DOI: https://doi.org/10.15587/2312-8372.2017.118338

Analysis and development of compromise solutions in multicriteria transport tasks

Lev Raskin, Oksana Sira, Yurii Parfeniuk

Abstract


The object of research is the multicriteria transport problem of linear programming. Simultaneous consideration of several criteria is a problematic problem, since the optimal solutions for different criteria do not coincide. The possible solution of the problem is investigated – finding a way to obtain a compromise solution. Based on the results of the analysis of known methods for solving multicriteria problems (Pareto-set formation, scalarization of the vector criterion, concessions method), the last is justified. To implement the method, an iterative procedure is suggested, in which the initial plan is optimal according to the main criterion. At subsequent iterations, an assignment is made to the main criterion in order to improve the values of the additional criteria. The solution of the problem is continued until a compromise solution is obtained, ensuring the best value for the main criterion, provided that the values for the remaining criteria are no worse than those given. Important advantages of the proposed method: the simplicity of the computational procedure, the grounded technology of forming a new solution at each iteration, realizing the concept of assignment, quality control of the solution obtained at each step. The application of the proposed method opens the prospect of its generalization to the case when the initial data for the solution of the problem contain uncertainty.


Keywords


multicriteria transport problem; iterative solution; method of consecutive concessions for obtaining a compromise solution

References


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Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8 (3), 338–353. doi:10.1016/s0019-9958(65)90241-x

Negoitse, K. (1981). Primenenie teorii sistem k problemam upravleniia. Moscow: MIR, 219.

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Diubua, D., Prad, A. (1990). Teoriia vozmozhnostei. Prilozhenie k predstavleniiu znanii v informatike. Moscow: Radio i sviaz, 286.

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Pawlak, Z. (1982). Rough sets. International Journal of Computer & Information Sciences, 11 (5), 341–356. doi:10.1007/bf01001956

Raskin, L., Sira, O. (2016). Fuzzy models of rough mathematics. Eastern-European Journal of Enterprise Technologies, 6 (4 (84)), 53–60. doi:10.15587/1729-4061.2016.86739


GOST Style Citations


Yudin, D. B. Zadachi lineinogo programmirovaniia transportnogo tipa [Text] / D. B. Yudin, E. G. Golshtein. – Moscow: Nauka, 1969. – 384 p.

Sira, O. V. Mnogomernye modeli logistiki v usloviiah neopredelennosti [Text] / O. V. Sira. – Kharkiv: FOP Stetsenko I. I., 2010. – 512 p.

Raskin, L. G. Mnogoindeksnye zadachi lineinogo programmirovaniia [Text] / L. G. Raskin, O. I. Kirichenko. – Moscow: Radio i sviaz, 1982. – 240 p.

Steuer, R. Multiple Criteria Optimization: Theory, Computation and Application [Text] / R. Steuer. – New York: John Wiley, 1986. – 546 p.

Savaragi, Y. Theory of Multiobjective Optimization [Text] / Y. Savaragi, H. Nakayama, T. Tanin. – Orlando: Academic Press Inc., 1985. – 296 p.

Keeney, R. L. Decisions with Multiple Objectives [Text] / R. L. Keeney, H. Raiffa. – Cambridge University Press, 1993. – 570 p. doi:10.1017/cbo9781139174084

Ehrgott, M. Multicriteria Optimization [Text] / M. Ehrgott. – Heidelberg: Springer, 2005. – 323 p. doi:10.1007/3-540-27659-9

Craft, D. L. Approximating convex Pareto surfaces in multiobjective radiotherapy planning [Text] / D. L. Craft, T. F. Halabi, H. A. Shih, T. R. Bortfeld // Medical Physics. – 2006. – Vol. 33, No. 9. – P. 3399–3407. doi:10.1118/1.2335486

Lotov, A. V. Mnogokriterial'nye zadachi priniatiia reshenii [Text] / A. V. Lotov, I. I. Pospelova. – Moscow: MAKS Press, 2008. – 197 p.

Intrillitator, M. Matematicheskie metody optimizatsii i ekonomicheskaia teoriia [Text] / M. Intrillitator. – Moscow: Antris-press, 2002. – 553 p.

Cohon, J. L. Multiobjective Programming and Planning [Text] / J. L. Cohon. – New York: Dover Publ, 2004. – 352 p.

Luque, M. Global formulation for interactive multiobjective optimization [Text] / M. Luque, F. Ruiz, K. Miettinen // OR Spectrum. – 2008. – Vol. 33, No. 1. – P. 27–48. doi:10.1007/s00291-008-0154-3

Panda, S. Multi-objective evolutionary algorithm for SSSC-based controller design [Text] / S. Panda // Electric Power Systems Research. – 2009. – Vol. 79, No. 6. – P. 937–944. doi:10.1016/j.epsr.2008.12.004

Zadeh, L. A. Fuzzy sets [Text] / L. A. Zadeh // Information and Control. – 1965. – Vol. 8, No. 3. – P. 338–353. doi:10.1016/s0019-9958(65)90241-x

Negoitse, K. Primenenie teorii sistem k problemam upravleniia [Text] / K. Negoitse. – Moscow: MIR, 1981. – 219 p.

Orlovskii, S. A. Problemy priniatiia reshenii pri nechetkoi informatsii [Text] / S. A. Orlovskii. – Moscow: Nauka, 1981. – 264 p.

Diubua, D. Teoriia vozmozhnostei. Prilozhenie k predstavleniiu znanii v informatike [Text] / D. Diubua, A. Prad. – Moscow: Radio i sviaz, 1990. – 286 p.

Raskin, L. G. Nechetkaia matematika. Osnovy teorii. Prilozheniia [Text] / L. G. Raskin, O. V. Sira. – Kharkiv: Parus, 2008. – 352 p.

Raskin, L. Method of solving fuzzy problems of mathematical programming [Text] / L. Raskin, O. Sira // Eastern-European Journal of Enterprise Technologies. – 2016. – Vol. 5, No. 4 (83). – P. 23–28. doi:10.15587/1729-4061.2016.81292

Pawlak, Z. Rough sets [Text] / Z. Pawlak // International Journal of Computer & Information Sciences. – 1982. – Vol. 11, No. 5. – P. 341–356. doi:10.1007/bf01001956

Raskin, L. Fuzzy models of rough mathematics [Text] / L. Raskin, O. Sira // Eastern-European Journal of Enterprise Technologies. – 2016. – Vol. 6, No. 4 (84). – P. 53–60. doi:10.15587/1729-4061.2016.86739







Copyright (c) 2017 Yurii Parfeniuk, Lev Raskin, Oksana Sira

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ISSN (print) 2664-9969, ISSN (on-line) 2706-5448