Skip to main content
SpringerLink
Log in

Apply the quantum particle swarm optimization for the K-traveling repairman problem

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

Abstract

This paper deals with an optimization problem encountered in the field of transport of goods and services, namely the K-traveling repairman problem (K-TRP). This problem is a generalization of the metric traveling repairman problem (TRP) which is also known as the deliveryman problem and the minimum latency problem. The K-TRP and the related problems can be considered as “customer-centric” routing problems because the objectif function consists in minimize the sum of the waiting times of customers rather than the vehicles travel time. These problems are also considered as problems with “cumulative costs.” In this paper, we propose a quantum particle swarm optimization (QPSO) method to solve the K-TRP. In order to avoid the violations of problem constraints, the proposed approach also incorporates a heuristic repair operator that uses problem-specific knowledge instead of the penalty function technique commonly used for constrained problem. To the best of our knowledge, this study is the first to report on the application of the QPSO method to the K-TRP. Experimental results obtained on sets of the Capacitated Vehicle Routing Problem test instances, of up to 100 customers, available in the literature clearly demonstrate the competitiveness of the proposed method compared to the commercial MIP solver CPLEX 12.5 of IBM-ILOG and the state-of-the-art heuristic methods. The results also demonstrate that the proposed approach was able to reach more optimal solutions and to improve 5 best known solutions in a short and reasonable computation time.

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

Similar content being viewed by others

References

  • Abraham A, Guo H, Liu H (2006) Swarm intelligence: foundations, perspectives and applications. Springer, New York

    Google Scholar 

  • Afrati F, Cosmadakis S, Papadimitriou CH, Papageorgiou G, Papakostantinou N (1986) The complexity of the travelling repairman problem. RAIRO Theor Inf Appl 20(1):79–87

    Article  MathSciNet  MATH  Google Scholar 

  • Angel-Bello F, Cardona-Valdés Y, Álvarez A (2017) Mixed integer formulations for the multiple minimum latency problem. Oper Res 1–30

  • Augerat P, Corberan A, Benavent E, Belenguer J (1995) Computational results with a branch and cut code for the capacitated vehicle routing problem. Tech. Rep. RR 949-M, Université Grenoble 1. IMAG (Saint Martin d’Hères)

  • Ausiello G, Leonardi S, Marchetti-Spaccamela A (2000) On salesmen, repairmen, spiders, and other traveling agents. In: Algorithms and complexity, 4th Italian conference, CIAC 2000, Rome, Italy, March 2000, Proceedings, pp 1–16

  • Bang BH (2017) A grasp+ vnd algorithm for the multiple traveling repairman problem with distance constraints. J Comput Sci Cybern 33(3):272–288

    Article  Google Scholar 

  • Bansal S (2018) Nature-inspired-based multi-objective hybrid algorithms to find near-OGRS for optical WDM systems and their comparison. In: Handbook of research on biomimicry in information retrieval and knowledge management. IGI Global, pp 175–211, pp 175–211

  • Bansal S (2014) Optimal golomb ruler sequence generation for fwm crosstalk elimination: soft computing versus conventional approaches. Appl Soft Comput 22:443–457

    Article  MathSciNet  Google Scholar 

  • Bansal S, Singh AK, Gupta N (2017) Optimal golomb ruler sequences generation for optical wdm systems: a novel parallel hybrid multi-objective bat algorithm. J Inst Eng (India) Ser B 98(1):43–64

    Article  Google Scholar 

  • Bansal S, Gupta N, Singh AK (2017) Nature-inspired metaheuristic algorithms to find near-ogr sequences for wdm channel allocation and their performance comparison. Open Math 15(1):520–547

    Article  MathSciNet  MATH  Google Scholar 

  • Bianco L, Mingozzi A, Ricciardelli S (1993) The traveling salesman problem with cumulative costs. Networks 23(2):81–91

    Article  MathSciNet  MATH  Google Scholar 

  • Bjelić N, Vidović M, Popović D (2013) Variable neighborhood search algorithm for heterogeneous traveling repairmen problem with time windows. Expert Syst. Appl. 40(15):5997–6006

    Article  Google Scholar 

  • Blum A, Chalasani P, Coppersmith D, Pulleyblank B, Raghavan P, Sudan M (1994) The minimum latency problem. In: Proceedings of the twenty-sixth annual acm symposium on theory of computing, STOC ’94. ACM, New York, pp. 163–171

  • Bruni M, Beraldi P, Khodaparasti S (2018) A heuristic approach for the k-traveling repairman problem with profits under uncertainty. Electron Notes Discrete Math 69:221–228

