed serach |
| Known As | It is also known as Heuristic Search | It is also known as Blind Search |
| Knowledge Used | Uses domain-specific knowledge (heuristics) to guide the search | It doesn’t use any domain specific knowledge during the process of searching. |
| Efficiency | More efficient, explores fewer nodes | Generally, less efficient, explores more nodes |
| Optimality | A* guarantees optimality if the heuristic is admissible; greedy search is not guaranteed to be optimal. | Sometimes guarantees optimality (e.g, BFS, UCS) |
| Completeness | Depends on the heuristic; may not find a solution if an inappropriate heuristic is used. | Depends on the algorithm (BFS and UCS are complete) |
| Problem Complexity | Well-suited for complex problems with large state spaces. | Better for simpler problems or when no domain knowledge is available. |
| Common Uses or Applications | GPS navigation, AI in games, robotics, pathfinding in large maps. | Maze solving, puzzle-solving, route finding in simple maps. |
| Examples | A few examples include A* Search, Graph Search and Greedy Best-First Search. | A few examples include Breadth-First Search, Depth-First Search, Iterative Deepening, Bidirectional Search. |