Application of fuzzy optimization to the orienteering problem
type: Item
instance of: scholarly article
title: Application of fuzzy optimization to the orienteering problem
zbMATH Open document ID: 1390.90485
DOI: 10.1155/2015/569248
author: Madhushi Verma
author: K. K. Shukla
published in: Advances in Fuzzy Systems
publication date: 2018-05-18T00:00:00Z
review text: Summary: This paper deals with the orienteering problem (OP) which is a combination of two well-known problems (i.e., travelling salesman problem and the knapsack problem). OP is an NP-hard problem and is useful in appropriately modeling several challenging applications. As the parameters involved in these applications cannot be measured precisely, depicting them using crisp numbers is unrealistic. Further, the decision maker may be satisfied with graded satisfaction levels of solutions, which cannot be formulated using a crisp program. To deal with the above-stated two issues, we formulate the \textit{fuzzy} orienteering problem (FOP) and provide a method to solve it. Here we state the two necessary conditions of OP of maximizing the total collected score and minimizing the time taken to traverse a path (within the specified time bound) as fuzzy goals and the remaining necessary conditions as crisp constraints. Using the max-min formulation of the fuzzy sets obtained from the fuzzy goals, we calculate the fuzzy decision sets (\(Z\) and \(Z^\ast\)) that contain the feasible paths and the desirable paths, respectively, along with the degrees to which they are acceptable. To efficiently solve large instances of FOP, we also present a parallel algorithm on CREW PRAM model.
Mathematics Subject Classification ID: 90C27
Mathematics Subject Classification ID: 90C70
zbMATH DE Number: 6870098
Wikidata QID: Q59101914
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/569248
OpenAlex ID: W1608467940
cites work: The orienteering problem: a survey
cites work: The orienteering problem
cites work: Using artificial neural networks to solve the orienteering problem
cites work: A fast and effective heuristic for the orienteering problem
cites work: Solving the Orienteering Problem through Branch-and-Cut
cites work: New Approximation Guarantees for Minimum-Weight k-Trees and Prize-Collecting Salesmen
cites work: Q4952698
cites work: Ranking fuzzy numbers with a distance method using circumcenter of centroids and an index of modality
cites work: Linear programming with fuzzy parameters: an interactive method resolution
cites work: Weighted constraint aggregation in fuzzy optimization
cites work: An experimental analysis of parallel sorting algorithms
description: scientific article; zbMATH DE number 6870098