    Article  MathSciNet  Google Scholar 

  • Chaudhuri K, Godfrey B, Rao S, Talwar K (2003) Paths, trees, and minimum latency tours. In: 44th symposium on foundations of computer science (FOCS 2003), 11–14 October 2003, Cambridge, MA, USA, Proceedings, pp 36–45

  • Chekuri C, Kumar A (2004) Maximum coverage problem with group budget constraints and applications. In: Approximation, randomization, and combinatorial optimization. algorithms and techniques. Springer, pp. 72–83

  • Christofides N, Eilon S (1969) An algorithm for the vehicle-dispatching problem. J Oper Res Soc 20:309–318

    Article  Google Scholar 

  • Clerc M (2006) Particle swarm optimization. ISTE Publishing Company, London

    Book  MATH  Google Scholar 

  • Conway RW, Maxwell WL, Miller LW (2003) Theory of scheduling. Dover, New York

    MATH  Google Scholar 

  • Engelbrecht AP (2005) Fundamentals of computational swarm intelligence. Wiley, Hoboken

    Google Scholar 

  • Ezzine IO, Elloumi S (2012) Polynomial formulation and heuristic based approach for the k-travelling repairman problem. IJMOR 4(5):503–514

    Article  MathSciNet  MATH  Google Scholar 

  • Fakcharoenphol J, Harrelson C, Rao S (2003) The k-traveling repairman problem. In: Proceedings of the 14th annual ACM-SIAM symposium on Discrete algorithms, pp 655–664

  • Fischetti M, Laporte G, Martello S (1993) The delivery man problem and cumulative matroids. Oper Res 41(6):1055–1064

    Article  MathSciNet  MATH  Google Scholar 

  • González F, Rivera JC (2015) A multi-start iterative local search for the k-traveling repairman problem. Technical Reports, Working paper

  • Hmayer A, Ezzine IO (2013) Clarans heuristic based approach for the k-traveling repairman problem. In: 2013 international conference on advanced logistics and transport (ICALT), pp 535–538

  • Hu W, Wang H, Qiu Z, Nie C, Yan L (2018) A quantum particle swarm optimization driven urban traffic light scheduling model. Neural Comput Appl 29(3):901–911

    Article  Google Scholar 

  • Jothi R, Raghavachari B (2007) Approximating the k-traveling repairman problem with repairtimes. J Discrete Algorithms 5(2):293–303

    Article  MathSciNet  MATH  Google Scholar 

  • Kara İ, Kara BY, Yetis MK (2008) Cumulative vehicle routing problems. Vehicle Routing Problem, pp 85–98

  • Kennedy J (1999) Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance. In: Proceedings of the 1999 congress on evolutionary computation, 1999. CEC 99, vol 3, pp 1938

  • Kennedy J (2000) Stereotyping: improving particle swarm performance with cluster analysis. In: Proceedings of the 2000 congress on evolutionary computation, vol 2, pp 1507–1512

  • Kennedy J (2003) Bare bones particle swarms. In: Proceedings of the 2003 swarm intelligence symposium. IEEE, pp 80–87

  • Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the 1995 IEEE international conference on neural networks, vol 4, pp 1942–1948

  • Kennedy J, Eberhart R (1997) A discrete binary version of the particle swarm algorithm. In: Proceedings of the 1997 IEEE international conference on computational cybernetics and simulation, vol 5, pp 4104–4108

  • Khanesar MA, Teshnehlab M, Shoorehdeli MA (2007) A novel binary particle swarm optimization. In: Mediterranean conference on control & automation, 2007. MED’07. IEEE, pp 1–6

  • Krohling RA, dos Santos Coelho L (2006) PSO-E: particle swarm with exponential distribution. In: IEEE congress on evolutionary computation, 2006. CEC 2006. IEEE, pp 1428–1433

  • Langeveld J, Engelbrecht AP (2012) Set-based particle swarm optimization applied to the multidimensional knapsack problem. Swarm Intell 6(4):297–342

    Article  Google Scholar 

  • Luo Z, Qin H, Lim A (2014) Branch-and-price-and-cut for the multiple traveling repairman problem with distance constraints. Eur J Oper Res 234(1):49–60

    Article  MathSciNet  MATH  Google Scholar 

  • Mohais A, Mendes R, Ward C, Posthoff C (2005) Neighborhood restructuring in particle swarm optimization. In: Proceedings of the 2005 advances in artificial intelligence, vol 3809. Lecture notes in computer science. Springer, pp. 776–785

