Search Space

A Search Space is a mathematical space that represents all possible solutions for a given search problem (supporting optimization tasks and decision making).

• Context:
  • It can represent Solution Set through parameters and constraints that define valid solutions.
  • It can enable Search Algorithm to systematically explore potential solutions for optimization.
  • It can support Local Search through neighborhood functions and solution proximity.
  • It can facilitate Global Search by mapping the complete solution landscape.
  • It can maintain Solution Quality through fitness functions and evaluation metrics.
  • It can implement Search Strategy based on problem characteristics and optimization goals.
  • It can handle Search Constraint through feasibility checks and boundary conditions.
  • It can range from being a Discrete Search Space to being a Continuous Search Space, depending on its solution type.
  • It can scale from being a Small Search Space to being a Large Search Space, depending on its problem complexity.
  • ...
• Examples:
  • Combinatorial Search Spaces, such as:
    • Traveling Salesman Spaces for route optimization.
    • Job Scheduling Spaces for resource allocation.
    • Graph Coloring Spaces for constraint satisfaction.
  • Continuous Optimization Spaces, such as:
    • Gradient Descent Spaces for function minimization.
    • Parameter Tuning Spaces for model optimization.
    • Control System Spaces for system response.
  • Machine Learning Spaces, such as:
    • Hyperparameter Spaces for model configuration.
    • Architecture Search Spaces for neural network design.
    • Feature Selection Spaces for model input.
  • Algorithmic Space, such as: ...
  • ...
• Counter-Examples:
  • Solution Space, which represents only valid solutions without search dynamics.
  • Problem Space, which defines problem characteristics rather than solution landscapes.
  • Decision Space, which focuses on choice selection rather than solution search.
• See: Search Algorithm, Optimization Space, Solution Landscape, Search Strategy, Problem Space.

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