HAN Yi (韩 毅), CAI Jian-hu (蔡建湖), IKOU Kaku, LI Yan-lai (李延来) CHEN Yi-zeng (陈以增), TANG Jia-fu (唐加福) . Evolutionary Algorithms for Solving Unconstrained Multilevel Lot-Sizing Problem with Series Structure[J]. Journal of Shanghai Jiaotong University(Science), 2012 , 17(1) : 39 -044 . DOI: 10.1007/s12204-012-1227-7

1 Afentakis P, Gavish B, Karmarkar U. Computationally efficient
optimal solutions to the lot-sizing problem in multistage assembly
systems [J]. Management Science, 1984, 30(2): 223-239.

2 Barany I, Van Roy T J, Wolsey L A. Uncapacitated lot
sizing: The convex hull of solutions [J]. Mathematical
Programming Studies, 1984, 22: 32-43.

3 Ball M O, Magnanti T L, Monma C L, et al. Handbooks in
operations research and management science: Network routing [M].
Amsterdam: Elsevier, 1995.

4 Crowston W B, Wagner M H. Dynamic lot size models for
multi-stage assembly systems [J]. Management Science, 1973,
20(1): 14-21.

5 Constantino M. Lower bounds in lot-sizing models: A polyhedral study
[J]. Mathematics of Operations Research, 1998, 23(1):
101-118.

6 Dorigo M, Maniezzo V, Colorni A. Ant system: Optimization by a
colony of cooperating agents [J]. IEEE Trans on System, Man,
and Cybernetics, 1996, 26(1): 28-41.

7 Dellaert N, Jeunet J. Solving large unconstrained multilevel
lot-sizing problems using a hybrid genetic algorithm [J].
International Journal of Production Research, 2000, 38(5):
1083-1099.

8 Eberhart R, Kennedy J. A new optimizer using particle swarm theory
[C]// Proceedings of 6th International Symposium on Micro
Machine and Human Science. Nagoya, Japan: IEEE, 1995: 39-43.

9 Eppen G D, Martin R K. Solving multi-item capacitated lot-sizing
problems using variable redefinition [J]. Operations Research,
1987, 35(6): 832-848.

10 Goldberg D E. Genetic algorithms in search, optimization and machine
learning [M]. Boston: Addison-Wesley, 1989.

11 Glover F, Kelly J P, Laguna M. Genetic algorithm and Tabu search:
Hybrid for optimizations [J]. Computers \& Operations
Research, 1995, 22(1): 111-134.

12 Holland J H. Adoption in natural and artificial systems [M].
Michigan: The University of Michigan Press, 1975.

13 Kirkpatrick S, Gelatt C D, Vecchi M P. Optimization by simulated
annealing [J]. Science, 1983, 220(4598): 671-680.

14 Karmarkar U S, Schrage L. The deterministic dynamic product cycling
problem [J]. Operations Research, 1985, 33(2): 326-345.

15 Kennedy J, Eberhart R. Particle swarm optimization [C]//
Proceedings of IEEE International Conference on Neural Networks.
Perth, WA, Australia: IEEE, 1995: 1942-1948.

16 Kennedy J, Spears W M. Matching algorithms to problems: An
experimental tests of the particle swarm and some genetic algorithms
on the multimodal problem generator [C]// Proceedings of IEEE
International Conference on Evolutionary Computation. Anchorage,
USA: IEEE, 1998: 78-83.

17 Kaku I, Xiao Y, Xia G. The deterministic annealing algorithms for
vehicle routing problems [J]. International Journal of Smart
Engineering System Design, 2003, 5(4): 327-339.

18 Lin F, Kao C, Hsu C. Applying the genetic approach to simulated
annealing in solving some NP-hard problems [J]. IEEE
Transactions on Systems, Man and Cybernetics, 1993, 23(6):
1752-1766.

19 Millonas M M. Swarms, phase transition, and collective intelligence [M]. Boston: Addison-Wesley, 1994.

20 Mitchell M. An introduction to genetic algorithms [M]. Cambridge:
MIT Press, 1996.

21 Pochet Y, Wolsey L A. Lot size model with backlogging: Strong
formulations and cut planes [J]. Mathematical Programming,
1988, 40(1-3): 317-335.

22 Rutenbar R A. Simulated annealing algorithms: An overview [J].
IEEE Circuits and Devices Magazine, 1989, 5(1): 19-26.

23 Su J, Hu A, He Z. Solving a kind of nonlinear programming problems
via analog neural networks [J]. Neurocomputing, 1998,
18(1-3): 1-9.

24 Shi Y, Eberhart R C. A modified particle swarm optimizer [C]//
Proceedings of IEEE International Confeence on Evolutionary
Computation. Anchorage, USA: IEEE, 1998: 69-73.

25 Suganthan P N. Particle swarm optimizer with neighborhood operator
[C]// Proceedings of the Congress on Evolutionary Computation.
Washington, USA: IEEE, 1999: 1958-1962.

26 Shi Y, Eberhart R C. Parameter selection in particle swarm
optimization [C]// Proceedings of the 7th Annual Conference on
Evolutionary Programming. Berlin, Germany: Springer-Verlag, 1998:
591-600.

27 Tang O. Simulated annealing in lot sizing problems [J].
International Journal of Production Economics, 2004, 88(2):
173-181.

28 Veral E A, Laforge R L. The performance of a simple incremental
lot-sizing rule in a multilevel inventory environment [J].
Decision Sciences, 1985, 16(1): 57-72.

29 Wolsey L A. Uncapacitated lot-sizing problems with start-up costs
[J]. Operations Research, 1989, 37(5): 741-747.

30 Wolsey L A. Solving multi-item lot-sizing problems with a MIP solver
using classification and reformulation [J]. Management
Science, 2002, 48(12): 1587-1602.

31 Wagner H M, Whitin T M. Dynamic version of the economic lot size
model [J]. Management Science, 1958, 5(1): 89-96.

32 Yelle L E. Materials requirements lot sizing: A multilevel approach
[J]. International Journal of Production Research, 1979,
17(3): 223-232.

33 Zangwill W I. Minimum concave cost flows in certain networks [J].
Management Science, 1968, 14(7): 429-450.

34 Zangwill W I. A backlogging model and a multi-echelon model of a
dynamic economic lot size production system---A network approach
[J]. Management Science, 1969, 15(9): 506-527.