  • Mousavi SM, Bahreininejad A, Musa SN, Yusof F (2017) A modified particle swarm optimization for solving the integrated location and inventory control problems in a two-echelon supply chain network. J Intell Manuf 28(1):191–206

    Article  Google Scholar 

  • Nezamabadi-pour H, Rostami Shahrbabaki M, Maghfoori-Farsangi M (2008) Binary particle swarm optimization: challenges and new solutions. CSI J Comput Sci Eng Persian 6(1):21–32

    Google Scholar 

  • Ngueveu SU, Prins C, Calvo RW (2010) An effective memetic algorithm for the cumulative capacitated vehicle routing problem. Comput Oper Res 37(11):1877–1885

    Article  MathSciNet  MATH  Google Scholar 

  • Nucamendi-Guillén S, Martínez-Salazar I, Angel-Bello F, Moreno-Vega MJ (2016) A mixed integer formulation and an efficient metaheuristic procedure for the k-travelling repairmen problem. J Oper Res Soc 67(8):1121–1134

    Article  Google Scholar 

  • Onder G (2015) New decision models for multiple traveling minimum latency problem. Master’s thesis, Baskent University Institute of Science and Engineering, Ankara

  • Onder G, Kara I, Derya T (2017) New integer programming formulation for multiple traveling repairmen problem. Transport Res Proc 22:355–361

    Article  Google Scholar 

  • Pampara G, Franken N, Engelbrecht AP (2005) Combining particle swarm optimisation with angle modulation to solve binary problems. In: The 2005 IEEE congress on evolutionary computation, 2005, vol 1. IEEE, pp 89–96

  • Parrott D, Li X (2006) Locating and tracking multiple dynamic optima by a particle swarm model using speciation. IEEE Trans Evol Comput 10(4):440–458

    Article  Google Scholar 

  • Rehman OU, Tu S, Khan S, Khan H, Yang S (2018) A modified quantum particle swarm optimizer applied to optimization design of electromagnetic devices. Int J Appl Electromagn Mech 56:1–11

    Article  Google Scholar 

  • Sahni S, Gonzalez T (1976) P-complete approximation problems. J. ACM 23(3):555–565

    Article  MathSciNet  MATH  Google Scholar 

  • Simchi-Levi D, Berman O (1991) Minimizing the total flow time of n jobs on a network. IIE Trans 23(3):236–244

    Article  Google Scholar 

  • Singh MR, Mahapatra SS (2016) A quantum behaved particle swarm optimization for flexible job shop scheduling. Comput Ind Eng 93:36–44

    Article  Google Scholar 

  • Sun J, Feng B, Xu W (2004) Particle swarm optimization with particles having quantum behavior. In: Proceedings of the 2004 congress on evolutionary computation, vol. 1, pp 325–331

  • Sun J, Xu W, Feng B (2004) A global search strategy of quantum-behaved particle swarm optimization. In: Proceedings of the 2004 IEEE conference on cybernetics and intelligent systems, vol 1, pp 111–116

  • Yang S, Wang M, Jiao L (2004) A quantum particle swarm optimization. In: Proceedings of the 2004 congress IEEE conference on evolutionary computation, vol 1, pp 320–324

  • Yao B, Yu B, Hu P, Gao J, Zhang M (2016) An improved particle swarm optimization for carton heterogeneous vehicle routing problem with a collection depot. Ann Oper Res 242(2):303–320

    Article  MathSciNet  MATH  Google Scholar 

  • Zandi F, Tavana M (2010) An optimisation model for traffic distribution forecasting in packet-switching networks. IJMOR 2:515–539

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors thank the anonymous referees for their helpful comments and suggestions which contributed to the improvement in the contents and the presentation of this paper.

Author information

Authors and Affiliations

  1. Université de Sfax, Institut Supérieur de Gestion Industrielle de Sfax, LOGIQ, UR13ES71, 3021, Sfax, Tunisia

    Sirine Jmal & Boukthir Haddar

  2. College of Business, Al Ain University of Science and Technology, Abu Dhabi, UAE

    Habib Chabchoub

Authors
  1. Sirine Jmal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Boukthir Haddar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Habib Chabchoub
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Boukthir Haddar.

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.

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

Jmal, S., Haddar, B. & Chabchoub, H. Apply the quantum particle swarm optimization for the K-traveling repairman problem. Soft Comput 23, 12547–12560 (2019). https://doi.org/10.1007/s00500-019-03805-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-019-03805-x

Keywords

Search

Navigation