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Heuristic algorithms for the inverse mixed integer linear programming problem

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Abstract

The recent development in inverse optimization, in particular the extension from the inverse linear programming problem to the inverse mixed integer linear programming problem (InvMILP), provides more powerful modeling tools but also presents more challenges to the design of efficient solution techniques. The only reported InvMILP algorithm, referred to as AlgInvMILP, although finitely converging to global optimality, suffers two limitations that greatly restrict its applicability: it is time consuming and does not generate a feasible solution except for the optimal one. This paper presents heuristic algorithms that are designed to be implemented and executed in parallel with AlgInvMILP in order to alleviate and overcome its two limitations. Computational experiments show that implementing the heuristic algorithm on one auxiliary processor in parallel with AlgInvMILP on the main processor significantly improves its computational efficiency, in addition to providing a series of improving feasible upper bound solutions. The additional speedup of parallel implementation on two or more auxiliary processors appears to be incremental, but the upper bound can be improved much faster.

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References

  1. Achterberg T., Koch T., Martin A.: MIPLIB 2003. Oper. Res. Lett. 34, 361–372 (2006)

    Article  Google Scholar 

  2. Ahuja R.K., Orlin J.B.: Inverse optimization. Oper. Res. 49, 771–783 (2001)

    Article  Google Scholar 

  3. Awerbuch S.: Portfolio-based electricity generation planning: policy implications for renewables and energy security. Mitigation Adapt. Strategies Global Change 11, 693–710 (2006)

    Article  Google Scholar 

  4. Beil D.R., Wein L.M.: An inverse-optimization-based auction mechanism to support a multiattribute RFQ process. Manage. Sci. 49, 1529–1545 (2003)

    Article  Google Scholar 

  5. Bitran G.R., Chandru V., Sempolinski D.E., Shapiro J.F.: Inverse optimization: an application to the capacitated plant location problem. Manage. Sci. 27, 1120–1141 (1981)

    Article  Google Scholar 

  6. Burton D., Toint P.L.: On an instance of the inverse shortest paths problem. Math. Program. 53, 45–61 (1992)

    Article  Google Scholar 

  7. Cai M.C., Yang X.G., Zhang J.Z.: The complexity analysis of the inverse center location problem. J. Global Optim. 15, 213–218 (1999)

    Article  Google Scholar 

  8. Dial R.B.: Minimal-revenue congestion pricing part I: a fast algorithm for the single-origin case. Transp. Res. B 33, 189–202 (1999)

    Article  Google Scholar 

  9. Dial R.B.: Minimal-revenue congestion pricing part II: an efficient algorithm for the general case. Transp. Res. B 34, 645–665 (2000)

    Article  Google Scholar 

  10. Faragó A., Szentesi Á., Szviatovszki B.: Inverse optimization in high-speed networks. Discrete Appl. Math. 129, 83–98 (2003)

    Article  Google Scholar 

  11. Heuberger C.: Inverse combinatorial optimization: a survey on problems, methods, and results. J. Comb. Optim. 8, 329–361 (2004)

    Article  Google Scholar 

  12. Hurkmans C.W., Meijer G.J., van Vliet-Vroegindeweij C., van der Sangen M.J., Cassee J.: High-dose simultaneously integrated breast boost using intensity-modulated radiotherapy and inverse optimization. Int. J. Radiat. Oncol. Biol. Phys. 66, 923–930 (2006)

    Article  Google Scholar 

  13. Kim H., Rho O.: Dual-point design of transonic airfoils using the hybrid inverse optimization method. J. Aircraft 34, 612–618 (1997)

    Article  Google Scholar 

  14. Menke W.: Geophysical Data Analysis: Discrete Inverse Theory. Academic Press, San Diego (1989)

    Google Scholar 

  15. Moser T.J.: Shortest paths calculation of seismic rays. Geophysics 56, 59–67 (1991)

    Article  Google Scholar 

  16. Tarantola A.: Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation. Elsevier, Amsterdam (1987)

    Google Scholar 

  17. Wang L., Mazumdar M.: Using a system model to decompose the effects of influential factors on locational marginal prices. IEEE Trans. Power Syst. 22, 1456–1465 (2007)

    Article  Google Scholar 

  18. Wang L.: Cutting plane algorithms for the inverse mixed integer linear programming problem. Oper. Res. Lett. 37, 114–117 (2009)

    Article  Google Scholar 

  19. Yang C., Zhang J.: Two general methods for inverse optimization problems. Appl. Math. Lett. 12, 69–72 (1999)

    Article  Google Scholar 

  20. Zhang B., Zhang J., He Y.: Constrained inverse minimum spanning tree problems under the bottleneck-type Hamming distance. J. Global Optim. 34, 467–474 (2006)

    Article  Google Scholar 

  21. Zhang J., Ma Z., Yang C.: A column generation method for inverse shortest path problems. Math. Methods Oper. Res. 41, 347–358 (1995)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Industrial and Manufacturing Systems Engineering, Iowa State University, Ames, IA, USA

    Zhaoyang Duan & Lizhi Wang

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  1. Zhaoyang Duan
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  2. Lizhi Wang
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Correspondence to Lizhi Wang.

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Duan, Z., Wang, L. Heuristic algorithms for the inverse mixed integer linear programming problem. J Glob Optim 51, 463–471 (2011). https://doi.org/10.1007/s10898-010-9637-2

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  • DOI: https://doi.org/10.1007/s10898-010-9637-2

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