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Planning Algorithms Algorithms

Planning algorithms solve sequential decision problems by finding optimal sequences of actions to achieve goals from initial states.

Planning Algorithms form a fundamental branch of artificial intelligence that focuses on solving

sequential decision problems. These algorithms find optimal or near-optimal sequences of actions that transform an initial state into a desired goal state, often in the presence of constraints and uncertainties.

Planning is essential for autonomous systems, robotics, game playing, and many other domains where agents must reason about future consequences of their actions. The field encompasses both classical planning (with complete information) and more complex variants that handle uncertainty, partial observability, and multi-agent scenarios.

Overview

Key Characteristics:

  • Sequential Decision Making

    Planning involves making a sequence of decisions over time to achieve goals

  • State Space Search

    Exploring possible states and transitions to find solution paths

  • Goal-Oriented Reasoning

    Working backwards or forwards from goals to find action sequences

  • Heuristic Guidance

    Using domain knowledge to guide search and improve efficiency

Common Applications:

  • path planning

  • manipulation planning

  • navigation

  • task planning

  • chess

  • go

  • puzzle solving

  • strategy games

  • scheduling

  • resource allocation

  • supply chain optimization

  • automated testing

  • code generation

  • workflow automation

  • experiment planning

  • data analysis workflows

  • simulation design

Key Concepts

  • State

    A complete description of the world at a particular point in time

  • Action

    An operation that transforms one state into another

  • Goal

    A desired state or set of conditions to be achieved

  • Plan

    A sequence of actions that transforms initial state to goal state

  • Heuristic Function

    A function that estimates the cost from a state to the goal

  • Search Space

    The set of all possible states reachable from the initial state

  • Admissibility

    Property of heuristics that never overestimate the true cost

  • Completeness

    Property that guarantees finding a solution if one exists

Complexity Analysis

Complexity Overview

Time: O(b^d) to O(b^(d/2)) Space: O(b^d) to O(b^(d/2))

Complexity depends on branching factor b, solution depth d, and heuristic quality. Good heuristics can dramatically reduce search space

Forward vs Backward Planning

Forward Planning (Progression):

  • Start from initial state, apply actions forward
  • Natural and intuitive approach
  • Can handle complex state transitions
  • May explore irrelevant states

Backward Planning (Regression):

  • Start from goal, work backwards
  • More focused search
  • Efficient for simple domains
  • Can be complex for rich state descriptions

Planning Search Methods

  1. Uninformed Search: BFS, DFS, uniform-cost search
  2. Informed Search: A*, best-first search with heuristics
  3. Local Search: Hill climbing, simulated annealing
  4. Constraint-Based: GraphPlan, SAT-based planning
  5. Hierarchical: Decompose problems into subproblems

Types of Planning Problems

Classical Planning: - Complete information about states and actions - Deterministic actions - Single agent - Examples: Blocks world, logistics

Temporal Planning: - Actions have duration - Concurrent actions possible - Time constraints and deadlines

Probabilistic Planning: - Actions have uncertain outcomes - Partial observability - Risk-aware decision making

Multi-Agent Planning: - Multiple agents with different goals - Coordination and cooperation - Game-theoretic considerations

Comparison Table

Algorithm Status Time Complexity Space Complexity Difficulty Applications
A* Search ❓ Unknown Varies Varies Medium Game AI, Robotics
Breadth-First Search ❓ Unknown Varies Varies Medium Shortest Path, Tree Traversal
Depth-First Search ❓ Unknown Varies Varies Medium Backtracking Problems, Graph Analysis
M* ❓ Unknown Varies Varies Medium Multi-Robot Systems, Game AI
Partial Order Planning ❓ Unknown Varies Varies Medium Project Management, Robotics
GraphPlan ❓ Unknown Varies Varies Medium Classical Planning, Automated Planning
Fast Forward ❓ Unknown Varies Varies Medium Classical Planning, Automated Planning

Algorithms in This Family

  • A* Search - Optimal pathfinding algorithm that uses heuristics to efficiently find the shortest path from start to goal in weighted graphs.

  • Breadth-First Search - Graph traversal algorithm that explores all nodes at the current depth level before moving to the next level, guaranteeing shortest path in unweighted graphs.

  • Depth-First Search - Graph traversal algorithm that explores as far as possible along each branch before backtracking, using stack-based or recursive implementation.

  • M* - Multi-agent pathfinding algorithm that finds collision-free paths for multiple agents by resolving conflicts and coordinating their movements.

  • Partial Order Planning - Planning algorithm that maintains partial ordering of actions, allowing flexible execution order and handling of uncertain environments.

  • GraphPlan - Classical planning algorithm that builds a planning graph to find parallel action sequences for achieving goals from initial states.

  • Fast Forward - Heuristic planning algorithm that uses relaxed planning graphs to efficiently find solutions to STRIPS planning problems.

Implementation Status

  • Complete

    0/7 algorithms (0%)

  • Planned

    0/7 algorithms (0%)

  • Search: Planning algorithms are built on search techniques and graph traversal

  • Optimization: Planning can be viewed as an optimization problem for finding optimal action sequences

  • Reinforcement-Learning: RL provides learning-based approaches to planning problems

  • Graph-Algorithms: Many planning problems can be represented as graph search problems

References

  1. Cormen, Thomas H. and Leiserson, Charles E. and Rivest, Ronald L. and Stein, Clifford (2009). Introduction to Algorithms. MIT Press

  2. Python Official Documentation. Python language reference

Tags

Planning Algorithms for automated planning and decision making

Optimization Algorithms that find optimal solutions to problems

Algorithms General algorithmic concepts and implementations