skip to main content
10.1145/3205455.3205545acmconferencesArticle/Chapter ViewAbstractPublication PagesgeccoConference Proceedingsconference-collections
research-article

A two-level diploid genetic based algorithm for solving the family traveling salesman problem

Published: 02 July 2018 Publication History

Abstract

In this paper, we consider the Family Traveling Salesman Problem (FTSP), which is a variant of the classical Traveling Salesman Problem (TSP). Given a partition of the nodes into a predefined number of clusters, called families, the aim of the FTSP is to find a minimum cost tour visiting a given number of nodes from each family. We describe a novel solution approach for solving the FTSP obtained by decomposing the problem into two smaller subproblems: a macro-level subproblem and a micro-level subproblem, and solving them separately. The goal of the first subproblem is to provide tours visiting the families using a classical genetic algorithm and a diploid genetic algorithm, while the aim of the second subproblem is to find the minimum-cost tour, corresponding to the above mentioned tours, visiting a given number of nodes from each family. The second subproblem is solved by transforming each global tour into a traveling salesman problem (TSP) which then is optimally computed using the Concorde TSP solver. The preliminary computational results on a usually used set of benchmark instances prove that our solution approach provides competitive solutions in comparison to the existing methods for solving the FTSP.

References

[1]
R. Bernardino and A. Paias. 2017. Solving the family traveling salesman problem. European Journal of Operational Research (2017).
[2]
J. A, Chisman. 1975. The clustered traveling salesman problem. Computers & Operations Research 2, 2 (1975), 115--119.
[3]
C. Expósito-Izquierdo, A. Rossi, and M. Sevaux. 2016. A Two-Level solution approach to solve the Clustered Capacitated Vehicle Routing Problem. Computers & Industrial Engineering 91 (2016), 274--289.
[4]
C. Feremans, M. Labbé, and G. Laporte. 2003. Generalized network design problems. European Journal of Operational Research 148, 1 (July 2003), 1--13.
[5]
D.E. Goldberg and R.E. Smith. 1987. Nonstationary Function Optimization Using Genetic Algorithms with Dominance and Diploidy. In Proc. of Second International Conference on Genetic Algorithms and their application. 59--68.
[6]
B. Golden, Z. Naji-Azimi, S. Raghavan, M. Salari, and P. Toth. 2012. The Generalized Covering Salesman Problem. INFORMS Journal on Computing 24, 4 (2012), 534--553.
[7]
A.L. Henry-Labordere. 1969. The record balancing problem: A dynamic programming solution of a generalized travelling salesman problem. RIRO (1969).
[8]
M. Mitchell. 1998. An introduction to genetic algorithms. MIT Press.
[9]
L.F. Morán-Mirabal, J.L. González-Velarde, and M.G.C. Resende. 2014. Randomized heuristics for the family traveling salesperson problem. International Transactions in Operational Research 21, 1 (2014), 41--57.
[10]
Camelia-M. Pintea, Petrică C. Pop, and Camelia Chira. 2017. The generalized traveling salesman problem solved with ant algorithms. Complex Adaptive Systems Modeling 5, 1 (07 Aug 2017), 8.
[11]
P.C. Pop, L. Fuksz, A. Horvat-Marc, and C. Sabo. 2018. A novel two-level optimization approach for clustered vehicle routing problem. Computers & Industrial Engineering 115 (2018), 304 -- 318.
[12]
P.C. Pop, O. Matei, and C. Sabo. 2017. A hybrid diploid genetic based algorithm for solving the generalized traveling salesman problem. In Lecture Notes in Computer Science, Vol. 10334. 149--160.
[13]
P.C. Pop, O. Matei, C. Sabo, and A. Petrovan. 2018. A two-level solution approach for solving the generalized minimum spanning tree problem. European Journal of Operational Research 265, 2 (2018), 478--487.
[14]
P. C. Pop. 2002. The Generalized Minimum Spanning Tree Problem. Twente University Press, the Netherlands.
[15]
P. C. Pop. 2012. Generalized Network Design Problems. Modeling and Optimization. De Gruyter, Germany.
[16]
Petrica C. Pop and Serban Iordache. 2011. A Hybrid Heuristic Approach for Solving the Generalized Traveling Salesman Problem. In Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation (GECCO '11). ACM, New York, NY, USA, 481--488.
[17]
P. C. Pop, O. Matei, and C. Sabo. 2010. A New Approach for Solving the Generalized Traveling Salesman Problem. In Hybrid Metaheuristics, María J. Blesa, Christian Blum, Günther Raidl, Andrea Roli, and Michael Sampels (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 62--72.
[18]
Jean-Yves Potvin and François Guertin. 1996. The Clustered Traveling Salesman Problem: A Genetic Approach. Springer US, Boston, MA, 619--631.
[19]
Mohammad H. Shaelaie, Majid Salari, and Zahra Naji-Azimi. 2014. The generalized covering traveling salesman problem. Applied Soft Computing 24 (2014), 867 -- 878.
[20]
S.S. Srivastava, S. Kumar, R.C. Garg, and P. Sen. 1969. Generalized travelling salesman problem through n sets of nodes. CORS.

