Term-sparse polynomial optimization for the design of frame structures

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F25%3A00384191" target="_blank" >RIV/68407700:21110/25:00384191 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s11081-025-10000-5" target="_blank" >https://doi.org/10.1007/s11081-025-10000-5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11081-025-10000-5" target="_blank" >10.1007/s11081-025-10000-5</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Term-sparse polynomial optimization for the design of frame structures

Popis výsledku v původním jazyce

This work investigates an efficient solution to two fundamental problems in topology optimization of frame structures. The first one involves minimizing structural compliance under linear-elastic equilibrium and weight constraint, while the second one minimizes the weight under compliance constraints. These problems are non-convex and generally challenging to solve globally, with the non-convexity concentrated in a polynomial matrix inequality. In Tyburec et al. (2021, 2023), the authors tackled the problems using the moment-sum-of-squares hierarchy (mSOS), but were only able to solve smaller instances globally. Here, we aim to improve the scalability of solution to these problems by using the mSOS hierarchy supplemented with the Term Sparsity Pattern technique (TSP), which was introduced by Magron and Wang (2023). Due to the unique polynomial structure of our problems in which the objective and constraint functions are separable polynomials, we further improve scalability by adopting a reduced monomial basis containing non-mixed terms only. From extensive numerical testing, we conclude that these techniques allow for a global solution to two times larger instances when compared to (Tyburec et al. 2021, 2023), and accelerate the solution of the problems from Tyburec et al. (2021, 2023) significantly.

Název v anglickém jazyce

Term-sparse polynomial optimization for the design of frame structures

Popis výsledku anglicky

This work investigates an efficient solution to two fundamental problems in topology optimization of frame structures. The first one involves minimizing structural compliance under linear-elastic equilibrium and weight constraint, while the second one minimizes the weight under compliance constraints. These problems are non-convex and generally challenging to solve globally, with the non-convexity concentrated in a polynomial matrix inequality. In Tyburec et al. (2021, 2023), the authors tackled the problems using the moment-sum-of-squares hierarchy (mSOS), but were only able to solve smaller instances globally. Here, we aim to improve the scalability of solution to these problems by using the mSOS hierarchy supplemented with the Term Sparsity Pattern technique (TSP), which was introduced by Magron and Wang (2023). Due to the unique polynomial structure of our problems in which the objective and constraint functions are separable polynomials, we further improve scalability by adopting a reduced monomial basis containing non-mixed terms only. From extensive numerical testing, we conclude that these techniques allow for a global solution to two times larger instances when compared to (Tyburec et al. 2021, 2023), and accelerate the solution of the problems from Tyburec et al. (2021, 2023) significantly.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA22-15524S" target="_blank" >GA22-15524S: Polynomiální optimalizace v návrhu globálně optimálních rámových konstrukcí namáhaných dynamickým zatížením</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Optimization and Engineering

ISSN

1389-4420

e-ISSN

1573-2924

Svazek periodika

26

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

44

Strana od-do

2867-2910

Kód UT WoS článku

001514307200001

EID výsledku v databázi Scopus

2-s2.0-105008928967