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Memetic algorithm based on extension step and statistical filtering for large-scale capacitated arc routing problems

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Abstract

The capacitated arc routing problem (CARP) is a classical NP-Hard combinatorial optimization problem. In this paper, we present a memetic algorithm based on Extension step and Statistical filtering for Large-Scale CARP (ESMAENS) which has improvements in both the global search strategy and the local search strategy. Firstly, ESMAENS adopts the Route Distance Grouping decomposition scheme (RDG) to decompose the large-scale CARP into some independent sub-problems. Then, the initial population would evolve into a new group by using the Evolutionary Algorithm. Furthermore, ESMAENS introduces the extension step search strategy to search the potential solutions around the current solution. As a result, with the increase of the iteration number, it avoids getting to the premature convergence. Meanwhile, the diversity of the population can be increased. Finally, in the local search strategy, the statistical filter is used to filter out some solutions and make the algorithm get the lower bound at a faster convergence rate with a high stability. Compared with RDG-MAENS, experimental results on Beullen’C, D, E, F, egl and EGL-G test set show that ESMAENS has a better convergence rate, and the stability of solutions obtained is improved. Furthermore, ESMAENS achieves a global search for the solutions. Especially for the large-scale EGL-G test set, ESMAENS can converge to a lower bound at a faster convergence rate, and it is suitable for solving large-scale CARP.

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References

  • Ahr D (2004) Contributions to multiple postmen problems. PHD thesis, Rupercht -Karls-Universitat, Heidelberg

  • Arpaia P, Maisto D, Manna C (2011) A quantum-inspired evolutionary algorithm with a competitive variation operator for multiple-fault diagnosis. Appl Soft Comput 11:4655–4666

    Article  Google Scholar 

  • Baldacci R, Maniezzo V (2006) Exact methods based on node routing formulations for arc routing problems. Networks 47:52–60

    Article  MathSciNet  MATH  Google Scholar 

  • Bektas T, Elmastas S (2007) Solving school bus routing problems through integer programming. J Oper Res Soc 58(12):1599–1604

    Article  MATH  Google Scholar 

  • Belenguer JM, Benavent E (2003) A cutting plane algorithm for the capacitated arc routing problem. Comput Oper Res 30(5):705–728

    Article  MathSciNet  MATH  Google Scholar 

  • Benavent E, Campos V, Corberan A, Mota E (1990) The capacitated arc routing problem. a heuristic algorithm. Qiiestiio 14(1–3):107–122

    MathSciNet  MATH  Google Scholar 

  • Benavent E, Campos V, Corberan A, Mota E (1992) The capacitated arc routing problem: lower bounds. Networks 22:669–690

    Article  MathSciNet  MATH  Google Scholar 

  • Beullens P, Muyldermans L, Cattrysse D, Oudheusden DV (2003) A guided local search heuristic for the capacitated arc routing problem. Eur J Oper Res 147(3):629–643

    Article  MathSciNet  MATH  Google Scholar 

  • Bianchi L, Dorigo M, Gambardella LM, Gutjahr WJ (2009) A survey on metaheuristics for stochastic combinatorial optimization. Nat Comput 8(2):239–287

    Article  MathSciNet  MATH  Google Scholar 

  • Brand˜ao J, Eglese R (2008) A deterministic tabu search algorithm for the capacitated arc routing problem. Comput Oper Res 35(4):112–1126

    MathSciNet  Google Scholar 

  • Campbell JF, Langevin A (2000) Roadway snow and ice control. Arc routing: theory, solutions and applications. Kluwer, Boston, pp 389–418

    Book  MATH  Google Scholar 

  • Doerner KF, Hartl RF, Maniezzo V, Reimann M (2004) Applying ant colony optimization to the capacitated arc routing problem. Soft Comput 3172:420–421

    Google Scholar 

  • Goh CK, Ong YS, Tan KC (2009) Multi-objective memetic algorithms. Springer, Berlin

    Book  MATH  Google Scholar 

  • Golden BL, Wong RT (1981) Capacitated arc routing problems. Networks 11(3):305–316

    Article  MathSciNet  MATH  Google Scholar 

  • Golden BL, DeArmon JS, Baker EK (1983) Computational experiments with algorithms for a class of routing Problems. Comput Oper Res 10(1):47–59

    Article  MathSciNet  Google Scholar 

  • Grover LK (1996) A fast quantum mechanical algorithm for database search. In: Proceeding of the 28th acm symposium on theory of computing, pp. 212–219

  • Handa H, Chapman L, Yao X (2006) Robust salting route optimization using evolutionary algorithms. In: Proceedings of the 2006 IEEE congress on evolutionay computation, vol. 1, pp. 10455–10456

