Minimization of the Total Traveling Distance and Maximum Distance by Using a Transformed-Based Encoding EDA to Solve the Multiple Traveling Salesmen Problem
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-09-17
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
Estimation of distribution algorithms (EDAs) have been used to solve numerous hard problems.
However, their use with in-group optimization problems has not been discussed extensively in the literature.
A well-known in-group optimization problem is the multiple traveling salesmen problem (mTSP), which involves simultaneous assignment and sequencing procedures and are shown in different forms.
This paper presents a new algorithm, named EDAMLA, which is based on self-guided genetic algorithm with a minimum loading assignment (MLA) rule.
This strategy uses the transformed-based encoding approach instead of direct encoding.
The solution space of the proposed method is only n!.
We compare the proposed algorithm against the optimal direct encoding technique, the two-part encoding genetic algorithm, and, in experiments on 34 TSP instances drawn from the TSPLIB, find that its solution space is n!n-1m-1.
The scale of the experiments exceeded that presented in prior studies.
The results show that the proposed algorithm was superior to the two-part encoding genetic algorithm in terms of minimizing the total traveling distance.
Notably, the proposed algorithm did not cause a longer traveling distance when the number of salesmen was increased from 3 to 10.
The results suggest that EDA researchers should employ the MLA rule instead of direct encoding in their proposed algorithms.
American Psychological Association (APA)
Chen, S. H.. 2015. Minimization of the Total Traveling Distance and Maximum Distance by Using a Transformed-Based Encoding EDA to Solve the Multiple Traveling Salesmen Problem. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-13.
https://search.emarefa.net/detail/BIM-1074362
Modern Language Association (MLA)
Chen, S. H.. Minimization of the Total Traveling Distance and Maximum Distance by Using a Transformed-Based Encoding EDA to Solve the Multiple Traveling Salesmen Problem. Mathematical Problems in Engineering No. 2015 (2015), pp.1-13.
https://search.emarefa.net/detail/BIM-1074362
American Medical Association (AMA)
Chen, S. H.. Minimization of the Total Traveling Distance and Maximum Distance by Using a Transformed-Based Encoding EDA to Solve the Multiple Traveling Salesmen Problem. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-13.
https://search.emarefa.net/detail/BIM-1074362
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1074362