New Dynamic Programming algorithm for the Multiobjective Minimum Spanning Tree problem

The Multiobjective Minimum Spanning Tree (MO-MST) problem generalizes the Minimum Spanning Tree problem by weighting the edges of the input graph using vectors instead of scalars. In this paper, we design a new Dynamic Programming MO-MST algorithm. Dynamic Programming for a MO-MST instance requests...

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Vydané v:Computers & operations research Ročník 173; s. 106852
Hlavní autori: Maristany de las Casas, Pedro, Sedeño-Noda, Antonio, Borndörfer, Ralf
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Ltd 01.01.2025
Predmet:
Dynamic Programming
Multiobjective Minimum Spanning Trees
Multiple objective programming
Dynamic Programming
Multiobjective Minimum Spanning Trees
Multiple objective programming
ISSN:0305-0548
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Shrnutí:The Multiobjective Minimum Spanning Tree (MO-MST) problem generalizes the Minimum Spanning Tree problem by weighting the edges of the input graph using vectors instead of scalars. In this paper, we design a new Dynamic Programming MO-MST algorithm. Dynamic Programming for a MO-MST instance requests solving a One-to-One Multiobjective Shortest Path (MOSP) instance and both instances have equivalent solution sets. The MOSP instance is defined on a so called transition graph. We study the original size of this graph in detail and reduce its size using cost-dependent arc pruning criteria. To solve the MOSP instance on the reduced transition graph, we design the Implicit Graph Multiobjective Dijkstra Algorithm (IG-MDA), exploiting recent improvements on MOSP algorithms from the literature. All in all, the new IG-MDA outperforms the current state of the art on a big set of instances from the literature. Our code and results are publicly available. •Dynamic Programming approach for the Multiobjective Minimum Spanning Tree problem.•New version of the Multiobjective Dijkstra Algorithm with implicit graph management.•Multiple pruning techniques reduce the size of the graph in a tree-independent way.•Implementation of the Built Network algorithm using recent advances from the literature.•Benchmark on a big set of instances with three and four objectives.
ISSN:0305-0548
DOI:10.1016/j.cor.2024.106852