Metoda za napoved zmogljivosti stohastičnih algoritmov na osnovi statističnih porazdelitev števila ovrednotenj in časa : doktorska disertacija

Herzog, Jana

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Title:	Metoda za napoved zmogljivosti stohastičnih algoritmov na osnovi statističnih porazdelitev števila ovrednotenj in časa : doktorska disertacija
Authors:	ID Herzog, Jana (Author) ID Bošković, Borko (Mentor) More about this mentor...
Files:	DOK_Herzog_Jana_2025.pdf (3,56 MB) MD5: 5B8D62CB07463C9BC5E9E003563A1D9A
Language:	Slovenian
Work type:	Doctoral dissertation
Typology:	2.08 - Doctoral Dissertation
Organization:	FERI - Faculty of Electrical Engineering and Computer Science
Abstract:	V doktorski disertaciji predstavimo metodo, namenjeno analizi in primerjavi stohastičnih algoritmov. Predlagana metoda se imenuje AS^3D (angl.~Analysis of the Stochastic Solvers based on Statistical Distributions). Ta temelji na statističnih porazdelitvah opazovanih spremenljivk, natančneje številu funkcijskih ovrednotenj in času. Pri tem uporablja pristop s ciljno vrednostjo. Ciljno vrednost določa kakovost rešitve, katero želimo, da jo algoritem doseže. Opazovani spremenljivki in njuni statistični porazdelitvi analizira na nizkodimenzionalnih in napoveduje za visokodimenzionalne različice optimizacijskega problema. Vzpostavljeni napovedni model na podlagi parametrov statističnih porazdelitev omogoča napovedovanje zaustavitvenih pogojev, torej časa in števila funkcijskih ovrednotenj za določeno verjetnost doseganja ciljne vrednost. Prav tako omogoča oceno verjetnosti, da bo zagon uspešen glede na dani zaustavitveni pogoj in kakovosti rešitve za višjedimenzionalne različice problema. Da pokažemo uporabnost predlagane metode, smo vzpostavljene napovedne modele empirično validirali za izbrane optimizacijske algoritme in probleme. Razlike med napovedanimi in empiričnimi vrednostmi so znašale manj kot 15 \% za problem LABS, testne funkcije CEC in problem potenciala Lennard-Jones. To nakazuje na to, da lahko metodo AS^3D uspešno uporabljamo za analizo in primerjavo stohastičnih algoritmov na različnih optimizacijskih problemih. S pomočjo metode smo pokazali tudi uporabnost stohastičnih algoritmov. Ti morajo, da dosežejo optimalno rešitev z visoko verjetnostjo, preiskati le majhen delež iskalnega prostora.
Keywords:	analiza stohastičnih algoritmov, statistična porazdelitev, napovedni model, pristop s ciljno vrednostjo
Publication status:	Published
Publication version:	Version of Record
Place of publishing:	Maribor
Place of performance:	Maribor
Publisher:	[J. Herzog]
Year of publishing:	2024
Number of pages:	XIV, 112 str.
PID:	20.500.12556/DKUM-90587
UDC:	303.712:519.856(043.3)
COBISS.SI-ID:	231809027
Publication date in DKUM:	08.04.2025
Views:	180
Downloads:	120
Metadata:
Categories:	KTFMB - FERI
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Licences

License:	CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International

Link:	http://creativecommons.org/licenses/by-nc-nd/4.0/
Description:	The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.
Licensing start date:	10.09.2024

Secondary language

Language:	English
Title:	A Method for Predicting the Performance of Stochastic Algorithms Based on Statistical Distributions of the Number of Evaluations and Runtime
Abstract:	In this doctoral dissertation, we present a method designed to analyse and compare stochastic algorithms. The proposed method is called AS^3D (Analysis of the Stochastic Solvers based on Statistical Distributions). It is based on statistical distributions of observed variables, namely the number of function evaluations or runtime. It employs a target value approach, analysing the observed variables of low-dimensional instances and making predictions for high-dimensional instances of the optimization problems. The target value is determined by the quality of the solution, which needs to be reached by the stochastic solver. The predictive model is established based on the parameters of statistical distributions. This allows for predicting stopping conditions runtime or number of function evaluations with a certain probability of reaching target values. It also allows for predicting the probability that a run will be successful for a given stopping condition and the quality of the solution for higher dimensions of the optimisation problem. To demonstrate the usefulness of the proposed method, we empirically validated the predictive models for chosen optimisation problems and algorithms. The differences between the predicted and empirical values were less than 15\% for optimisation problem LABS, benchmark functions CEC and potential of Lennard-Jones. This indicates that the proposed method AS^3D can be successfully used to analyse and compare the stochastic algorithms for various optimisation problems. With the help of the method, we also demonstrated the usefulness of the stochastic solvers. They need to search only a fraction of the search space to reach the optimal solution with high probability.
Keywords:	stochastic algorithm analysis, statistical distribution, predictive model, target approach

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