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A deterministic and nature-inspired algorithm for the fuzzy multi-objective path optimization problem
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Ma, Yi-Ming, Hu, Xiao-Bing and Zhou, Hang (2023) A deterministic and nature-inspired algorithm for the fuzzy multi-objective path optimization problem. Complex & Intelligent Systems, 9 . pp. 753-765. doi:10.1007/s40747-022-00825-3 ISSN 2199-4536.
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Official URL: https://doi.org/10.1007/s40747-022-00825-3
Abstract
Increasing evaluation indexes have been involved in the network modeling, and some parameters cannot be described precisely. Fuzzy set theory becomes a promising mathematical method to characterize such uncertain parameters. This study investigates the fuzzy multi-objective path optimization problem (FMOPOP), in which each arc has multiple crisp and fuzzy weights simultaneously. Fuzzy weights are characterized by triangular fuzzy numbers or trapezoidal fuzzy numbers. We adopt two fuzzy number ranking methods based on their fuzzy graded mean values and distances from the fuzzy minimum number. Motivated by the ripple spreading patterns on the natural water surface, we propose a novel ripple-spreading algorithm (RSA) to solve the FMOPOP. Theoretical analyses prove that the RSA can find all Pareto optimal paths from the source node to all other nodes within a single run. Numerical examples and comparative experiments demonstrate the efficiency and robustness of the newly proposed RSA. Moreover, in the first numerical example, the processes of the RSA are illustrated using metaphor-based language and ripple spreading phenomena to be more comprehensible. To the best of our knowledge, the RSA is the first algorithm for the FMOPOP that can adopt various fuzzy numbers and ranking methods while maintaining optimality.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering | ||||||||
Library of Congress Subject Headings (LCSH): | Fuzzy graphs, Mathematical optimization, Combinatorial probabilities, Fuzzy algorithms, Fuzzy sets | ||||||||
Journal or Publication Title: | Complex & Intelligent Systems | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 2199-4536 | ||||||||
Official Date: | February 2023 | ||||||||
Dates: |
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Volume: | 9 | ||||||||
Page Range: | pp. 753-765 | ||||||||
DOI: | 10.1007/s40747-022-00825-3 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 30 August 2022 | ||||||||
Date of first compliant Open Access: | 30 August 2022 | ||||||||
RIOXX Funder/Project Grant: |
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