Skip to main content
SpringerLink
Log in

Solving travelling salesman problem using black hole algorithm

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Over the last few decades, many nature-inspired algorithms have been proposed for solving complex and difficult problems. Each algorithm has its own merits and drawbacks. One of the most recent nature-inspired algorithms, which has been applied successfully in many applications, is black hole (BH) algorithm. BH algorithm is a population-based meta-heuristic algorithm that is inspired by the black hole phenomenon. It starts with a random population of solutions to the given optimization problem. The most excellent solution at each iteration which has the best fitness is chosen to be the black hole and the other form the stars. The black hole pulls the stars towards it and causes them to search the problem space for finding optimal solution. In this paper, the application of the BH algorithm on solving travelling salesman problem (TSP) is investigated. The aim of TSP is to find a tour in a set of cities in such a way, each city is visited exactly once and return to the starting city where the length of the tour is minimized. In order to evaluate the efficiency of the BH algorithm, it has been tested on several benchmark data sets and compared to other well-known algorithms. The experimental results show that the BH algorithm can find high-quality solutions compared to genetic algorithm, ant colony optimization and particle swarms optimization algorithms. Moreover, the BH algorithm is faster than other test algorithms.

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

Similar content being viewed by others

References

  • Adham MT, Bentley PJ (2014) An artificial ecosystem algorithm applied to the travelling salesman problem. In: Proceedings of the 2014 conference companion on Genetic and evolutionary computation companion. ACM

  • Ahmed ZH (2014) Improved genetic algorithms for the travelling salesman problem. Int J Process Manag Benchmark 4(1):109–124

    Article  MathSciNet  Google Scholar 

  • Baltz A et al (2014) Exact and heuristic algorithms for the Travelling salesman problem with multiple time windows and hotel selection. J Oper Res Soc 66(4):615–626

    Article  Google Scholar 

  • Battarra M et al (2014a) Exact algorithms for the traveling salesman problem with draft limits. Eur J Oper Res 235(1):115–128

    Article  MathSciNet  Google Scholar 

  • Bouchekara H (2014a) Optimal power flow using black-hole-based optimization approach. Appl Soft Comput 24:879–888

    Article  Google Scholar 

  • Bouchekara H (2014b) Optimal design of electromagnetic devices using a black-hole-based optimization technique. IEEE Trans Magn 49(12):5709–5714

    Article  Google Scholar 

  • Changdar C, Mahapatra GS, Pal R Kumar (2014) An efficient genetic algorithm for multi-objective solid travelling salesman problem under fuzziness. Swarm Evol Comput 15:27–37

    Article  Google Scholar 

  • Dorigo M, Blum C (2005) Ant colony optimization theory: a survey. Theor Comput Sci 344(2–3):243–278

    Article  MathSciNet  Google Scholar 

  • Elloumi W et al (2014) A comparative study of the improvement of performance using a PSO modified by ACO applied to TSP. Appl Soft Comput 25:234–241

    Article  Google Scholar 

  • Escario JB, Jimenez JF, Giron-Sierra JM (2015) Ant colony extended: experiments on the travelling salesman problem. Expert Syst Appl 42(1):390–410

    Article  Google Scholar 

  • Fei T et al (2014) The artificial fish swarm algorithm to solve traveling salesman problem. In: Proceedings of international conference on computer science and information technology. Springer, New Delhi. doi:10.1007/978-81-322-1759-6_78

    Google Scholar 

  • Hatamlou A (2017) A hybrid bio-inspired algorithm and its application. Appl Intell. doi:10.1007/s10489-017-0951-y

    Article  Google Scholar 

  • Hatamlou A (2013) Black hole: a new heuristic optimization approach for data clustering. Inf Sci 222:175–184

    Article  MathSciNet  Google Scholar 

  • Hatamlou A (2014) Heart: a novel optimization algorithm for cluster analysis. Progr Artif Intell 2(2–3):167–173

    Article  Google Scholar 

  • Hatamlou A, Ghaniyarlou E (2016) Solving knapsack problems using heart algorithm. Int J Artif Intell Soft Comput 5(4):285–293

    Article  Google Scholar 

  • Hatamlou A, Hatamlou M (2013) PSOHS: an efficient two-stage approach for data clustering. Memet Comput 5(2):155–161

    Article  Google Scholar 

  • Hatamlou A, Hatamlou M (2013) Hybridization of the gravitational search algorithm and big bang-big crunch algorithm for data clustering. Fund Inf 126(4):319–333

    MathSciNet  Google Scholar 

  • Hatamlou A, Abdullah S, Nezamabadi-pour H (2011) Application of gravitational search algorithm on data clustering, rough sets and knowledge technology. Springer, Berlin

    Google Scholar 

  • Hatamlou A, Abdullah S, Nezamabadi-pour H (2012) A combined approach for clustering based on K-means and gravitational search algorithms. Swarm Evolut Comput 6:47–52

    Article  Google Scholar 

  • Hatamlou A, Abdullah S, Hatamlou M (2011) Data clustering using big bang-big crunch algorithm. In: Communications in computer and information science, pp 383–388

    Google Scholar 

  • Hatamlou A, Abdullah S, Othman Z (2011) Gravitational search algorithm with heuristic search for clustering problems. In: 3rd conference on data mining and optimization (DMO)

