Position vector
A position vector is a vector from an origin to a point, representing that point’s location through its components.
Grokking AI Algorithms, Second Edition
A position is the point or vector in a search space that represents a particle's candidate solution in particle swarm optimization.
- How it is used
- Represents each PSO particle’s candidate solution so its fitness can be evaluated as the particle moves through the search space.
- How deep it goes
- Defines position as coordinates in all dimensions and traces initialization and updates through a two-coordinate example, without a general vector derivation.
- Examples
- Uses two-coordinate Python particles, randomly generated starting positions, and a numerical move from (-1, 9) to (0.52, 10.52).
- What you can do after
- Build it from scratch as current and best coordinates in a Python Particle class, then update and evaluate the current position.
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Optimization Algorithms: AI techniques for design, planning, and control problems
A permutation encoding the candidate solution represented by a particle in permutation-based particle swarm optimization.
- How it is used
- Represents each particle’s candidate solution when PSO searches permutation problems such as route orderings.
- How deep it goes
- Explains permutation representation and redefines multiplication, subtraction, and addition through swap-based operations.
- Examples
- Uses an eight-city TSP permutation and figures showing velocity multiplication, subtraction, and addition.
- What you can do after
- Apply permutation-based PSO updates by representing routes as permutations and manipulating swap sequences.
Geometry for Programmers
A point vector is a vector conventionally interpreted as representing a point by its components from the origin.
- How it is used
- Connects coordinate descriptions of points with vector arithmetic for geometric transformations.
- How deep it goes
- Defines the origin convention, coordinate forms, basis decomposition, translation, and scaling, but does not develop vector products.
- Examples
- Uses (0.5, 1.5), its 3D extension, basis form 0.5i + 1.5j, and point-vector models undergoing translation or scaling.
- What you can do after
- Evaluate when a vector can conventionally represent a point and apply vector addition or scalar multiplication to point-vector models.
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Related concepts
- vectorkind of · A vector is an ordered collection of components representing an element of a vector space.
- particlepart of · A particle is an individual entity represented or managed as a unit within a physical or computational model.
- vectorkind of · A vector is an ordered, indexed sequence of elements, often numerical, represented as a mathematical quantity or a computational collection.
- rayused by · A ray is a geometric object with one endpoint that extends infinitely in a single direction.
- particle swarm optimizationpart of · Particle swarm optimization is a population-based optimization method in which candidate solutions adjust their positions using individual and collective search information.
- permutation problemequivalent to · A problem whose candidate solutions are ordered arrangements of a specified set of elements.
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