Memetic Computing

, Volume 10, Issue 1, pp 81–102 | Cite as

Quantum-Inspired Immune Clonal Algorithm for solving large-scale capacitated arc routing problems

  • Ronghua Shang
  • Bingqi Du
  • Kaiyun Dai
  • Licheng Jiao
  • Amir M. Ghalamzan Esfahani
  • Rustam Stolkin
Regular Research Paper


In this paper, we present an approach to Large-Scale CARP called Quantum-Inspired Immune Clonal Algorithm (QICA-CARP). This algorithm combines the feature of artificial immune system and quantum computation ground on the qubit and the quantum superposition. We call an antibody of population quantum bit encoding, in QICA-CARP. For this encoding, to control the population with a high probability evolution towards a good schema we use the information on the current optimal antibody. The mutation strategy of quantum rotation gate accelerates the convergence of the original clone operator. Moreover, quantum crossover operator enhances the exchange of information and increases the diversity of the population. Furthermore, it avoids falling into local optimum. We also use the repair operator to amend the infeasible solutions to ensure the diversity of solutions. This makes QICA-CARP approximating the optimal solution. We demonstrate the effectiveness of our approach by a set of experiments and by Comparing the results of our approach with ones obtained with the RDG-MAENS and RAM using different test sets. Experimental results show that QICA-CARP outperforms other algorithms in terms of convergence rate and the quality of the obtained solutions. Especially, QICA-CARP converges to a better lower bound at a faster rate illustrating that it is suitable for solving large-scale CARP.


Large-scale CARP Quantum rotation gate Quantum crossover operator The repair operator 



We would like to express our sincere appreciation to the editors and the anonymous reviewers for their insightful comments, which have greatly helped us in improving the quality of the paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Ronghua Shang
    • 1
  • Bingqi Du
    • 1
  • Kaiyun Dai
    • 1
  • Licheng Jiao
    • 1
  • Amir M. Ghalamzan Esfahani
    • 2
  • Rustam Stolkin
    • 2
  1. 1.Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of ChinaXidian UniversityXi’anChina
  2. 2.Extreme Robotics LabUniversity of BirminghamEdgbaston, BirminghamUK

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