  • Handa H, Chapman L, Yao X (2006b) Robust route optimization for gritting/salting trucks: a CERCIA experienee. IEEE Comput Intell Mag 1(1):6–9

    Article  Google Scholar 

  • Hertz A, Mittaz M (2001) A variable neighborhood descent algorithm for the undirected capacitated arc routing problem. Trans Sci 35(4):425–434

    Article  MATH  Google Scholar 

  • Hertz A, Laporte G, Mittaz M (2000) A tabu search heuristic for the capacitated arc routing problem. Oper Res 48(1):129–135

    Article  MathSciNet  MATH  Google Scholar 

  • Keskin ME, Altinel iK, Aras N (2015) Combining simulated annealing with Lagrangian relaxation and weighted Dantzig-Wolfe decomposition for integrated design decisions in wireless sensor. Comput Oper Res 59:132–143

    Article  MathSciNet  MATH  Google Scholar 

  • Lacomme P, Prins C, Ramdane-Cherif W (2001) A genetic algorithm for the capacitated arc routing problem and its extensions. In: Proceedings of evolutionary workshops on application evolutionary computation Como, pp. 473–483

  • Lacomme P, Prins C, Ramdane-Cherif W (2004) Competitive memetic algorithms for arc routing problem. Ann Oper Res 131(1–4):159–185

    Article  MathSciNet  MATH  Google Scholar 

  • Lacomme P, Prins C, Sevaux M (2006) A genetic algorithm for a bi-objective capacitated arc routing problem. Comput Oper Res 33:3473–3493

    Article  MATH  Google Scholar 

  • Le MN, Ong YS, Jin Y, Sendhoff B (2009) Lamarckian memetic algorithms: local optimum and connectivity structure analysis. Meme Comput J 1(3):175–190

    Article  Google Scholar 

  • Li YY, He HY, Wang Y, Xu X, Jiao LC (2015) An improved multiobjective estimation of distribution algorithm for environmental economic dispatch of hydrothermal power systems. Appl Soft Comput 28:559–568

    Article  Google Scholar 

  • Longo H, De Aragao MP, Uchoa E (2006) Solving capacitated arc routing problems using a transformation to the CARP. Comput Oper Res 33(6):1823–1837

    Article  MATH  Google Scholar 

  • Marinakis Y, Marinaki M, Dounias G (2010) Honey bees mating optimization algorithm for large scale vehicle routing problems. Nat Comput 9(1):5–27

    Article  MathSciNet  MATH  Google Scholar 

  • Mei Y, Tang K, Yao X (2009) Improved memetic algorithm for capacitated arc routing problem. In: Proceedings of the 2009 IEEE congress on evolutionary computation, pp. 1699-1706

  • Mei Y, Tang K, Yao X (2011a) Decomposition-based memetic algorithm for multi-objective capacitated arc routing problems. IEEE Trans Evol Comput 15(2):151–165

    Article  Google Scholar 

  • Mei Y, Tang K, Yao X (2011b) A memetic algorithm for periodic capacitated arc routing problem. IEEE Trans Syst Man Cybern 41(6):1654–1667

    Article  Google Scholar 

  • Mei Y, Li X D, Yao X (2013) Decomposing large-scale capacitated arc routing problems using a random route grouping method. In: Proceedings of the 2013 IEEE congress on evolutionary computation (CEC2013), Cancun, Mexico: pp. 20–23

  • Mei Y, Tang K, Yao X (2013b) Evolutionary computation for dynamic capacitated arc routing problem. Soft Comput 490:377–401

    Google Scholar 

  • Mei Y, Li XD, Yao X (2014) Cooperative co-evolution with route distance grouping for large-scale capacitated arc routing problems. IEEE Trans Evol Comput 18(3):435–449

    Article  Google Scholar 

  • Mourão MC, Nunes AC, Prins C (2009) Heuristic methods for the sectoring arc routing problem. Eur J Oper Res 196(3):856–868

    Article  MATH  Google Scholar 

  • Muyldermans L, Cattrysse D, VanOudheusden D, Lotan T (2002) Districting for salt spreading operations. Eur J Oper Res 139(3):521–532

    Article  MATH  Google Scholar 

  • Omidvar MN, Li XD, Mei Y, Yao X (2014) Cooperative co-evolution with differential grouping for large scale optimization. IEEE Trans Evol Comput 18(3):378–393

    Article  Google Scholar 

  • Prais M, Ribeiro CC (2000) Reactive GRASP: an application to a matrix decomposition problem in TDMA traffic assignment. INFORMS J Comput 12:164–176

    Article  MathSciNet  MATH  Google Scholar 

  • Resende MGC, Ribeiro CC (2005) GRASP with path-relinking: recent advances and applications. In: Meta-heuristics: progress as real problem solvers, Springer, Berlin, pp. 29–63

