Skip to main content
SpringerLink
Log in

A multi-objective antlion optimizer for the ring tree problem with secondary sub-depots

  • Original Paper
  • Published:
Operational Research Aims and scope Submit manuscript

Abstract

This article proposes a multi-objective ring tree problem with secondary sub-depots (MORTPSSD), which focusses on the problems of telecommunication and logistics networks. In this problem, we have considered a fixed node as the main depot. Other nodes are divided into primary sub-depots, secondary sub-depots, and left-out nodes referred to type 1, type 2, and type 3 customers. The first objective of the proposed model MORTPSSD is to minimize the circuits’ total routing cost through type 1 and type 2 customers added by the minimal spanning tree cost of type 3 customers. The second objective is to minimize the total number of type 3 customers, which influences the first objective. The model is solved by a discrete multi-objective antlion optimizer (DMOALO) with a ternary encoding. The proposed algorithm is also tested on some instances derived from TSP benchmark problems. Statistical analyses are performed to compare the convergence and the diversity of the proposed DMOALO against NSGAII and MOPSO, which yields a better efficiency of DMOALO for most instances.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

Notes

  1. http://elib.zib.de/pub/mp-testdata/tsp/tsplib/tsp.

  2. http://vassarstats.net/wilcoxon.html.

References

  • Abe FHN, Hoshino EA, Hill A (2015) The ring star facility location problem. Electron Notes Discrete Math 50:331–336

    Article  Google Scholar 

  • Baldacci R, Dell’Amico M (2010) Heuristic algorithms for the multi-depot ring star problem. Eur J Oper Res 203(1):270–281

    Article  Google Scholar 

  • Baldacci R, Dell’Amico M, Salazar González JJ (2007) The capacitated m-ring star problem. Oper Res 55(6):1147–1162

    Article  Google Scholar 

  • Beheshti Z, Shamsuddin SM, Hasan S (2015) Memetic binary particle swarm optimization for discrete optimization problems. Inf Sci 299:58–84

    Article  Google Scholar 

  • Belgin O, Karaoglan I, Altiparmak F (2018) Two-echelon vehicle routing problem with simultaneous pickup and delivery: mathematical model and heuristic approach. Comput Ind Eng 115:1–16

    Article  Google Scholar 

  • Calvete HI, Galé C, Iranzo JA (2013) An efficient evolutionary algorithm for the ring star problem. Eur J Oper Res 231:22–33

    Article  Google Scholar 

  • Current JR, Schilling DA (1989) The covering salesman problem. Transp Sci 23(3):208–213

    Article  Google Scholar 

  • Das M, Roy R, Dehuri S, Cho SB (2011) A new approach to associative classification based on binary multi-objective particle swarm optimization. Int J Appl Metaheuristic Comput 2(2):51–73

    Article  Google Scholar 

  • Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast elitist multiobjective genetic algorithm: NSGAII. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  • Dias TCS, de Sousa Filho GF, Macambira EM, Cabral LAF, Fampa MHC (2006) An efficient heuristic for the ring star problem. In: Alvarez C, Serna M (eds) Experimental algorithms. Lecture Notes in Computer Science, vol 4007. Springer, Berlin, pp 24–35

  • Golden BL, Naji-Azimi Z, Raghavan S, Salari M, Toth P (2012) The generalized covering salesman problem. INFORMS J Comput 24(4):534–553

    Article  Google Scholar 

  • Gunawan A, Lau HC, Vansteenwegen P (2016) Orienteering problem: a survey of recent variants, solution approaches and applications. Eur J Oper Res 255:315–332

    Article  Google Scholar 

  • Helsgaun K (2000) Effective implementation of the Lin–Kerninghan traveling salesman heuristic. Eur J Oper Res 126:106–130

    Article  Google Scholar 

  • Hill A, Schwarze S (2018) Exact algorithms for bi-objective ring tree problems with reliability measures. Comput Oper Res 94:38–51

    Article  Google Scholar 

  • Hill A, Voß S (2016) Optimal capacitated ring trees. EURO J Comput Optim 4:137–166

    Article  Google Scholar 

  • Hill A, Voß S (2018) Generalized local branching heuristics and the capacitated ring tree problem. Discrete Appl Math 242:34–52

    Article  Google Scholar 

  • Kedad-Sidhoum S, Nguyen VH (2010) An exact algorithm for solving the ring star problem. Optimization 59(1):125–140

    Article  Google Scholar 

  • Labbe M, Laporte G, Rodriguez Martin I, Salazar Gonzalez JJ (1999) The median cycle problem, Working paper, CRT-99-29, Université de Montréal, Corpus ID: 10164962

  • Labbe M, Laporte G, Rodriguez Martin I, Salazar Gonzalez JJ (2004) The ring star problem: polyhedral analysis and exact algorithm. Networks 43(3):177–189

    Article  Google Scholar 

  • Laporte G (1992) The vehicle routing problem: an overview of exact and approximate algorithms. Eur J Oper Res 59:345–358

