20.500.12556/DKUM-90587 Metoda za napoved zmogljivosti stohastičnih algoritmov na osnovi statističnih porazdelitev števila ovrednotenj in časa doktorska disertacija A Method for Predicting the Performance of Stochastic Algorithms Based on Statistical Distributions of the Number of Evaluations and Runtime 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. 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. analiza stohastičnih algoritmov statistična porazdelitev napovedni model pristop s ciljno vrednostjo stochastic algorithm analysis statistical distribution predictive model target approach true true false [J. Herzog] Slovenski jezik Angleški jezik Doktorsko delo/naloga 2024-09-10 10:03:01 2025-04-08 07:55:08 2025-04-09 03:06:58 0000-00-00 00:00:00 2024 0 Maribor 0 Maribor XIV, 112 str. 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 303.712:519.856(043.3) 231809027 DOK_Herzog_Jana_2025.pdf DOK_Herzog_Jana_2025.pdf 1 5B8D62CB07463C9BC5E9E003563A1D9A 6f94e6b5478cc34f37d67aa1079bd0343b9e8c580c10bc547e5d74108d599a24 f592b0d3-fa75-11ef-a67a-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=189025 Fakulteta za elektrotehniko, računalništvo in informatiko 0 0 0