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Breakout local search for the cyclic cutwidth minimization problem

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Abstract

The cyclic cutwidth minimization problem (CCMP) is a graph layout problem that involves embedding a graph onto a circle to minimize the maximum cutwidth of the graph. In this paper, we present breakout local search (BLS) for solving CCMP, which combines a dedicated local search procedure to discover high-quality local optimal solutions and an adaptive diversification strategy to escape from local optima. Extensive computational results on a wide set of 179 publicly available benchmark instances show that the proposed BLS algorithm has excellent performance with respect to the best-performing state-of-the-art approaches in terms of solution quality and computational time. In particular, it reports improved best-known solutions for 31 instances, while finding matching best-known results on 139 instances.

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Notes

  1. The source code will be publicly available at https://github.com/muhe2020/mu-CCMP.

References

  • Allmond, H.: On the cyclic cutwidth of complete tripartite and n-partite graphs. CSUSB REU (2006)

  • Bansal, R., Srivastava, K., Srivastava, S.: A hybrid evolutionary algorithm for the cutwidth minimization problem. In: 2012 IEEE Congress on Evolutionary Computation, pp. 1–8. IEEE (2012)

  • Benlic, U., Hao, J.-K.: A study of breakout local search for the minimum sum coloring problem. In: Asia-Pacific Conference on Simulated Evolution and Learning, pp. 128–137. Springer (2012)

  • Benlic, U., Hao, J.-K.: Breakout local search for the vertex separator problem. In: Twenty-Third International Joint Conference on Artificial Intelligence (2013)

  • Benlic, U., Hao, J.-K.: Breakout local search for maximum clique problems. Comput. Oper. Res. 40(1), 192–206 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  • Benlic, U., Hao, J.-K.: Breakout local search for the max-cut problem. Eng. Appl. Artificial Intell. 26(3), 1162–1173 (2013)

    Article  MATH  Google Scholar 

  • Benlic, U., Hao, J.-K.: Breakout local search for the quadratic assignment problem. Appl. Math. Comput. 219(9), 4800–4815 (2013)

    MathSciNet  MATH  Google Scholar 

  • Benlic, U., Burke, E.K., Woodward, J.R.: Breakout local search for the multi-objective gate allocation problem. Comput. Oper. Res. 78, 80–93 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  • Benlic, U., Epitropakis, M.G., Burke, E.K.: A hybrid breakout local search and reinforcement learning approach to the vertex separator problem. Eur. J. Oper. Res. 261(3), 803–818 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  • Cavero, S., Pardo, E.G., Laguna, M., Duarte, A.: Multistart search for the cyclic cutwidth minimization problem. Comput. Oper. Res. 126, 105116 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  • Chavez, J.D., Trapp, R.: The cyclic cutwidth of trees. Discrete Appl. Math. 87(1–3), 25–32 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  • Clarke, D.W.: The cyclic cutwidth of mesh cubes. Theses digitization project. 2329 (2002). https://scholarworks.lib.csusb.edu/etdproject/2329

  • Cohoon, J.P., Sahni, S.: Heuristics for backplane ordering. J. VLSI Comput. Syst. 2(1–2), 37–60 (1987)

    Google Scholar 

  • Díaz, J., Petit, J., Serna, M.: A survey of graph layout problems. ACM Comput. Surv. (CSUR) 34(3), 313–356 (2002)

    Article  Google Scholar 

  • El Krari, M., Ahiod, B., El Benani, B.: Breakout local search for the travelling salesman problem. Comput. Inform. 37(3), 656–672 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  • Erbele, J., Chavez, J., Trapp, R.: The cyclic cutwidth of qn. California State University, San Bernardino (2003)

    Google Scholar 

  • Fu, Z.-H., Hao, J.-K.: Breakout local search for the steiner tree problem with revenue, budget and hop constraints. Eur. J. Oper. Res. 232(1), 209–220 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  • Ghandi, S., Masehian, E.: A breakout local search (bls) method for solving the assembly sequence planning problem. Eng. Appl. Artif. Intell. 39, 245–266 (2015)

