Meta-optimization of dimension adaptive parameter schema for Nelder–Mead algorithm in high-dimensional problems

Rojec, Žiga (avtor), Tuma, Tadej (avtor), Olenšek, Jernej (avtor), Bűrmen, Árpád (avtor), Puhan, Janez (avtor)

Although proposed more than half a century ago, the Nelder–Mead simplex search algorithm is still widely used. Four numeric constants define the operations and behavior of the algorithm. The algorithm with the original constant values performs fine on most low-dimensional, but poorly on high-dimensional, problems. Therefore, to improve its behavior in high dimensions, several adaptive schemas setting the constants according to the problem dimension were proposed in the past. In this work, we present a novel adaptive schema obtained by a meta-optimization procedure. We describe a schema candidate with eight parameters subject to meta-optimization and define an objective function evaluating the candidate’s performance. The schema is optimized on up to 100-dimensional problems using the Parallel Simulated Annealing with Differential Evolution global method. The obtained global minimum represents the proposed schema. We compare the performance of the optimized schema with the existing adaptive schemas. The data profiles on the Gao–Han modified quadratic, Moré–Garbow–Hilstrom, and CUTEr (Constrained and Unconstrained Testing Environment, revisited) benchmark problem sets show that the obtained schema outperforms the existing adaptive schemas in terms of accuracy and convergence speed.

• Jezik: Angleški jezik
• Ključne besede: meta-optimization, Nelder-Mead algorithm, adaptive parameter schema, high-dimensional optimization problems
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FE - Fakulteta za elektrotehniko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2022
• Št. strani: 16 str.
• Številčenje: Vol. 10, iss. 13, art. 2288
• PID: 20.500.12556/RUL-145174
• UDK: 004
• ISSN pri članku: 2227-7390
• DOI: 10.3390/math10132288
• COBISS.SI-ID: 118971139
• Datum objave v RUL: 12.04.2023

Gradivo je del revije

• Naslov: Mathematics
• Skrajšan naslov: Mathematics
• Založnik: MDPI AG
• ISSN: 2227-7390
• COBISS.SI-ID: 523267865

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: metaoptimizacija, algoritem Nelder-Mead, adaptivni parametri, visokodimenzionalni optimizacijski problemi

Projekti

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: P2-0246
• Naslov: ICT4QoL - Informacijsko komunikacijske tehnologije za kakovostno življenje