Optimizacija preiskovanja grafov z vložitvami grafov

CIGLARIČ, TIMOTEJ (author), Robnik Šikonja, Marko (mentor)

Problem usmerjanja vozil s kapaciteto je NP-poln kombinatorični problem. Poleg njegove uporabnosti za dostavne službe se lahko nanj učinkovito preslika tudi veliko drugih problemov. Za reševanje problema uporabim rekurenčno nevronsko mrežo GRU z mehanizmom pozornosti. Po fazi učenja, ki traja toliko časa kot uporaba stohastičnih optimizacijskih algoritmov na več tisoč primerih, dobimo na majhnih grafih primerljivo dobre rezultate, na večjih grafih pa se zaradi povečevanja kompleksnosti problema nevronski model ne uči več dovolj hitro in je slabši. Med vložitvami grafov, ki sem jih preizkusil, dajeta najboljše rezultate node2vec in GraRep.

• Language: Slovenian
• Keywords: nevronska mreža, graf, kombinatorična optimizacija, problem usmerjanja vozil, vložitve grafov
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FRI - Faculty of Computer and Information Science
• Year: 2021
• PID: 20.500.12556/RUL-130322
• COBISS.SI-ID: 77579779
• Publication date in RUL: 13.09.2021

CIGLARIČ, TIMOTEJ, 2021, Optimizacija preiskovanja grafov z vložitvami grafov [online]. Bachelor’s thesis. [Accessed 18 March 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=130322

Secondary language

• Language: English
• Title: Graph search optimization using graph embeddings

Abstract

The capacitated vehicle routing problem is an NP-complete combinatorial problem. In addition to its usefulness for delivery services, many other problems can be efficiently mapped to it. To solve the problem, I use the GRU recurrent neural network with the attention mechanism. After a learning phase that lasts as long as using stochastic optimization algorithms on thousands of cases, we get comparatively good results on small graphs. On larger graphs the neural models do not learn fast enough and produce worse results due to an increasing problem complexity. Among the tested graph embedding methods, node2vec and GraRep give the best results.

• Keywords: neural net, graph, combinatorial optimization, vehicle routing problem, graph embeddings