    Article  Google Scholar 

  • Liu YH (2010) Different initial solution generators in genetic algorithms for solving the probabilistic travelling salesman problem. Appl Math Comput 216:125–137

    Google Scholar 

  • Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98

    Article  Google Scholar 

  • Mirjalili S, Jangir P, Saremi S (2017) Multi-objective ant lion optimizer: a multiobjective optimization algorithm for solving engineering problems. Appl Intell 45(1):79–95

    Article  Google Scholar 

  • Majumder S, Kar S, Pal T (2019a) Uncertain multi-objective Chinese postman problem. Soft Comput 23:11557–11572

    Article  Google Scholar 

  • Majumder S, Kundu P, Kar S, Pal T (2019b) Uncertain multi-objective multi-item fixed charge solid transportation problem with budget constraint. Soft Comput 23:3279–3301

    Article  Google Scholar 

  • Merz P, Freisleben B (2001) Memetic algorithms for the traveling salesman problem. Complex Syst 13:297–345

    Google Scholar 

  • Moreno Pérez JA, Moreno Vega JM, Rodríguez Martín I (2003) Variable neighborhood Tabu search and its application to the median cycle problem. Eur J Oper Res 151(2):365–378

    Article  Google Scholar 

  • Mukherjee A, Maity S, Panigrahi G, Maiti M (2017a) Imprecise constrained covering solid travelling salesman problem with credibility. In: Giri D, Mohapatra R, Begehr H, Obaidat M (eds) Mathematics and computing. ICMC 2017 communications in computer and information science, vol 655. Springer, Singapore, pp 181–195

  • Mukherjee A, Panigrahi G, Kar S, Maiti M (2017b) Constrained covering solid travelling salesman problems in uncertain environment. J Ambient Intell Human Comput 10:125–141

    Article  Google Scholar 

  • Naji-Azimi Z, Salari M, Toth P (2012) An integer linear programming based heuristic for the capacitated m-ring-star problem. Eur J Oper Res 217(1):17–25

    Article  Google Scholar 

  • Prins C (2004) A simple and effective evolutionary algorithm for the vehicle routing problem. Comput Oper Res 31:1985–2002

    Article  Google Scholar 

  • Rikalovic A, Soares GA, Ignjatic J (2018) Spatial analysis of logistics center location: a comprehensive approach. Decis Mak Appl Manag Eng 1(1):38–50

    Article  Google Scholar 

  • Roy R, Dehuri S, Cho SB (2011) A novel particle swarm optimization algorithm for multi-objective combinatorial optimization problem. Int J Appl Metaheuristic Comput 2(4):41–57

    Article  Google Scholar 

  • Salari M, Naji-Azimi Z (2012) An integer programming-based local search for the covering salesman problem. Comput Oper Res 39:2594–2602

    Article  Google Scholar 

  • Salari M, Reihaneh M, Sabbagh MS (2015) Combining ant colony optimization algorithm and dynamic programming technique for solving the covering salesman problem. Comput Ind Eng 83:244–251

    Article  Google Scholar 

  • Sbai I, Krichen S, Limam O (2020) Two meta-heuristics for solving the capacitated vehicle routing problem: the case of the Tunisian Post Office. Oper Res. https://doi.org/10.1007/s12351-019-00543-8

    Article  Google Scholar 

  • Simonetti L, Frota Y, De Souza CC (2011) The ring-star problem: a new integer programming formulation and a branch-and-cut algorithm. Discrete Appl Math 159(16):1901–1914

    Article  Google Scholar 

  • Yogaranjan G, Revathi T (2016) A discrete ant lion optimization (DALO) algorithm for solving data gathering tour problem in wireless sensor networks. Middle-East J Sci Res 24(10):3113–3120

    Google Scholar 

  • Zhao F, Sun J, Li S, Liu W (2009) A hybrid genetic algorithm for the traveling salesman problem with pickup and delivery. Int J Autom Comput 06(1):97–102

    Article  Google Scholar 

  • Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3(4):257–271

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Durgapur, Durgapur, West Bengal, 713209, India

    Anupam Mukherjee, Goutam Panigrahi & Samarjit Kar

  2. Department of Computer Science and Engineering, NSHM Knowledge Campus, Durgapur, West Bengal, 713212, India

    Partha Sarathi Barma

  3. Department of Computer Science, Kazi Nazrul University, Asansol, West Bengal, 713340, India

    Joydeep Dutta

  4. Department of Applied Mathematics, Vidyasagar University, Midnapore, West Bengal, 721102, India

    Manoranjan Maiti

Authors
  1. Anupam Mukherjee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Partha Sarathi Barma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Joydeep Dutta
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Goutam Panigrahi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Samarjit Kar
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Manoranjan Maiti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anupam Mukherjee.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mukherjee, A., Barma, P.S., Dutta, J. et al. A multi-objective antlion optimizer for the ring tree problem with secondary sub-depots. Oper Res Int J 22, 1813–1851 (2022). https://doi.org/10.1007/s12351-021-00623-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12351-021-00623-8

Keywords

Search

Navigation