| c1, c2 | personal cognition coefficient, social cognition coefficient |
| c1max, c2max | maximum values of acceleration coefficients |
| c1min, c2min | minimum values of acceleration coefficients |
| D | optimal route length |
| i | i-th particle |
| K | evaluation parameter |
| M | maximum number of iterations |
| m | current number of iterations |
| mcri | critical number of iterations |
| N | number of particles |
| P | number of successfully converged particles in a single iteration |
| Pis | individual best known position |
| Pgs | swarm best known position |
| Q | number of planned points |
| r1, r2 | random numbers |
| R | swarm size |
| s | s-th dimension |
| vis | velocity value for s-th dimension and i-th particle |
| Vi | velocity vector |
| w | inertia weight |
| wmax, wmin | maximum and minimum value of inertia weight |
| Xi | position vector |
| xis | position value for s-th dimension and i-th particle |
| Abbreviations | |
| ACO | ant colony optimization |
| APSO | particle swarm optimization with adaptively controlled acceleration coefficients |
| AWIPSO | particle swarm optimization with adaptively controlled acceleration coefficients, linearly descending inertia weight, and random grouping inversion |
| AWPSO | particle swarm optimization with adaptively controlled acceleration coefficients and linearly descending inertia weight |
| CPSO | conventional particle swarm optimization |
| NGC | navigation, guidance and control system |
| PSO | particle swam optimization |
| TSP | traveling salesman problem |
| USV | unmanned surface vehicle |