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

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## 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.

## Keywords

Combinatorial optimization*K*-traveling repairman problem Quantum particle swarm optimization Repair operator

## Notes

### 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.

### Compliance with ethical standards

### 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.

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