PSO 2D: Fitness Heatmap & Convergence Chart

Neighborhood Topology

PSO Parameters

Swarm size 30

Inertia weight w 0.72

Cognitive c₁ (self) 1.49

Social c₂ (neighbors) 1.49

Live State

Iteration

Diversity (avg |x - x̄|)

0.00

Best fitness found f(x*)

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Best position x*

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How it works

This is the 2D companion to the 3D PSO terrain sim: the same particle swarm search, computed independently, but drawn without a fake third dimension. Each particle i keeps a position x_i, velocity v_i, and personal-best p_i, and every step also reads the best position among its neighbors — the neighborhood best g_i:

v_i ← w·v_i + c1·r1·(p_i − x_i) + c2·r2·(g_i − x_i)
x_i ← x_i + v_i          (r1, r2 ~ Uniform(0,1), resampled every step)

Global-best (star): g_i is the single best position anyone in the swarm has ever found — fast convergence, but the whole population can rush one promising dip and get stuck (premature convergence).
Local-best (ring): particles sit on a ring and each only sees its 2 immediate neighbors, so g_i is the best of just those 3. Good solutions spread gradually, which slows convergence but keeps diversity higher for longer.

The upper panel is the Rastrigin function painted directly onto a 2D grid as a colour field — dark for low fitness value (near optimum), bright orange for the ridges of local minima surrounding it — instead of a 3D terrain viewed through a camera:

f(x, y) = 20 + x² + y² − 10·cos(2πx) − 10·cos(2πy)     global min: f(0,0) = 0

The lower strip is a genuinely distinct representation: a convergence chart plotting the swarm's best-found fitness (log scale) and its diversity against iteration number — a parameter-space view that a 3D spatial camera can't show at all. Watch how global-best usually drives diversity toward zero quickly, while the ring topology keeps it higher for longer as sub-groups explore independently.

Particles (cyan = ring topology) Global incumbent best