On Multi-Objective Minimum Spanning Tree Problem under Uncertain Paradigm

Symmetry

Partha Sarathi Barma¹  Bijoy Kumar Mandal²  Saibal Majumder²  Samarjit Kar³  Pradip Banerjee³  Paweł Ziemba⁴  Arindam Biswas⁵ 

[1] Center for Distance and Online Education, The University of Burdwan, Burdwan 713104, India;Department of Computer Science and Engineering, NSHM Knowledge Campus Durgapur, Durgapur 713212, India;Department of Mathematics, National Institute of Technology Durgapur, Durgapur 713209, India;Institute of Management, University of Szczecin, 70-453 Szczecin, Poland;School of Mines and Metallurgy, Kazi Nazrul University (Public University), Asansol 713340, India;

关键词: uncertain programming;    multi-objective minimum spanning tree problem;    epsilon-constraint method;    NSGAII;    DENSEA;    distribution network management;   

DOI  :  10.3390/sym14010106

来源: DOAJ

【 摘 要 】

Minimum spanning tree problem (MSTP) has allured many researchers and practitioners due to its varied range of applications in real world scenarios. Modelling these applications involves the incorporation of indeterminate phenomena based on their subjective estimations. Such phenomena can be represented rationally using uncertainty theory. Being a more realistic variant of MSTP, in this article, based on the principles of the uncertainty theory, we have studied a multi-objective minimum spanning tree problem (MMSTP) with indeterminate problem parameters. Subsequently, two uncertain programming models of the proposed uncertain multi-objective minimum spanning tree problem (UMMSTP) are developed and their corresponding crisp equivalence models are investigated, and eventually solved using a classical multi-objective solution technique, the epsilon-constraint method. Additionally, two multi-objective evolutionary algorithms (MOEAs), non-dominated sorting genetic algorithm II (NSGAII) and duplicate elimination non-dominated sorting evolutionary algorithm (DENSEA) are also employed as solution methodologies. With the help of the proposed UMMSTP models, the practical problem of optimizing the distribution of petroleum products was solved, consisting in the search for symmetry (balance) between the transportation cost and the transportation time. Thereafter, the performance of the MOEAs is analyzed on five randomly developed instances of the proposed problem.

【 授权许可】

Unknown