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An Efficient Method for Solving Multi-Objective Signomial Programming Problems in Real Life

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Abstract

In this present era, real-life problems are profoundly nonlinear and multi-objective. These objectives are usually clashing with one another and their solutions are not unique. Numerous techniques have been accommodated in finding optimal solutions to these problems. However, the present paper deciphers to solve multi-objective signomial programming problems by consolidating \(\epsilon \)-constraint method with the geometric programming (GP) technique. The GP technique is used to address posynomial (problems with positive coefficients) nonlinear programming problems whereas signomial programming is a generalization of geometric programming in which the coefficients are not necessarily positive. This technique can be used in several fields of engineering analysis, aircraft design, finance, etc. A numerical example of a multi-objective signomial programming problem is stated to prove the proposed technique.

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Software used- Lingo.

References

  1. Aliabadi, L., Yazdanparast, R., Nasiri, M.M.: An inventory model for non-instantaneous deteriorating items with credit period and carbon emission sensitive demand: a signomial geometric programming approach. Int. J. Manag. Sci. Eng. Manag. 14(2), 124–136 (2019)

    Google Scholar 

  2. Beightler, C.S., Phillips, D.T., Wilde, D.J.: Foundations of Optimization. Prentice-Hall, New Jersy (1979)

    Google Scholar 

  3. Biswal, M.P.: Fuzzy Programming technique to solve multi-objective geometric programming problem. Fuzzy Sets Syst. 51, 67–71 (1992)

    Article  MathSciNet  Google Scholar 

  4. Bjork, K.M., Lindberg, P.O., Westerlund, T.: Some convexifications in global optimization of problems containing signomial terms. Comput. Chem. Eng. 27, 669–679 (2003)

    Article  Google Scholar 

  5. Bjork, K.M., Westerlund, T.: A class of transformations convexifying and underestimating negative signomial terms, Report 02-182- A, Process Design Laboratory at Abo Akademi University, Finland, ISBN 952-12-0968-2 (2002)

  6. Boyd, S.J., Vandenberghe, L., Hossib, A.: A tutorial on geometric programming. Optim. Eng. 8(1), 67–127 (2007)

    Article  MathSciNet  Google Scholar 

  7. Cao, B.Y.: Solution and theory of question for a kind of fuzzy geometric program. In: Proceedings of 2nd IFSA Congress, Tokyo, vol. 1, pp. 205–208 (1987)

  8. Cao, B.Y.: Fuzzy geometric programming(1). Fuzzy Sets Syst. 53(2), 135–153 (1993)

    Article  MathSciNet  Google Scholar 

  9. Dahmani, N., Krichen, S., Talbi, E.G., Kaddoura, S.: Solving the multi-objective 2-dimensional vector packing problem using \(\epsilon \)-constraint method, Trends and Applications in Information Systems and Technologies, Advances in Intelligent Systems and Computing book series (AISC,volume 1368), pp. 96-104 (2021)

  10. Dowdle, A.P., Hall, D.K., Lang, J.H.: Electric Propulsion Architecture Assessment via Signomial Programming, AIAA/IEEE Electric Aircraft Technologies Symposium (EATS), July 9–11. Cincinnati, Ohio (2018)

  11. Duffin, R.J., Peterson, E.L., Zener, C.M.: Geometric Programming Theory and Application. Wiley, New York (1967)

    MATH  Google Scholar 

  12. Duffin, R.J., Peterson, E.L.: Geometric programing with signomials, geometric programing with signomials. J. Optim. Theory Appl. 11, 3–35 (1973)

    Article  MathSciNet  Google Scholar 

  13. Haimes, Y., Lasdon, L., Wismer, D.: On a bicriterion formulation of the problems of integrated system identification and system optimization. IEEE Trans. Syst. Man Cybern. 1, 296–297 (1971)

    MathSciNet  MATH  Google Scholar 

  14. Kirschen, G.P., York, M.A., Ozturk, B., Hoburg, W.W.: Application of signomial programming to aircraft design. J. Aircr. 55(3), 1–23 (2017)

    Google Scholar 

  15. Mandal, W.A., Islam, S.: Modified signomial geometric programming (MSGP) and its Applications. Independent J. Manag. Prod. (IJMP) 10(2), 440–458 (2014)

    Article  Google Scholar 

  16. Mehrotra, S.: On the Implementation of a Primal-Dual Interior Point Method. SIAM J. Optim. 2(4), 575–601 (1992). https://doi.org/10.1137/0802028

    Article  MathSciNet  MATH  Google Scholar 

  17. Murray, R., Chandrasekaran, V., Wierman, A.: Signomial and polynomial optimization via relative entropy and partial dualization. Math. Program. Comput. 13, 297–299 (2021)

    Article  MathSciNet  Google Scholar 

  18. Ojha, A.K., Ota, R.R.: A hybrid method for solving multi-objective geometric programming problem. Int. J. Math. Oper. Res. 7(2), 119–137 (2015)

    Article  MathSciNet  Google Scholar 

  19. Peterson, E.L.: The fundamental relations between geometric programming duality, Parametric programming duality, and ordinary Lagrangian duality. Ann. Oper. Res. 105, 109–153 (2001)

    Article  MathSciNet  Google Scholar 

  20. Porn, R., Harjunkoski, I., Westerlund, T.: Convexification of different classes of non-convex MINLP problems. Comput. Chem. Eng. 23, 439–448 (1999)

    Article  Google Scholar 

  21. Rajgopal, J., Bricker, D.L.: Solving Posynomial geometric programming problems via generalised linear programming. Comput. Optim. Appl. 21, 95–109 (2002)

    Article  MathSciNet  Google Scholar 

  22. Roy, S.K., Midya, S., Yu, V.F.: Multi-objective fixed-charge Transportation problem with Random Rough Variables. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 26(06), 971–996 (2018)

    Article  MathSciNet  Google Scholar 

  23. Tsai, J.F., Lin, M.H.: Global optimization of signomial mixed integer nonlinear programming problems with free variables. J. Glob. Optim. 42, 39–49 (2008). https://doi.org/10.1007/s10898-007-9211-8

    Article  MathSciNet  MATH  Google Scholar 

  24. Westerlund, T., Bjork, K.M.: A class of transformations convexifying and underestimating positive signomial terms, Report 02-183-A, Process Design Laboratory at Abo Akademi University, Finland, ISBN 952-12-1018-4 (2002)

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  1. ITER, SOA (Deemed to be) University, Bhubaneswar, Odisha, India

    Sudipta Mishra & Rashmi Ranjan Ota

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  1. Sudipta Mishra
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  2. Rashmi Ranjan Ota
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Both authors tried to solve “An efficient method for solving multi objective signomial programming problems in real life” with help of Lingo software and studied the importance.

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Correspondence to Rashmi Ranjan Ota.

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Mishra, S., Ota, R.R. An Efficient Method for Solving Multi-Objective Signomial Programming Problems in Real Life. Int. J. Appl. Comput. Math 8, 204 (2022). https://doi.org/10.1007/s40819-022-01416-z

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