Advertisement

Computational Optimization and Applications

, Volume 72, Issue 3, pp 589–608 | Cite as

An algorithm for binary linear chance-constrained problems using IIS

  • Gianpiero CanessaEmail author
  • Julian A. Gallego
  • Lewis Ntaimo
  • Bernardo K. Pagnoncelli
Article
  • 147 Downloads

Abstract

We propose an algorithm based on infeasible irreducible subsystems to solve binary linear chance-constrained problems with random technology matrix. By leveraging on the problem structure we are able to generate good quality upper bounds to the optimal value early in the algorithm, and the discrete domain is used to guide us efficiently in the search of solutions. We apply our methodology to individual and joint binary linear chance-constrained problems, demonstrating the ability of our approach to solve those problems. Extensive numerical experiments show that, in some cases, the number of nodes explored by our algorithm is drastically reduced when compared to a commercial solver.

Keywords

Chance-constrained programming Infeasible irreducible subsystems Integer programming 

Notes

References

  1. 1.
    Abdelaziz, F.B., Aouni, B., El Fayedh, R.: Multi-objective stochastic programming for portfolio selection. Eur. J. Oper. Res. 177(3), 1811–1823 (2007)CrossRefzbMATHGoogle Scholar
  2. 2.
    Abdi, A., Fukasawa, R.: On the mixing set with a knapsack constraint. Math. Program. 157(1), 191–217 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Ahmed, S., Papageorgiou, D.J.: Probabilistic set covering with correlations. Oper. Res. 61(2), 438–452 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Beasley, J.E.: An algorithm for set covering problem. Eur. J. Oper. Res. 31(1), 85–93 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Beraldi, P., Ruszczyński, A.: The probabilistic set-covering problem. Oper. Res. 50(6), 956–967 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Campi, M.C., Garatti, S.: The exact feasibility of randomized solutions of uncertain convex programs. SIAM J. Optimiz. 19(3), 1211–1230 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Campi, M.C., Garatti, S., Prandini, M.: The scenario approach for systems and control design. Annu. Rev. Control 33(2), 149–157 (2009)CrossRefGoogle Scholar
  8. 8.
    Charnes, A., Cooper, W.W., Symonds, G.H.: Cost horizons and certainty equivalents: an approach to stochastic programming of heating oil. Manag. Sci. 4(3), 235–263 (1958)CrossRefGoogle Scholar
  9. 9.
    Chinneck, J.W.: Feasibility and infeasibility in optimization: algorithms and computational methods, vol. 118. Springer, Berlin (2007)zbMATHGoogle Scholar
  10. 10.
    Dentcheva, D., Prékopa, A., Ruszczynski, A.: Concavity and efficient points of discrete distributions in probabilistic programming. Math. Program. 89(1), 55–77 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Gleeson, J., Ryan, J.: Identifying minimally infeasible subsystems of inequalities. ORSA J. Comput. 2(1), 61–63 (1990)CrossRefzbMATHGoogle Scholar
  12. 12.
    Küçükyavuz, S.: On mixing sets arising in chance-constrained programming. Math. Program. 132(1–2), 31–56 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Kumral, M.: Application of chance-constrained programming based on multi-objective simulated annealing to solve a mineral blending problem. Eng. Optimiz. 35(6), 661–673 (2003)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Lejeune, M., Noyan, N.: Mathematical programming approaches for generating p-efficient points. Eur. J. Oper. Res. 207(2), 590–600 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Lejeune, M.A.: Pattern-based modeling and solution of probabilistically constrained optimization problems. Oper. Res. 60(6), 1356–1372 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Luedtke, J., Ahmed, S.: A sample approximation approach for optimization with probabilistic constraints. SIAM J. Optimiz. 19(2), 674–699 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Pagnoncelli, B., Ahmed, S., Shapiro, A.: Sample average approximation method for chance constrained programming: theory and applications. J. Optimiz. Theory Appl. 142(2), 399–416 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Prékopa, A.: Dual method for the solution of a one-stage stochastic programming problem with random rhs obeying a discrete probability distribution. Z. Oper. Res. 34(6), 441–461 (1990)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Saxena, A., Goyal, V., Lejeune, M.A.: Mip reformulations of the probabilistic set covering problem. Math. Program. 121(1), 1–31 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Song, Y., Luedtke, J.R., Küçükyavuz, S.: Chance-constrained binary packing problems. INFORMS J. Comput. 26(4), 735–747 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Tanner, M.W., Ntaimo, L.: IIS branch-and-cut for joint chance-constrained stochastic programs and application to optimal vaccine allocation. Eur. J. Oper. Res. 207(1), 290–296 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Zhu, M., Taylor, D.B., Sarin, S.C., Kramer, R., et al.: Chance constrained programming models for risk-based economic and policy analysis of soil conservation. Agric. Resour. Econ. Rev. 23(1), 58–65 (1994)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Universidad Adolfo IbañezSantiagoChile
  2. 2.AT Kearney IncChicagoUSA
  3. 3.Texas A&M UniversityCollege StationUSA
  4. 4.Universidad Adolfo IbañezSantiagoChile
  5. 5.IEMS Department, Northwestern UniversityEvanstonUSA

Personalised recommendations