HFF

Hyperspherical Fitness Functions — one ordering over thousands of objectives.

Real systems are judged on many axes at once. Classical many-objective methods stall as objectives multiply: dominance collapses (everything ties), and weighted sums smuggle in arbitrary trade-offs. HFF takes a geometric route — orient the objective axes so the ideal sits at a single point, project candidates onto the hypersphere, and rank by angle to the ideal. Direction and magnitude are preserved, and the spherical CDF correction keeps scores comparable as the number of objectives changes.

Why it matters

• Stable, holistic orderings at 1,000+ simultaneous objectives
• O(MN) cost — fast enough inside an evolutionary loop
• Dimension-corrected: scores comparable as objectives are born and die
• Applications: reinforcement learning, design optimisation, portfolio and policy selection

HFF is published research — Hyperspherical Fitness Functions for Many-Objective Optimization, GECCO Companion 2026 — with a Rust/Python implementation, and it runs GPU-accelerated inside UltraDim as the evaluation stage of our optimisation tooling.