Design problems for machine products are generally hierarchically expressed. With conventional product optimization methods, however, it is difficult to concurrently optimize all design variables of portions within such hierarchical structures. This paper proposes a design optimization method using genetic algorithms containing hierarchical genotype representations, so that the hierarchical structures of machine system designs are exactly expressed through genotype coding, and optimization can be concurrently conducted for all of the hierarchical structures. Crossover and mutation operations for manipulating the hierarchical genotype representations are also developed. The proposed method is applied to a machine-tool structural design and a 2 DOF robot arm design to demonstrate its effectiveness.

1.
Holland, J. H., 1975, Adaptation in Natural and Artificial Systems, University of Michigan Press.
2.
Goldberg, D. E., 1989, Genetic Algorithms in Search, Optimization & Machine Learning, Addison-Wesley.
3.
Kirkpatrick
,
S.
,
Gelat
,
C. D.
, and
Vecchi
,
M. P.
,
1983
, “
Optimization by Simulated Annealing
,”
Science
,
220
(
4598
), pp.
671
680
.
4.
Michalewicz, Z., 1994, Genetic Algorithms+DataStructures=Evolution Programs, Second, extended edition, Springer.
5.
Schaffer, J. D., 1985, “Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms,” Proceedings of the First International Conference on Genetic Algorithms and Their Applications, Lawrence Erlbaum Associates, pp. 160–168.
6.
Chapman, C. D., and Jakiela, M. J., 1994, “Genetic Algorithm-Based Structural Topology Design with Compliance and Manufacturability Considerations,” ASME Advances in Design Automation, Vol. 2, pp. 309–322.
7.
Yoshimura, M., and Kimura, A., 1994, “Evolutional Optimization of Product Design Based on Concurrent Processing of Design and Manufacturing Information,” AIAA, 5th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, pp. 434–442.
8.
Yoshimura, M., and Izui, K., 1998, “Machine System Design Optimization Strategies Based on Expansion and Contraction of Design Spaces,” AIAA, 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, pp. 320–330.
9.
Lasdon, L. S., 1970, Optimization Theory for Large Systems, The Macmillan Company.
10.
Kusiak
,
A.
, and
Wang
,
J.
,
1993
, “
Decomposition of the Design Process
,”
ASME J. Mech. Des.
,
115
, pp.
687
694
.
11.
Krishnamachari
,
R. S.
, and
Papalambros
,
P. Y.
,
1997
, “
Optimal Hierarchical Decomposition Synthesis Using Integer Programming
,”
ASME J. Mech. Des.
,
119
, pp.
440
447
.
12.
Krishnamachari
,
R. S.
, and
Papalambros
,
P. Y.
,
1997
, “
Hierarchical Decomposition Systhesis in Optimal Systems Design
,”
ASME J. Mech. Des.
,
119
, pp.
448
457
.
13.
Sobieski, J., 1982, “A Linear Decomposition Method for Optimization Problems—Blueprint for Development,” NASA Technical Memorandum 83248.
14.
Steward
,
D. V.
,
1981
, “
The Design Structure System: A Method for Managing the Design of Complex Systems
,”
IEEE Trans. Eng. Manage.
,
em-28
(
3
), pp.
71
74
.
15.
McCulley
,
C.
, and
Bloebaum
,
C. L.
,
1996
, “
A Genetic Tool for Optimal Design Sequencing in Complex Engineering Systems
,”
Struct. Optim.
,
12
, pp.
186
201
.
16.
Rogers
,
J. L.
,
McCulley
,
C. M.
, and
Bloebaum
,
C. L.
,
1999
, “
Optimizing the Process Flow for Complex Design Projects, Design Optimization
,”
International Journal for Product & Process Improvement
,
1
(
3
), pp.
281
292
.
17.
Wujek
,
B. A.
,
Renaud
,
J. E.
,
Batill
,
S. M.
, and
Brockman
,
J. B.
,
1996
, “
Concurrent Subspace Optimization Using Design Variable Sharing in a Distributed Computing Environment
,”
Concurrent Engineering Research and Applications
,
4
(
4
), pp.
361
377
.
18.
Koch, P. N., Mavris, D., and Mistree, F., 1998, “Multi-Level, Partitioned Response Surfaces for Modeling Complex Systems,” AIAA, 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, pp. 1954–1968.
19.
Grefenstette, J. J., Gopal, R., Rosmaita, B., and Van Gucht, D., 1985, “Genetic Algorithms for the Traveling Salesman Problem,” Proceedings of the First International Conference on Genetic Algorithms and Their Applications, Lawrence Erlbaum Associates, Publishers, pp. 160–168.
20.
Goldberg, D. E., and Lingle, R., 1985, “Alleles, Loci and the Traveling Salesman Problem,” Proceedings of the First International Conference on Genetic Algorithms and Their Applications, Lawrence Erlbaum Associates, Hillsdale, NJ, pp. 154–159.
21.
Goldberg
,
D. E.
,
Korb
,
B.
, and
Deb
,
K.
,
1989
, “
Messy Genetic Algorithms, Motivation, Analysis, and First Results
,”
Complex Syst.
,
3
, pp.
493
530
.
22.
Tamaki, H., and Nishikawa, Y., 1992, “A Paralleled Genetic Algorithm Based on a Neighborhood Model and Its Application to the Jobshop Scheduling,” Parallel Problem Solving from Nature 2, Elsevier Science Publishers, pp. 573–582.
23.
Koza, J. R., 1991, Genetic Programming, MIT Press.
24.
Yoshimura
,
M.
,
1987
, “
Design Optimization of Machine-Tool Dynamics Based on Clarification of Competitive-Cooperative Relationships Between Characteristics
,”
ASME J. Mech. Des.
,
109
, pp.
143
150
.
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