  • Santos L, Coutinho-Rodrigues J, Current JR (2009) An improved heuristic for the capacitated arc routing problem. Comput Oper Res 36:2632–2637

    Article  MathSciNet  MATH  Google Scholar 

  • Shang RH, Jiao LC, Liu F, Ma WP (2012) A Novel Immune Clonal Algorithm for MO Problems. IEEE Trans Evol Comput 16(1):35–49

    Article  Google Scholar 

  • Shang RH, Wang J, Jiao LC, Wang YY (2014a) An improved decomposition-based memetic algorithm for multi-objective capacitated arc routing problem. Appl Soft Comput 19:343–361

    Article  Google Scholar 

  • Shang RH, Wang YY, Wang J, Jiao LC, Wang S, Qi LP (2014b) A multi-population cooperative coevolutionary algorithm for multi-objective capacitated arc routing problem. Inf Sci 27(7):609–642

    Article  MathSciNet  MATH  Google Scholar 

  • Shang RH, Jiao LC, Ren YJ, Wang J, Li YY (2014c) Immune clonal coevolutionary algorithm for dynamic multiobjective optimization. Nat Comput 13(3):421–445

    Article  MathSciNet  MATH  Google Scholar 

  • Shang RH, Dai KY, Jiao LC, Stolkin R (2016) Improved memetic algorithm based on route distance grouping for multi-objective large scale capacitated arc routing problems. IEEE Trans Cybern 6(4):1000–1013

    Article  Google Scholar 

  • Shen XN, Yao X (2015) Mathematical modeling and multi-objective evolutionary algorithms applied to dynamic flexible job shop scheduling problems. Inf Sci 298(3):198–224

    Article  MathSciNet  Google Scholar 

  • Shen J, Tan HW, Wang J, Wang JW, Lee SY (2015) A novel routing protocol providing good transmission reliability in underwater sensor networks. J Internet Technol 16(1):171–178

    Google Scholar 

  • Tang K, Mei Y, Yao X (2009) Memetic algorithm with extended neighborhood search for capacitated arc routing problems. IEEE Trans Evol Comput 13(5):1151–1166

    Article  Google Scholar 

  • Tang K, Wang J, Li X, Yao X (2016) A scalable approach to capacitated arc routing problems based on hierarchical decomposition. IEEE Trans Cybern. doi:10.1109/TCYB.2016.2590558

    Google Scholar 

  • Ulusoy G (1985) The fleet size and mix problem for capacitated arc routing. Eur J Oper Res 22(3):329–337

    Article  MathSciNet  MATH  Google Scholar 

  • Villegas JG, Prins C, Prodhon C, Medaglia AL, Velasco N (2011) A GRASP with evolutionary path relinking for the truck and trailer routing problem. Comput Oper Res 38(13):19–34

    MATH  Google Scholar 

  • Wang J, Tang K, Lozano JA, Yao X (2016) Estimation of the distribution algorithm with a stochastic local search for uncertain capacitated arc routing problems. IEEE Trans Evol Comput 20(1):96–109

    Article  Google Scholar 

  • Wen XZ, Shao L, Xue Y, Fang W (2015) A rapid learning algorithm for vehicle classification. Inf Sci 295(1):395–406

    Article  Google Scholar 

  • Xia ZH, Wang XH, Sun XM, Wang Q (2015) A secure and dynamic multi-keyword ranked search scheme over encrypted cloud data. IEEE Trans Parallel Distrib Syst 27(2):340–352

    Article  Google Scholar 

  • Zheng YH, Jeon B, Xu DH, Wu QMJ, Zhang H (2015) Image segmentation by generalized hierarchical fuzzy C-means algorithm. J Intell Fuzzy Syst 28(2):961–973

    Google Scholar 

Download references

Acknowledgements

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. This work was partially supported by the National Basic Research Program (973 Program) of China under Grant 2013CB329402, the National Natural Science Foundation of China, under Grants 61371201, 61203303 and 61272279, the Program for Cheung Kong Scholars and Innovative Research Team in University under Grant IRT1170, and the EU FP7project (Grant No. 247619) on “NICaiA: Nature Inspired Computation and its Applications”.

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Authors and Affiliations

  1. Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of China, Xidian University, Xi’an, 710071, China

    Ronghua Shang, Bingqi Du, Kaiyun Dai & Licheng Jiao

  2. School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing, China

    Yu Xue

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  1. Ronghua Shang
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  2. Bingqi Du
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  3. Kaiyun Dai
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Correspondence to Ronghua Shang.

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Shang, R., Du, B., Dai, K. et al. Memetic algorithm based on extension step and statistical filtering for large-scale capacitated arc routing problems. Nat Comput 17, 375–391 (2018). https://doi.org/10.1007/s11047-016-9606-x

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