Skip to main content
SpringerLink
Log in

Military system of systems architecting with individual system contracts

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

This paper studies the process of architecting a System of Systems (SoS) where the SoS architect can negotiate with individual systems. Particularly, the SoS architect aims to select a set of systems to provide a set of capabilities required for the SoS as well as the interfaces that enable communications amongst the selected systems. The SoS architect regards a set of three objectives: cost and deadline minimization and performance maximization. The performance levels of the capabilities provided by a system can be improved through additional funds contracted by the SoS architect. The system decides on how to use the allocated funds. We model the resulting Stackelberg game between the SoS architect and the individual systems as a multi-objective multi-level optimization problem. Three evolutionary heuristic methods are proposed and compared in a set of numerical studies. Further numerical studies illustrate the benefits of the modeling approach compared to system contracting after system selection.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abo-Sinna, M.A., Baky, I.A.: Interactive balance space approach for solving multi-level multi-objective programming problems. Inf. Sci. 177, 3397–3410 (2007)

    Article  MATH  Google Scholar 

  2. Alves, M.J., Dempe, S., Judice, J.J.: Computing the Pareto frontier of a bi-objective bi-level linear problem using a multiobjective mixed-integer programming algorithm. Optimization 61, 335–358 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  3. Baky, I.A.: Fuzzy goal programming algorithm for solving decentralized bi-level multi-objective programming problems. Fuzzy Sets Syst. 160, 2701–2713 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  4. Baky, I.A.: Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach. Appl. Math. Model. 34, 2377–2387 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bergey, J.K., Blanchette, S., Clements, P.C., Gagliardi, M.J., Klein, J., Wojcik, R. Wood, W.: U.S. Army Workshop on Exploring Enterprise, System of Systems, System, and Software Architectures, Software Engineering Institute, Paper 46 (2009)

  6. Deb, K., Sinha, A.: Evolutionary multi-criterion optimization, pp. 110–124. Springer, Berlin (2009)

    Book  Google Scholar 

  7. Deb, K., Sinha, A.: An efficient and accurate solution methodology for bilevel multi-objective programming problems using a hybrid evolutionary-local-search algorithm. Evolut. Comput. 18, 403–449 (2010)

    Article  Google Scholar 

  8. Eichfelder, G.: Multiobjective bilevel optimization. Math. Program. 123, 419–449 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  9. Gao, Y., Xhang, G., Lu, J.: A fuzzy multi-objective bilevel decision support system. Int. J. Inf. Technol. Decis. Mak. 8, 93–108 (2009)

    Article  MATH  Google Scholar 

  10. Hansen, P., Jaumard, B., Savard, G.: New branch-and-bound rules for linear bilevel programming. SIAM J. Sci. Stat. Comput. 13, 1194–1217 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  11. Klein, J., van Vliet, H.: A systematic review of system-of-systems architecture research, QoSA’13. In: Proceedings of the 9th international ACM Sigsoft conference on Quality of software architectures, pp. 13–22 (2013)

  12. Konur, D., Golias, M.M.: Cost-stable truck scheduling at a cross-dock facility with unknown truck arrivals: A meta-heuristic approach. Transp. Res. Part E 49, 71–91 (2013)

    Article  Google Scholar 

  13. Li, M., Lin, D., Wang, S.: Solving a type of biobjective bilevel programming problem using NSGA-II. Comput. Math. Appl. 59, 706–715 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  14. Lu, J., Zhang, G., Dillon, T.S.: Fuzzy multi-objective bilevel decision making by an approximation kth-best approach. J. Mult. Valued Logic Soft Comput. 14, 205–232 (2008)

    MATH  MathSciNet  Google Scholar 

  15. Manthorpe, W.H.J.: The emerging joint system of systems: a systems engineering challenge and opportunity for APL. John Hopkins APL Tech. Dig. 17, 305–313 (1996)

    Google Scholar 

  16. Office of the Deputy Under Secretary of Defense for Acquisition and Technology, Systems and Software Engineering. In: Systems Engineering Guide for Systems of Systems, Version 1.0. Washington, DC: ODUSD(A&T)SSE, (2008)

  17. Osman, M.S., Abo-Sinn, M.A., Amer, A.H., Emam, O.E.: A multi-level non-linear multi-objective decision-making under fuzziness. Appl. Math. Comput. 153, 239–252 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  18. W.A. Owens, The Emerging U.S. System-of-Systems, National Defense University Strategic Forum, 63 (1996)

  19. Pramanik, S., Dey, P.P.: Bi-level multi-objective programming problem with fuzzy parameters. Int. J. Comput. Appl. 30, 13–20 (2011)

    Google Scholar 

  20. Pramanik, S., Dey, P.P., Giri, B.C.: Fuzzy goal programming approach to quadratic bi-level multi-objective programming problem. Int. J. Comput. Appl. 29, 9–14 (2011)

    Google Scholar 

  21. Shan, X., Zhang, J.: Hybrid defensive resource allocations in the face of partially strategic attackers in a sequential defenderattacker game. Eur. J. Oper. Res. 228, 262–272 (2013)

    Article  Google Scholar 

  22. Sinha, S., Sinha, S.B.: KKT transformation approach for multi-objective multi-level linear programming problems. Eur. J. Oper. Res. 143, 19–31 (2002)

    Article  MATH  Google Scholar 

  23. Zhang, G., Lu, J.: Fuzzy bilevel programming with multiple objectives and cooperative multiple followers. J. Glob. Optim. 47, 403–419 (2010)

    Article  MATH  Google Scholar 

  24. Zheng, Y., Wan, Z., Wang, G.: A fuzzy interactive method for a class of bilevel multiobjective programming problem. Expert Syst. Appl. 38, 10384–10388 (2011)

    Article  Google Scholar 

  25. Zhuang, J.: Impacts of subsidized security on stability and total social costs of equilibrium solutions in an n-player game with error. Eng. Econ. 55, 131–149 (2010)

    Article  Google Scholar 

  26. Zhuang, J., Bier, V.M.: Balancing terrorism and natural disasters-defensive strategy with endogenous attacker effort. Oper. Res. 55, 976–991 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  27. Zhuang, J., Bier, V.M., Alagoz, O.: Modeling secrecy and deception in a multiple-period attackerdefender signaling game. Eur. J. Oper. Res. 203, 409–418 (2010)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

This material is based upon work supported, in whole or in part, by the U.S. Department of Defense through the Systems Engineering Research Center (SERC) under Contract H98230-08-D-0171. SERC is a federally funded University Affiliated Research Center managed by Stevens Institute of Technology.

Author information

Authors and Affiliations

  1. Engineering Management and Systems Engineering, Missouri University of Science and Technology, 600 W. 14th Street, Rolla, MO, 65409-0370, USA

    Dinçer Konur & Cihan H. Dagli

Authors
  1. Dinçer Konur
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cihan H. Dagli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dinçer Konur.

Appendix

Appendix

figure a
figure b
figure c
figure d
figure e

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Konur, D., Dagli, C.H. Military system of systems architecting with individual system contracts. Optim Lett 9, 1749–1767 (2015). https://doi.org/10.1007/s11590-014-0821-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-014-0821-z

Keywords

Search

Navigation