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• LIPO and AdaLIPO require significantly fewer function evaluations to reach the target maximum than Pure Random Search (PRS) across all tested benchmark functions. — LIPO required 46 ± 10 evaluations for the Sphere function vs 1811 ± 436 for PRS (2D benchmark functions, n=2000 max steps, t=0.99 stopping criterion)
• AdaLIPO converges faster than LIPO on specific functions, likely due to local underestimation of the Lipschitz constant. — AdaLIPO required 28 ± 8 evaluations for the Sphere function vs 46 ± 10 for LIPO (2D Sphere function, p=0.5, α=0.01)
• LIPO and AdaLIPO are highly susceptible to the curse of dimensionality. (Increasing dimension d)

Setup

100 experimental runs per algorithm per function; 6 benchmark functions (Himmelblau, Hölder table, Rastrigin, Rosenbrock, Sphere, Square); max 2000 function evaluations per run.

How

The authors implemented LIPO and AdaLIPO using object-oriented programming and compared them against Pure Random Search (PRS) using six 2D benchmark functions. They introduced an enhanced version (LIPO-E/AdaLIPO-E) featuring a decreasing exploration-exploitation parameter and a specific stopping criterion based on rejected samples.

Limitations

Not suitable for high-dimensional functions in reasonable time. · Performance depends on the choice of exploration parameter p in AdaLIPO. · Benchmark functions used are fast to evaluate, unlike typical industrial simulations.

Summarized by Gemma 4 from the open-access full text · 8 Oct 2026. Read it