  • Heidari AA, Abbaspour RA (2014) Improved black hole algorithm for efficient low observable UCAV path planning in constrained aerospace. Adv Comput Sci Int J 3(3):87–92

    Google Scholar 

  • Hoffman KL, Padberg M, Rinaldi G (2013) Traveling salesman problem. In: Encyclopedia of operations research and management science. Springer, Berlin. pp 1573–1578

    Chapter  Google Scholar 

  • Hoos HH, Stützle T (2014) On the empirical scaling of run-time for finding optimal solutions to the travelling salesman problem. Eur J Oper Res 238(1):87–94

    Article  MathSciNet  Google Scholar 

  • Hougardy S, Wilde M (2014) On the nearest neighbor rule for the metric traveling salesman problem. Discrete Appl Math 195(2015):101–103

    MathSciNet  MATH  Google Scholar 

  • Jones J, Adamatzky A (2014) Computation of the travelling salesman problem by a shrinking blob. Nat Comput 13(1):1–16

    Article  MathSciNet  Google Scholar 

  • Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim 39(3):459–471

    Article  MathSciNet  Google Scholar 

  • Karabulut K, Tasgetiren M Fatih (2014) A variable iterated greedy algorithm for the traveling salesman problem with time windows. Inf Sci 279:383–395

    Article  MathSciNet  Google Scholar 

  • Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE international conference on neural networks: proceedings

  • Leardi R et al (2009) Genetic algorithms. In: Comprehensive chemometrics. Elsevier, Oxford, pp 631–653

    Chapter  Google Scholar 

  • Lenin K, Reddy BR, Kalavathi MS (2014) Black hole algorithm for solving optimal reactive power dispatch problem. Int J Res Manag Sci Technol 2:2321–3264

    Google Scholar 

  • Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  • Mohemmed AW, Sahoo NC, Geok TK (2008) Solving shortest path problem using particle swarm optimization. Appl Soft Comput 8(4):1643–1653

    Article  Google Scholar 

  • Ouaarab A, Ahiod Bd, Yang X-S (2014) Discrete cuckoo search algorithm for the travelling salesman problem. Neural Comput Appl 24(7–8):1659–1669

    Article  Google Scholar 

  • Ouaarab A, Ahiod Bd, Yang XS (2014) Improved and discrete cuckoo search for solving the travelling salesman problem. In: Cuckoo search and firefly algorithm. Springer, Berlin, pp 63–84

    Google Scholar 

  • Rajabioun R (2011) Cuckoo optimization algorithm. Appl Soft Comput 11(8):5508–5518

    Article  Google Scholar 

  • Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248

    Article  Google Scholar 

  • Sahana SK, Jain A (2014) High performance ant colony optimizer (HPACO) for travelling salesman problem (TSP). In: Tan Y, Shi Y, Coello CAC (eds) Advances in swarm intelligence. Springer, Berlin, pp 165–172

    Google Scholar 

  • Semwal VB et al (2015) Biologically-inspired push recovery capable bipedal locomotion modeling through hybrid automata. Robot Auton Syst 70:181–190

    Article  Google Scholar 

  • Semwal VB, Chakraborty P, Nandi GC (2015) Less computationally intensive fuzzy logic (type-1)-based controller for humanoid push recovery. Robot Auton Syst 63:122–135

    Article  Google Scholar 

  • Semwal VB, Mondal K, Nandi GC (2017) Robust and accurate feature selection for humanoid push recovery and classification: deep learning approach. Neural Comput Appl 28(3):565–574

    Article  Google Scholar 

  • Uchida A, Ito Y, Nakano K (2014) Accelerating ant colony optimisation for the travelling salesman problem on the GPU. Int J Parallel Emerg Distrib Syst 29(4):401–420

    Article  Google Scholar 

  • Vallade B, Nakashima T (2014) Improving particle swarm optimization algorithm and its application to physical travelling salesman problems with a dynamic search space. In: Lee R (ed) Applied computing and information technology. Springer, Berlin, pp 105–119

    Chapter  Google Scholar 

  • Verma OP, Jain R, Chhabra V (2014) Solution of travelling salesman problem using bacterial foraging optimisation algorithm. Int J Swarm Intell 1(2):179–192

    Article  Google Scholar 

  • Wang Y (2014) The hybrid genetic algorithm with two local optimization strategies for traveling salesman problem. Comput Ind Eng 70:124–133

    Article  Google Scholar 

  • Wang P, Sanin C, Szczerbicki E (2015) Evolutionary algorithm and decisional DNA for multiple travelling salesman problem. Neurocomputing 150:50–57

    Article  Google Scholar 

  • Yang XS (2010) Nature-inspired metaheuristic algorithms. Luniver Press, Bristol

    Google Scholar 

  • Zong D, Wang K (2014) Hybrid nested partitions method for the traveling salesman problem. In: Wen Z, Li T (eds) Foundations of intelligent systems. Springer, Berlin, pp 55–67

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Khoy Branch, Islamic Azad University, Khoy, Iran

    Abdolreza Hatamlou

Authors
  1. Abdolreza Hatamlou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abdolreza Hatamlou.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

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

Additional information

Communicated by V. Loia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hatamlou, A. Solving travelling salesman problem using black hole algorithm. Soft Comput 22, 8167–8175 (2018). https://doi.org/10.1007/s00500-017-2760-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-017-2760-y

Keywords

Search

Navigation