1. State Space Search

State Space Search

Introduction to Intelligent Systems

  • Subject: Intelligent Systems

  • Class: T. E (Sem V) CSE-Data Science

Problem Solving

  • The goal of an Intelligent System is to build an autonomous agent that exists in a specific world.

  • Goal: The agent strives to achieve a predetermined goal.

  • Actions: The agent has a set of actions to choose from to reach its goal.

Complexity of the Real World

  • The real world presents complexity due to:

    • Actions of other agents

    • Events that change the state of the world

    • The need to perceive the environment

    • Goals that need to be maintained

Simplifying Problem Solving

  • Approach to Simplification: Begin by dealing with simple problems. Considerations include:

    • The world is static.

    • The world is completely known or understood.

    • Only one agent is changing the world.

    • Actions executed do not fail.

    • Initial representation of the world is sufficient.

Problem Solving Framework

  • Humans are naturally problem-solving beings. The essential elements include:

    • First Principles of Knowledge

    • Ontology and Semantics

    • Experience-based approaches

    • Model-Based Reasoning

    • Memory-Based Reasoning

Case Studies in Problem Solving

Water Jug Problem

  • Scenario: You have three jugs of capacities 8 liters, 5 liters, and 3 liters. The 8-liter jug is full, while the others are empty.

  • Objective: Measure exactly 4 liters of water.

Solution Steps

  • Sample Moves: The solution involves various moves such as transferring water among jugs to eventually achieve the desired measurement of 4 liters.

The Eight-Puzzle Problem

  • Setup: The Eight Puzzle consists of eight tiles arranged in a 3x3 grid with one empty space.

  • Movement: Tiles can slide into an adjacent empty space. Moves are denoted as R (right), U (up), D (down), L (left).

The MGLC Problem (Man, Goat, Lion, Cabbage)

  • Problem: A man must transport a lion, goat, and cabbage across a river using a boat that can carry only one at a time.

  • Restrictions: The man cannot leave the goat alone with the lion or the cabbage alone with the goat during transport.

Possible States

  • States involve various configurations on the left bank (G L C B) or right bank, as the man transports the items.

The Six Queens Problem

  • Description: The objective is to position six queens on a 6x6 chessboard such that no two queens threaten each other.

The Traveling Salesman Problem

  • Importance: Recognized as one of the most significant problems in computer science due to its applications in optimization and logistics.

Search Algorithms and State Space

Domain Independent Algorithms

  • Emphasizing algorithms that work irrespective of specific problems (domain-independent).

Concept of State Space

  • State Space: Defined by the initial state, goal state, and the set of possible moves.

Search Nodes

  • Search Node: Functions like a junction in a maze, revealing options only as specific decisions are made.

Move Generation and Goal Test

  • The MoveGen function returns neighbors of a node.

  • GoalTest function checks if the current node is the goal node.

Strategy for Traversing State Space

  • New nodes are generated and tested through MoveGen and GoalTest functions.

Simple Search Algorithms

Simple Search 1

  • Involves checking nodes from an OPEN set until the goal node is found or all candidates are exhausted.

SimpleSearch2

  • Introduces a CLOSED set to avoid revisiting nodes.

Search Trees and Cycles

  • Search Space: Typically represented as trees. Every exploration involves maintaining track of previously seen nodes to avoid cycles and redundancies.

Depth First Search (DFS) and Breadth First Search (BFS)

  • DFS: Utilizes a stack; explores down one path until it cannot continue and then backtracks.

  • BFS: Utilizes a queue; explores all neighboring nodes at the present depth prior to moving on to nodes at the subsequent depth level.

Comparison of DFS and BFS

  • Time Complexity: Both have exponential time complexity. BFS tends to explore and find solutions quicker than DFS in general cases.

  • Space Complexity: DFS has linear space requirements, while BFS can grow exponentially.

Further Developments in Search Algorithms

Depth Bounded DFS (DBDFS)

  • Goal: Implements limits in depth to optimize search processes but sacrifices completeness.

Depth First Iterative Deepening (DFID)

  • Combines the advantages of DFS and BFS by performing repeated depth searches with incrementally increasing limits, ensuring guaranteed paths at minimal depth.

Practical Considerations in Search Algorithm Implementation

  • Careful tracking of visited nodes (CLOSED) is critical in implementing features like iterative deepening.

  • Defensive programming to avoid infinite loops when dealing with complex search scenarios.

Conclusion

  • Illustrating through multiple problem scenarios exemplifies the framework of problem solving in intelligent systems. By understanding the different search strategies and their applications, students can better grasp the intricacies of algorithmic problem solving.