Cited By

View all
  • (2024)An intensification-driven search algorithm for the family traveling salesman problem with incompatibility constraintsKnowledge-Based Systems10.1016/j.knosys.2024.112378302(112378)Online publication date: Oct-2024
  • (2024)A Comparative Study of Different Genetic Algorithms Approaches to Capacitated Vehicle Routing Problem for Collection of Agricultural ProductsThe 19th International Conference on Soft Computing Models in Industrial and Environmental Applications SOCO 202410.1007/978-3-031-75010-6_13(127-136)Online publication date: 20-Nov-2024
  • (2024)On the Design of Diploid Memetic Algorithms for Solving the Multidimensional Multi-way Number Partitioning ProblemParallel Problem Solving from Nature – PPSN XVIII10.1007/978-3-031-70055-2_1(3-19)Online publication date: 7-Sep-2024
  • Show More Cited By

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences
GECCO '18: Proceedings of the Genetic and Evolutionary Computation Conference
July 2018
1578 pages
ISBN:9781450356183
DOI:10.1145/3205455
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 02 July 2018

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. combinatorial optimization
  2. diploid genetic algorithms
  3. family traveling salesman problem
  4. generalized traveling salesman problem
  5. traveling salesman problem

Qualifiers

  • Research-article

Conference

GECCO '18
Sponsor:

Acceptance Rates

Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)9
  • Downloads (Last 6 weeks)0
Reflects downloads up to 17 Jan 2025

Other Metrics

Citations

Cited By

View all
  • (2024)An intensification-driven search algorithm for the family traveling salesman problem with incompatibility constraintsKnowledge-Based Systems10.1016/j.knosys.2024.112378302(112378)Online publication date: Oct-2024
  • (2024)A Comparative Study of Different Genetic Algorithms Approaches to Capacitated Vehicle Routing Problem for Collection of Agricultural ProductsThe 19th International Conference on Soft Computing Models in Industrial and Environmental Applications SOCO 202410.1007/978-3-031-75010-6_13(127-136)Online publication date: 20-Nov-2024
  • (2024)On the Design of Diploid Memetic Algorithms for Solving the Multidimensional Multi-way Number Partitioning ProblemParallel Problem Solving from Nature – PPSN XVIII10.1007/978-3-031-70055-2_1(3-19)Online publication date: 7-Sep-2024
  • (2023)A Diploid Genetic Algorithm for Solving the Multidimensional Multi-way Number Partitioning ProblemProceedings of the Companion Conference on Genetic and Evolutionary Computation10.1145/3583133.3590672(231-234)Online publication date: 15-Jul-2023
  • (2022)Solving the Family Traveling Salesperson Problem in the Adleman–Lipton Model Based on DNA ComputingIEEE Transactions on NanoBioscience10.1109/TNB.2021.310906721:1(75-85)Online publication date: Jan-2022
  • (2021)A Multifactorial Evolutionary Algorithm For Minimum Energy Cost Data Aggregation Tree In Wireless Sensor Networks2021 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC45853.2021.9504807(1656-1663)Online publication date: 28-Jun-2021
  • (2020)Multifactorial Evolutionary Algorithm for Inter-Domain Path Computation under Domain Uniqueness Constraint2020 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC48606.2020.9185701(1-8)Online publication date: 19-Jul-2020
  • (2020)A Behavioural Study of the Crossover Operator in Diploid Genetic Algorithms15th International Conference on Soft Computing Models in Industrial and Environmental Applications (SOCO 2020)10.1007/978-3-030-57802-2_8(79-88)Online publication date: 29-Aug-2020
  • (2019)Haploid Versus Diploid Genetic Algorithms. A Comparative StudyHybrid Artificial Intelligent Systems10.1007/978-3-030-29859-3_17(193-205)Online publication date: 4-Sep-2019

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media