zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A hybrid of genetic algorithm and particle swarm optimization for solving bi-level linear programming problem -- a case study on supply chain model. (English) Zbl 1221.90064
Summary: The main goal of supply chain management is to coordinate and collaborate the supply chain partners seamlessly. On the other hand, bi-level linear programming is a technique for modeling decentralized decision. It consists of the upper level and lower level objectives. Thus, this paper intends to apply bi-level linear programming to supply chain distribution problem and develop an efficient method based on hybrid of genetic algorithm (GA) and particle swarm optimization (PSO). The performance of the proposed method is ascertained by comparing the results with GA and PSO using four problems in the literature and a supply chain distribution model.

90B90Case-oriented studies in OR
90B06Transportation, logistics
90C59Approximation methods and heuristics
Full Text: DOI
[1] Khilwani, N.; Prakash, A.; Shankar, R.; Tiwari, M. K.: Fast clonal algorithm, Eng. appl. Artif. intell. 21, 106-128 (2008)
[2] Clerc, M.; Kennedy, J.: The particle swarm-explosion stability and convergence in a multidimensional complex space, IEEE trans. Evol. comput. 6, No. 1, 58-73 (2002)
[3] Simchi-Levi, D.; Kaminsky, P.; Simchi-Levi, E.: Managing the supply chain: the definitive guide for the business professional, (2004) · Zbl 1163.90522
[4] Dantzing, G. B.; Wolfe, P.: Decomposition principle for linear programs, Oper. res. 8, No. 1, 101-111 (1960) · Zbl 0093.32806 · doi:10.1287/opre.8.1.101
[5] Wen, U. P.; Hsu, S. T.: Linear bi-level programming problems -- a review, J. oper. Res. soc. 42, No. 2, 25-133 (1991) · Zbl 0722.90046
[6] H.S. Shih, Fuzzy Multi-Level Optimization, Ph.D. Dissertation, Department of Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, Kansas, USA, 1995.
[7] Sakawa, M.; Nishizaki, I.: Interactive fuzzy programming for two-level nonconvex programming problems with fuzzy parameters through genetic algorithms, Fuzzy set. Syst. 127, 185-197 (2002) · Zbl 0994.90146 · doi:10.1016/S0165-0114(01)00134-8
[8] Hejazi, S. R.; Memarian, A. I.; Jahanshahloo, G.; Sepehri, M. M.: Linear bi-level programming solution by genetic algorithm, Comput. oper. Res. 29, 1913-1925 (2002) · Zbl 1259.90120
[9] Mathieu, R.; Pittard, L.; Anandalingam, G.: Genetic algorithm based approach to bi-level linear programming, Oper. res. 28, No. 1, 1-21 (1994) · Zbl 0857.90083
[10] Gendreau, M.; Marcotte, P.; Savard, G.: A hybrid tabu-ascent algorithm for the linear bilevel programming problem, J. global optim. 8, No. 3, 217-233 (1996) · Zbl 0859.90097 · doi:10.1007/BF00121266
[11] Oduguwa, V.; Roy, R.: Bi-level optimization using genetic algorithm, IEEE int. Conf. artif. Intell. syst., 322-327 (2002)
[12] Wang, Y.; Jiao, Y.; Li, H.: An evolutionary algorithm for solving nonlinear bi-level programming problem based on a new constraint-handling scheme, IEEE trans. Syst. man cybernet. -- part C 35, No. 2, 221-232 (2005)
[13] G.M. Wang, X.J. Wang, Z.P. Wan, Y.L. Chen, Genetic algorithms for solving linear bilevel programming, in: Proceedings of the IEEE Sixth international Conference on Parallel and Distributed Computing, 2005.
