Skip to main content
Log in

An efficient scenario penalization matheuristic for a stochastic scheduling problem

  • Published:
Journal of Heuristics Aims and scope Submit manuscript

Abstract

We propose a new scenario penalization matheuristic for a stochastic scheduling problem based on both mathematical programming models and local search methods. The application considered is an NP-hard problem expressed as a risk minimization model involving quantiles related to value at risk which is formulated as a non-linear binary optimization problem with linear constraints. The proposed matheuritic involves a parameterization of the objective function that is progressively modified to generate feasible solutions which are improved by local search procedure. This matheuristic is related to the ghost image process approach by Glover (Comput Oper Res 21(8):801–822, 1994) which is a highly general framework for heuristic search optimization. This approach won the first prize in the senior category of the EURO/ROADEF 2020 challenge. Experimental results are presented which demonstrate the effectiveness of our approach on large instances provided by the French electricity transmission network RTE.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Benati, S., Rizzi, R.: A mixed integer linear programming formulation of the optimal mean/value-at-risk portfolio problem. Eur. J. Oper. Res. 176(1), 423–434 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Buljubašić, M., Vasquez, M., Gavranović, H.: Two-phase heuristic for SNCF rolling stock problem. Ann. Oper. Res. 271(2), 1107–1129 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  • Cattaruzza, D., Labbé, M., Petris, M., Roland, M., Schmidt, M.: Exact and heuristic solution techniques for mixed-integer quantile minimization problems (2022)

  • Crainic, T.G., Gendron, B., Hernu, G.: A slope scaling/Lagrangean perturbation heuristic with long-term memory for multicommodity capacitated fixed-charge network design. J. Heuristics 10(5), 525–545 (2004)

    Article  MATH  Google Scholar 

  • Crognier, G., Tournebise, P., Ruiz, M., Panciatici, P.: Grid operation-based outage maintenance planning. Electric Power Syst. Res. 190 (2021)

  • Di Gaspero, L., Schaerf, A.: Neighborhood portfolio approach for local search applied to timetabling problems. J. Math. Model. Algorithms 5(1), 65–89 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Froger, A., Gendreau, M., Mendoza, J.E., Pinson, E., Rousseau, L.-M.: Maintenance scheduling in the electricity industry: a literature review. Eur. J. Oper. Res. 251(3), 695–706 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  • Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Comput. Math. Appl. 2(1), 17–40 (1976)

    Article  MATH  Google Scholar 

  • Gavranović, H., Buljubašić, M.: An efficient local search with noising strategy for google machine reassignment problem. Ann. Oper. Res. 242(1), 19–31 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  • Gendron, B., Potvin, J.-Y., Soriano, P.: A Tabu search with slope scaling for the multicommodity capacitated location problem with balancing requirements. Ann. Oper. Res. 122(1), 193–217 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • Gendron, B., Hanafi, S., Todosijević, R.: Matheuristics based on iterative linear programming and slope scaling for multicommodity capacitated fixed charge network design. Eur. J. Oper. Res. 268(1), 70–81 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  • Glover, F.: Optimization by ghost image processes in neural networks. Comput. Oper. Res. 21(8), 801–822 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  • Glover, F.: Parametric ghost image processes for fixed-charge problems: a study of transportation networks. J. Heuristics 11(4), 307–336 (2005)

    Article  Google Scholar 

  • Glover, F., Laguna, M.: Tabu Search. Kluwer Academic Publishers, Boston (1997)

    Book  MATH  Google Scholar 

  • Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de dirichlet non linéaires. Revue française d’automatique, informatique, recherche opérationnelle. Analyse numérique 9(R2), 41–76 (1975)

  • Gouvine, G.: Mixed-integer programming for the ROADEF/EURO 2020 challenge. arXiv preprint arXiv:2111.01047 (2021)

  • Hanafi, S., Todosijević, R.: Mathematical programming based heuristics for the 0–1 MIP: a survey. J. Heuristics 23(4), 165–206 (2017)

    Article  MATH  Google Scholar 

  • Hansen, N., Müller, S.D., Koumoutsakos, P.: Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol. Comput. 11(1), 1–18 (2003)

