Uncertain programming models for multi-objective shortest path problem with uncertain parameters

Autor: Samarjit Kar, Saibal Majumder, Mohuya B. Kar, Tandra Pal
Rok vydání: 2019
Předmět:
Zdroj: Soft Computing. 24:8975-8996
ISSN: 1433-7479
1432-7643
Popis: The shortest path problem is considered as one of the essential problems in network optimization with a wide range of real-world applications. Modelling such real-world applications involves various indeterminate phenomena which can be estimated through human beliefs. The uncertainty theory proposed by Liu (Uncertain theory, 2nd edn., Springer, Berlin, 2007) is widely regarded as a legitimate tool to deal with such uncertainty. This paper presents an uncertain multi-objective shortest path problem (UMSPP) for a weighted connected directed graph (WCDG), where every edge weight is associated with two uncertain parameters: cost and time. These parameters are represented as uncertain variables. Here, we have formulated the expected value model and chance-constrained model of the proposed UMSPP, and the corresponding deterministic transformation of these models is also presented. Subsequently, the deterministic models are solved with a classical multi-objective solution method, namely the global criterion method. Furthermore, two multi-objective genetic algorithms (MOGAs): nondominated sorting genetic algorithm II (NSGA-II) and multi-objective cross-generational elitist selection, heterogeneous recombination and cataclysmic mutation (MOCHC), are employed to solve these models. A suitable example is provided to illustrate the proposed model. Finally, the performance of MOGAs is compared for five randomly generated instances of UMSPP.
Databáze: OpenAIRE
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