[14] Wen, U. P.; Huang, A. D.: A simple tabu search method to solve the mixed-integer problem bi-level programming problem, Eur. J. Oper. res. 88, 563-571 (1996) · Zbl 0908.90194 · doi:10.1016/0377-2217(94)00215-0
[15] Wen, U. P.; Huang, A. D.: A tabu search approach for solving the linear bilevel programming problem, J. chin. Inst. indus. Eng. 13, 113-119 (1996)
[16] Shih, H. S.; Wen, U. P.; Lee, E. S.; Lan, K. M.; Hsiao, H. C.: A neural network approach to multi-objective and multilevel programming problems, Comput. math. Appl. 48, 95-108 (2004) · Zbl 1062.90060 · doi:10.1016/j.camwa.2003.12.003
[17] Lan, K. M.; Wen, U. P.; Shih, H. S.; Lee, E. S.: A hybrid neural network approach to bilevel programming problems, Appl. math. Lett. 20, 880-884 (2007) · Zbl 1162.90514 · doi:10.1016/j.aml.2006.07.013
[18] Kuo, R. J.; Huang, C. J.: Application of particle swarm optimization algorithm for solving bi-level linear programming problem, Comput. math. Appl. 58, 678-685 (2009) · Zbl 1189.90212 · doi:10.1016/j.camwa.2009.02.028
[19] Holland, J. H.: Adaptation in natural and artificial systems, (1975) · Zbl 0317.68006
[20] Goldberg, D. E.: Genetic algorithm in search, optimization & machine learning, (1989) · Zbl 0721.68056
[21] R.C. Eberhart, J. Kennedy, Particle swarm optimization, in: Proceedings of the IEEE International Conference on Neural Networks Perth Australia, 1995, pp. 1942 -- 1948.
[22] Boeringer, D. W.; Werner, D. H.: Particle swarm optimization versus genetic algorithms for phased array synthesis, IEEE trans. Antennas propag., 771-779 (2004)
[23] Boyd, R.; Richerson, P. J.: Culture and the evolutionary process, (1985)
[24] Wang, F.; Qiu, Y.: A modified particle swarm optimizer with roulette selection operator, Proc. nat. Lang. process. Knowl. eng., 765-768 (2005)
[25] J. Liu, X. Fan, Z. Qu, An improved particle swarm optimization with mutation based on similarity, in: Third International Conference on Natural Computation (ICNC 2007), vol. 4, 2007, pp. 824 -- 828.
[26] Arumugam, M. S.; Rao, M. V. C.: On the improved performances of the particle swarm optimization algorithms with adaptive parameters, cross-over operators and root mean square (RMS) variants for computing optimal control of a class of hybrid systems, Appl. soft comput. 8, No. 1, 324-336 (2008)
[27] Fan, S. K. S.; Liang, Y. C.; Zahara, E.: A genetic algorithm and a particle swarm optimizer hybridized with Nelder-Mead simplex search, Comput.ind. eng. 50, 401-425 (2006)
[28] Fan, S. K. S.; Zahara, E.: A hybrid simplex search and particle swarm optimization for unconstrained optimization, Eur. J. Oper. res. 181, No. 2, 527-548 (2007) · Zbl 1121.90116 · doi:10.1016/j.ejor.2006.06.034
[29] S. Du, W. Li, K. Cao, A learning algorithm of artificial neural network based on GA -- PSO, in: The Sixth World Congress on Intelligent Control and Automation WCICA, vol. 1, IEEE, 2006, pp. 3633 -- 3637.
[30] Kao, Y. T.; Zahara, E.: A hybrid genetic algorithm and particle swarm optimization for multimodal functions, Appl. soft comput. 8, No. 2, 849-857 (2007)
[31] Bialas, W. F.; Karwan, M. H.: Two-level linear programming, Manage. sci. 30, No. 8, 1004-1020 (1984) · Zbl 0559.90053 · doi:10.1287/mnsc.30.8.1004
[32] Liu, Y. H.; Hart, S. M.: Characterizing an optimal solution to the linear bilevel programming problem, Eur. J. Oper. res. 79, 164-166 (1994) · Zbl 0806.90084 · doi:10.1016/0377-2217(94)90155-4
[33] Bard, J. F.; Falk, J. E.: An explicit solution to the multi-level programming problem, Comput. oper. Res. 9, No. 1, 77-100 (1982)