    Article  Google Scholar 

  • Hansen, P., Mladenović, N., Todosijević, R., Hanafi, S.: Variable neighborhood search: basics and variants. EURO J. Comput. Optim. 5(3), 423–454 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  • Hashimoto, H., Boussier, S., Vasquez, M., Wilbaut, C.: A grasp-based approach for technicians and interventions scheduling for telecommunications. Ann. Oper. Res. 183(1), 143–161 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Hoos, H.H., Stützle, T.: Stochastic Local Search: Foundations and Applications. Elsevier, Amsterdam (2004)

    MATH  Google Scholar 

  • Jorion, P.: Value at Risk: The New Benchmark for Controlling Market Risk, vol. 2. McGraw-Hill, New York (1997)

    Google Scholar 

  • Kim, D., Pardalos, P.M.: A solution approach to the fixed charge network flow problem using a dynamic slope scaling procedure. Oper. Res. Lett. 24(4), 195–203 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  • Kohonen, T.: Self Organization and Associative Memory. Springer, Berlin (1988)

    Book  MATH  Google Scholar 

  • Lü, Z., Hao, J.-K., Glover, F.: Neighborhood analysis: a case study on curriculum-based course timetabling. J. Heuristics 17(2), 97–118 (2011)

    Article  Google Scholar 

  • Markowitz, H.: Portfolio selection. J. Finance 7(1) (1952)

  • Markowitz, H.M., Todd, G.P.: Mean-variance Analysis in Portfolio Choice and Capital Markets, vol. 66. John Wiley & Sons, London (2000)

    Google Scholar 

  • Mjirda, A., Todosijević, R., Hanafi, S., Hansen, P., Mladenović, N.: Sequential variable neighborhood descent variants: an empirical study on the traveling salesman problem. Int. Trans. Oper. Res. 24(3), 615–633 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  • Ogryczak, W., Ruszczynski, A.: Dual stochastic dominance and related mean-risk models. SIAM J. Optim. 13(1), 60–78 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Ogryczak, W., Ruszczyński, A.: Dual stochastic dominance and quantile risk measures. Int. Trans. Oper. Res. 9(5), 661–680 (2002)

    Article  MATH  Google Scholar 

  • Padberg, M., Rinaldi, G.: A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems. SIAM Rev. 33(1), 60–100 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  • Rahmaniani, R., Crainic, T.G., Gendreau, M., Rei, W.: The benders decomposition algorithm: a literature review. Eur. J. Oper. Res. 259(3), 801–817 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  • ROADEF/EURO challenge (2020). https://www.euro-online.org/media_site/reports/Challenge_Subject

  • Sharpe, W.F.: A linear programming approximation for the general portfolio analysis problem. J. Financial Quant. Anal. 6(5), 1263–1275 (1971)

    Article  Google Scholar 

  • Whitmore, G.A., Findlay, M.C.: Stochastic Dominance: An Approach to Decision-making Under Risk. Lexington Books, Lexington (1978)

    Google Scholar 

  • Woodruff, D.L.: Ghost image processing for minimum covariance determinants. ORSA J. Comput. 7(4), 468–473 (1995)

    Article  MATH  Google Scholar 

  • Zholobova, A., Zholobov, Y., Polyakov, I., Petrosian, O., Vlasova, T.: An industry maintenance planning optimization problem using CMA-VNS and its variations. In: International Conference on Mathematical Optimization Theory and Operations Research, pp. 429–443. Springer, Berlin (2021)

Download references

Acknowledgements

The authors are grateful to two referees for valuable suggestions to improve the exposition of this paper. Many thanks also to Fred Glover for his constructive comments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michel Vasquez.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Annexes

Annexes

See Tables 789 and 10.

Table 8 Better matrix: \({\textit{Better}}_{k,a}, k \in C+X, a \in {\mathcal {A}}\)
Table 9 Gap matrix: \(\Delta ^{15}_{k,a}, k \in C+X, a \in {\mathcal {A}}\)
Table 10 Gap matrix: \(\Delta ^{90}_{k,a}, k \in C+X, a \in {\mathcal {A}}\)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vasquez, M., Buljubasic, M. & Hanafi, S. An efficient scenario penalization matheuristic for a stochastic scheduling problem. J Heuristics 29, 383–408 (2023). https://doi.org/10.1007/s10732-023-09513-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10732-023-09513-y

Keywords

Navigation