    Article  Google Scholar 

  • Glover, F., Laguna, M.: Tabu search. In: Handbook of Combinatorial Optimization, pp. 2093–2229. Springer (1998)

  • Jain, P., Srivastava, K., Saran, G.: Minimizing cyclic cutwidth of graphs using a memetic algorithm. J. Heuristics 22(6), 815–848 (2016)

    Article  Google Scholar 

  • Johnson, M.: The Linear and Cyclic Cutwidth of the Complete Bipartite Graph. Cal State Univ, San Bernardino, REU Project (2003)

    Google Scholar 

  • Lourenço, H.R., Martin, O.C., Stützle, T.: Iterated local search. In: Handbook of Metaheuristics, pp. 320–353 . Springer (2003)

  • Pantrigo, J.J., Martí, R., Duarte, A., Pardo, E.G.: Scatter search for the cutwidth minimization problem. Ann. Oper. Res. 199(1), 285–304 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Pardo, E.G., Mladenović, N., Pantrigo, J.J., Duarte, A.: Variable formulation search for the cutwidth minimization problem. Appl. Soft Comput. 13(5), 2242–2252 (2013)

    Article  MATH  Google Scholar 

  • Raspaud, A., Sỳkora, O., Vrto, I.: Congestion and dilation, similarities and differences: a survey. In: SIROCCO, pp. 269–280 (2000)

  • Resende, M.G., Martí, R., Gallego, M., Duarte, A.: Grasp and path relinking for the max-min diversity problem. Comput. Oper. Res. 37(3), 498–508 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • Schröder, H., Sỳkora, O., Vrt’o, I.: Cyclic cutwidths of the two-dimensional ordinary and cylindrical meshes. Discrete Appl. Math. 143(1–3), 123–129 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Sciortino, V., Chavez, J., Trapp, R.: The Cyclic Cutwidth of a p2\(\times \) p2\(\times \) pn Mesh. Cal State Univ, San Bernardino, REU Project (2002)

    Google Scholar 

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Acknowledgements

We are grateful to the anonymous referees for valuable suggestions and comments which helped us improve the paper. This work is partially supported by the National Natural Science Foundation Program of China [Grant No. 72122006].

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Authors and Affiliations

  1. School of Management, Huazhong University of Science and Technology, Wuhan, 430074, China

    Mu He & Qinghua Wu

  2. School of Economics and Management, Fuzhou University, Fuzhou, 350116, China

    Yongliang Lu

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  1. Mu He
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  2. Qinghua Wu
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  3. Yongliang Lu
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Correspondence to Yongliang Lu.

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Appendix

Appendix

Tables 7, 8, 9, 10, 11 and 12 give the detailed computational results of our proposed BLS algorithm compared with the MTS proposed by Cavero et al. (2021) and MA proposed by Jain et al. (2016) over the six problem groups (i.e., Small instances, Harwell_Boeing instances, Completesplit instances, Cones instances, JoinHypercubes instances, and Toroidalmesh instances) described in Sect. 4.1. The first column indicates the instance name. Columns 2-6 present detailed computational results for BLS: the best objective value (\(f_{best}\)) over 30 independent runs, the average objective value (\(f_{avg}\)) over 30 independent runs, the average computational time in seconds (t(s)), the total computational time of the 30 runs (T(s)), and the deviation of the best objective value with respect to the updated best-known objective value (Dev. (%)). Columns 7-12 show detailed computational results for the MTS and MA algorithms: the best objective value (\(f_{best}\)) over 30 independent runs, the computational time in seconds (t(s)) corresponds only to the run where the best solution was found, and the deviation of the best objective value with respect to the updated best-known objective value (Dev. (%)). The row ‘Avg.’ lists the average value of each column. The entries in bold indicate the cases where the new best-known solution is found.

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He, M., Wu, Q. & Lu, Y. Breakout local search for the cyclic cutwidth minimization problem. J Heuristics 28, 583–618 (2022). https://doi.org/10.1007/s10732-022-09504-5

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