Neighborhood topology

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

A neighborhood topology is a communication structure that determines which particles in a particle swarm can share information.

A neighborhood topology defines which particles in a particle swarm communicate and share successful positions. Its social structure influences convergence speed and the risk of getting trapped in local minima. section 9.2.4

Common PSO topologies make different exploration–convergence trade-offs:

• Star, or global best (gbest), connects every particle to the entire swarm. It usually converges quickly and suits unimodal problems, but can lose exploration and become trapped in local minima. section 9.2.4
• Ring, or local best (lbest), lets each particle communicate with adjacent neighbors. It converges more slowly but explores more of the search space and is recommended for multimodal problems. section 9.2.4
• The Von Neumann model arranges particles in a grid, connecting each particle with neighbors above, below, left, and right. section 9.2.4
• The wheel topology is identified as another common PSO neighborhood structure. section 9.2.4

Figure 9.5 PSO neighborhood topologies: a) the star social structure, b) the ring topology, c) the Von Neumann model, and d) the wheel topology

Compare the star, ring, Von Neumann, and wheel connection patterns visually before selecting a swarm communication structure. section 9.2.4

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

How deep it goes

Defines four structures and their trade-offs, but stops short of implementation details for configuring each topology.

Examples

Uses star, ring, grid-based Von Neumann, and wheel communication patterns as concrete topology examples.

What it assumes

Assumes familiarity with particle swarm optimization and particles sharing information about successful positions.

What you can do after

Evaluate and choose a PSO communication structure according to convergence needs and whether the problem is unimodal or multimodal.

How it connects

Connects particle swarm optimization with global best, local best, unimodal optimization, multimodal optimization, and local minima.

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Related concepts

• global-best PSOincludes · Global-best PSO is a particle swarm optimization variant in which every particle can access the best solution found by the entire swarm.
• local-best PSOincludes · Local-best PSO is a particle swarm optimization variant in which each particle follows the best solution found within its local neighborhood.

This explainer was generated by Manning's knowledge graph from the text of Optimization Algorithms: AI techniques for design, planning, and control problems. The section links point to the parts of the book it draws on.