GP-Enhanced TOENS: Evolutionary Optimization of Numerical Uncertainty Control via Genetic Programming

This paper proposes GP-TOENS, a novel framework integrating Genetic Programming (GP) with the Third-Order Exact Number System (TOENS) to optimize numerical uncertainty control. TOENS uses type operators (·, *, ~, ?) and intensity parameters (s = 0 — 4095) to represent numerical uncertainty (ε = 2-s ), but its parameter configuration relies on manual experience in dynamic scenarios. GP’s tree-based evolution ary capability can automatically optimize complex parameter systems but suffers from bloat (tree inflation). GP-TOENS addresses these challenges by introducing tree compression technology based on TOENS er ror bounds and hardware co-design. Experimental results show that GP-TOENS achieves 50× speedup in quantum calibration, reduces false alarms in structural monitoring to 4.2% (compared to 7.6% in TOENS), and lowers energy consumption by 40.2% in matrix inversion on ASIC chips. The mathematical foundation includes a theorem proving GP tree complexity constraints. This work extends TOENS’ core philosophy: "True computational revolution lies in elegantly embracing uncertainty" to "Evolutionary Intelligence for Dynamic Precision".