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A class of multiobjective linear programming models with random rough coefficients. (English) Zbl 1165.90614
Summary: We concentrate on dealing with a class of multiobjective programming problems with random rough coefficients. We first discuss how to turn a constrained model with random rough variables into crisp equivalent models. Then an interactive algorithm which is similar to the interactive fuzzy satisfying method is introduced to obtain the decision maker’s satisfying solution. In addition, the technique of random rough simulation is applied to deal with general random rough objective functions and random rough constraints which are usually hard to convert into their crisp equivalents. Furthermore, combined with the techniques of random rough simulation, a genetic algorithm using the compromise approach is designed for solving a random rough multiobjective programming problem. Finally, illustrative examples are given in order to show the application of the proposed models and algorithms.

90C27Combinatorial optimization
90C70Fuzzy programming
90C05Linear programming
Full Text: DOI
[1] Lemple, R.; Moran, S.: The stochastic approach for link-structure analysis (SALSA) and the TKC effect, Computer networks 33, 387-401 (2000)
[2] Liu, B.: Theory and practice of uncertain programming, (2002) · Zbl 1029.90084
[3] Terol, Amelia Bilbao: A new approach for multiobjective decision making based on fuzzy distance minimization, Mathematical and computer modelling (2007) · Zbl 1144.90486
[4] Wu, Hsien-Chung: Using the technique of scalarization to solve the multiobjective programming problems with fuzzy coefficients, Mathematical and computer modelling (2007) · Zbl 1145.90445
[5] Slowinski, K.: Rough sets approach to analysis of data from peritoneal lavage in acute pancreatitis, Medical informatics 13, 143-159 (1988)
[6] Li, Jun; Xu, Jiuping; Gen, Mitsuo: A class of multiobjective linear programming model with fuzzy random coefficients, Mathematical and computer modelling 44, 1097-1113 (2006) · Zbl 1165.90701 · doi:10.1016/j.mcm.2006.03.013
[7] Gerstenkorn, Tadeusz; Manko, Jacek: Bifuzzy probabilistic sets, Fuzzy sets and systems 71, 207-214 (1995) · Zbl 0845.60004 · doi:10.1016/0165-0114(94)00254-5
[8] Peng, Jin; Liu, Baoding: Birandom variables and birandom programming, Computers industrial engineering 53, 433-453 (2007)
[9] Liu, B.: Uncertain theory: an introduction to its axiomatic foundations, (2004) · Zbl 1072.28012
[10] Thiele, H.: On axiomatic characterisations of crisp approximation operators, Information sciences 129, 221-226 (2000) · Zbl 0985.03044 · doi:10.1016/S0020-0255(00)00019-0
[11] Greco, Salvatore; Matarazzo, Benedetto; Slowinski, Roman: Rough sets methodology for sorting problems in presence of multiple attributes and criteria, European journal of operational research 138, 247-259 (2002) · Zbl 1008.90509 · doi:10.1016/S0377-2217(01)00244-2
[12] Pawlak, Z.: Rough sets, (1991) · Zbl 0758.68054
[13] Masud, A.; Hwang, C.: Interactive sequential goal programming, Journal of the operational research society 32, 391-400 (1981) · Zbl 0452.90069 · doi:10.2307/2581556
[14] Weistroffer, H.: An interactive goal programming method for nonlinear multiple-criteria decision-making problems, Computers and operations research 4, No. 10, 311-320 (1983)
[15] Hwang, C.; Yoon, K.: Multiple attribute decision making: methods and applications, (1981) · Zbl 0453.90002
[16] Zitzler, E.; Deb, K.; Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results, Evolutionary computation 8, No. 2, 173-195 (2000)
[17] Farina, M.; Deb, K.; Amato, P.: Dynamic multiobjective optimization problems: test cases, approximations, and applications, IEEE transactions on evolutionary computation 8, No. 5, 425-442 (2004)
[18] Bingul, Zafer: Adaptive genetic algorithms applied to dynamic multiobjective problems, Applied soft computing 7, 791-799 (2007)
[19] Pareto, V.: Manuale di economica polittica, (1906)
[20] Stadler, W.: A survey of multicriteria optimization or the vector maximization problem: I. 1776-1960, Journal of optimization theory and applications 69, 1-52 (1979) · Zbl 0388.90001 · doi:10.1007/BF00932634
[21] W. Stadler, A comprehensive bibliography on multicriteria decision making and related areas, Technical Report, University of California-Berkeley, 1981
[22] Fonseca, C.; Fleming, P.: An overview of evolutionary algorithms in multiobjective optimization, Evolutionary computation 3, 1-16 (1995)
[23] H. Holland, Adaptation in Natural and Artificial Systems, University of Michigan, Ann Arbor, 1975 · Zbl 0317.68006
[24] Michalewicz, Z.: Genetic algorithms + data structures = evolution programs, (1994) · Zbl 0818.68017
[25] Fogel, D. B.: Evolution computation: toward a new philosophy of machine intelligence, (1995)
[26] Goldberg, D. E.: Genetic algorithms in search, optimization and machine learning, (1989) · Zbl 0721.68056
[27] Gen, M.; Cheng, R.: Genetic algorithms and engineering design, (1997)
[28] Gen, M.; Cheng, R.: Genetic algorithms and engineering optimization, (2000)