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Particle Swarm Optimisation

A swarm of tour-particles updates each epoch. Each particle's velocity is a list of city-swap moves built from three components: ω keeps momentum from the previous epoch, C₁ pulls toward the particle's own personal best, and C₂ pulls toward the global best. Inertia ω decays over time, shifting the swarm from exploration toward exploitation.

01234567891011
Particles
02370
dist 2370
12074
dist 2074
22179
dist 2179
32000
dist 2000
41592
gbest
52104
dist 2104
gbest tour best particle swarm city
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ω (inertia) = 0.900
High — broad exploration
epoch
0
gbest dist
1592.4
avg dist
2053
v_max
5 swaps
Balanced swarm size
cities: 12particles: 6ω: 0.4→0.9C₁=C₂=1.5v_max: 5