| pc | Probability that two parents exchange genetic material (crossover) |
| pm | Probability that each offspring is perturbed by mutation |
| σm | Gaussian step size of mutation — controls how far an individual can jump per mutation event |
| σx | Std. dev. of all individual x positions — a measure of population spatial diversity. No arrow: smaller = converged (good for single-peak), larger = spread across peaks (good for MMO). |
| σshare | Niche radius for Fitness Sharing — individuals within this distance share fitness, reducing the effective payoff of crowded peaks |
| σclear | Niche radius for Clearing — only the best individual within this radius retains its fitness; others are zeroed out |
| Det. Crowding | Each offspring competes for survival against whichever parent it most resembles; no explicit radius needed |
| Peaks occupied | Count of landscape peaks with ≥ 1 individual within 1.5 × peak σ |
| pc | Probability of applying arithmetic crossover; offspring are convex combinations of the two parents |
| pm | Per-gene probability of applying Gaussian mutation |
| σm | Std. dev. of the Gaussian perturbation added during mutation |
| Crowding dist. | How isolated a rank-1 point is relative to its neighbors along the front; used as a diversity tie-breaker so that less-crowded points are preferred |
| HV | Hypervolume: area of objective space simultaneously dominated by the rank-1 (or archive) set, measured from a reference corner. Increases as the front converges and spreads; higher = better |
| σcd | Std. dev. of crowding distances across rank-1 individuals. Low σ means evenly distributed; high σ means some regions are dense, others sparse |
| Archive (RWGA) | Persistent set of all non-dominated solutions found across all generations; grows monotonically and visualized as orange dots |
| σm | Gaussian mutation step size — larger values give each island more local exploration |
| Migration rate | Fraction of each island's population that copies to a neighbor each migration event |
| Migration interval | How many generations between migration events — longer intervals = more isolation = more drift |
| σx | Std. dev. of each island's mean x position — measures how spread out the islands are in genome space; drops toward 0 when all islands converge on the same peak. No arrow: large = diverse exploration, small = convergence — which is desirable depends on context. |
| Shaded bands | Per-island min / mean / max fitness over generations; overlap shows when islands have found similar fitness values on different peaks |
| Single-peak | Sphere or Rosenbrock — use tournament selection, no niching, small σm |
| Multimodal | Rastrigin or Ackley — try fitness sharing with σshare ≈ 1.0; watch how many peaks the population occupies |
| Multiple equal optima | Himmelblau or Cross-in-tray — 4 global minima at equal depth; deterministic crowding naturally splits the population |
| Island mode | Each island is initialized in a different region; set migration interval high (≥ 10) to let islands diverge before synchronizing |
| Needle-in-haystack | Easom — flat everywhere except a tiny basin at (π, π); standard GA struggles; try large σm or many islands |