Reliable pathfinding problems for a correlated network: A linear programming problem in a hypergraph

•Reformulate non‐additive nonlinear integer problems (m-s & m-v) in reliable shortest paths as linear programs.•Convert the constraint matrix to a totally unimodular form, prove via topological network theory.•Propose a global optimization algorithm for the m-s problem. This study addresses the...

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Vydané v:European journal of operational research Ročník 326; číslo 2; s. 234 - 254
Hlavní autori: Uchida, Kenetsu, Wang, Yifan, Tani, Ryuichi
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 16.10.2025
Predmet:
Hypergraph
Reliable path
Stochastic travel time
Total unimodularity
Transportation
Hypergraph
Stochastic travel time
Total unimodularity
Transportation
Reliable path
ISSN:0377-2217
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Shrnutí:•Reformulate non‐additive nonlinear integer problems (m-s & m-v) in reliable shortest paths as linear programs.•Convert the constraint matrix to a totally unimodular form, prove via topological network theory.•Propose a global optimization algorithm for the m-s problem. This study addresses the NP-hard reliable path problem, which seeks the path with minimum travel cost in correlated road networks, formulated as mean-variance (m-v) and mean-standard deviation (m-s) shortest path problems. This study proposes a novel approach that transforms these nonlinear binary integer programming models into standard linear programming (LP) problems using structure-preserving linearization and graph transformation techniques. The resulting LP formulations guarantee global optimality, overcoming the computational challenges of real-world networks. Numerical experiments on real-world networks demonstrate that the proposed method efficiently identifies the globally optimal path, matching the performance of exact methods like branch-and-bound while offering greater model flexibility. These findings provide a scalable and robust framework for reliable path selection in complex transportation networks.
ISSN:0377-2217
DOI:10.1016/j.ejor.2025.04.046