Abstract
This article introduces variable chromosome lengths (VCL) in the context of a genetic algorithm (GA). This concept is applied to structural topology optimization but is also suitable to a broader class of design problems. In traditional genetic algorithms, the chromosome length is determined a priori when the phenotype is encoded into the corresponding genotype. Subsequently, the chromosome length does not change. This approach does not effectively solve problems with large numbers of design variables in complex design spaces such as those encountered in structural topology optimization. We propose an alternative approach based on a progressive refinement strategy, where a GA starts with a short chromosome and first finds an ‘optimum’ solution in the simple design space. The ‘optimum’ solutions are then transferred to the following stages with longer chromosomes, while maintaining diversity in the population. Progressively refined solutions are obtained in subsequent stages. A strain energy filter is used in order to filter out inefficiently used design cells such as protrusions or isolated islands. The variable chromosome length genetic algorithm (VCL-GA) is applied to two structural topology optimization problems: a short cantilever and a bridge problem. The performance of the method is compared to a brute-force approach GA, which operates ab initio at the highest level of resolution.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bendsoe88 Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71:197–224
Bendsoe95 Bendsøe MP (1995) Optimization of structural topology, shape, and material. Springer, Berlin Heidelberg New York
Cea81 Cea J (1981) Numerical methods in shape optimal design. Optimization of distributed parameter structures. Sijthoff & Noordhof, Netherlands, pp.1049–1087
Chapman94 Chapman CD, Saitou K, Jakiela MJ (1994) Genetic Algorithms as an approach to configuration and topology design. J Mech Des Trans ASME 116:1005–1012
Chapman96 Chapman CD, Jakiela MJ (1996) Genetic algorithm-based structural topology design with compliance and topology simplification considerations. J Mech Des Trans ASME 118:89–98
DeRose00 DeRose GCA, Diaz AR (2000) Solving three-dimensional layout optimization problems using fixed scale wavelets. Comput Mech 25:274–285
Diaz92b Diaz AR, Bendsøe MP (1992) Shape optimization of structures for multiple loading conditions using homogenization method. Struct Optim 4:17–22
Diaz99 Diaz AR (1999) A wavelet-Galerkin scheme for analysis of large-scale problems on simple domains. Int J Numer Methods Eng 44:1599–1616
Esch01 Eschenauer HA, Olhoff N (2001) Topology optimization of continuum structures: a review. Appl Mech Rev 54:331–389
Gold89 Goldberg D (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Reading, MA
Guan03 Guan H. et al. (2003) Bridge topology optimization with stress, displacement and frequency constraints. Comput Struct 81:131–145
Haftka86 Haftka RT, Grandhi RV (1986) Structural shape optimization — a survey. Comput Methods Appl Mech Eng 57:91–106
Hajela95 Hajela P, Lee E (1995) Genetic algorithms in truss topological optimization. J Solids Struct 32:3341–3357
Haug86 Haug EJ, Choi KK, Komkov V (1986) Design sensitivity analysis of structural systems. Academic, Amsterdam
Holland75 Holland J (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, Michigan
Jakiela00 Jakiela MJ et al. (2000) Continuum structural topology design with genetic algorithms. Comput Methods Appl Mech Eng 186:339–356
Kim02a Kim H, Querin OM, Steven GP (2002) On the development of structural optimisation and its relevance in engineering design. Des Stud 23:85–102
Kim02b Kim IY, Kwak BM (2002) Design space optimization using a numerical design continuation method. Int J Numer Methods Eng 53:1979–2002
Kim03 Kim JE, Jang GW, Kim YY (2003) Adaptive multiscale wavelet-Galerkin analysis for plane elasticity problems and its applications to multiscale topology design optimization. Int J Solids Struct 40:6473–6496
Kim00 Kim YY, Yoon GH (2000) Multi-resolution multi-scale topology optimization — a new paradigm. Int J Solids Struct 37:5529–5559
Kirsch89 Kirsch U (1989) Optimal topologies of structures. Appl Mech Rev 42:223–239
Krus03 Krus P, Andersson J (2003) Optimizing optimization for design optimization. Proceedings of DETC’03, ASME 2003 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Chicago, Illinois, USA, September 2–6
Kwak94 Kwak BM (1994) A review on shape optimal design and sensitivity analysis. JSCE J Struct Eng/Earthquake Eng 10(4):159s–174s
Lin94 Lin C-Y, Hajela P (1994) Design optimization with advanced genetic search strategies. J Adv Eng Softw 21:179–189
Lin93 Lin C-Y, Hajela P (1993) Genetic search strategies in large scale optimization. Proceedings of the 34th AIAA/ASME/ASCE/AHS/ASC SDM Conference, La Jolla, California, 2437–2447
Mackerle03 Mackerle J (2003) Topology and shape optimization of structures using FEM and BEM — a bibliography (1999–2001). Finite Elem Anal Des 39:243–253
Maute95 Maute K, Ramm E (1995) Adaptive topology optimization. Struct Optim 10:100–112
Michell04 Michell AGM (1904) The limits of economy of material in frame-structures. Philos Mag 8:589–597
imos95 Milman MH, Briggs HC, Ledeboer W, Molody JW, Norton RL, Needels L (1995) Integrated modeling of optical systems user’s manual, release 2.0. JPL D-13040
Min00 Min S, Nishiwaki S, Kikuchi N (2000) Unified topology design of static and vibrating structures using multiobjective optimization. Comput Struct 75:93–116
Rousselet81 Rousselet B (1981) Implementation of some methods of shape design. Optimization of distributed parameter structures. Sijthoff & Noordhof, Netherlands
Rozvany95 Rozvany GIN, Bendsøe MP, Kirsch U (1995) Layout optimization of structures. Appl Mech Rev 42:41–119
Ryoo04 Ryoo J, Hajela P (2004) Handling variable string lengths in ga based structural topology optimization. Struct Multidisc Optim 26:318–325
Todoroki97 Todoroki A, Haftka RT (1997) Stacking sequence matching by a two-stage genetic algorithm with consanguineous initial population. Proc. of the 1997 38th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf., Part 2 (of 4), Paper AIAA-97-1228, 1297–1302
Xie93 Xie YM, Steven GP (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49:885–896
Zolesio81 Zolésio JP (1981) The material derivative (or speed) method for shape optimization. Optimization of distributed parameter structures. Sijthoff & Noordhof, Netherlands, pp.1089–1151
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kim, I., de Weck, O. Variable chromosome length genetic algorithm for progressive refinement in topology optimization. Struct Multidisc Optim 29, 445–456 (2005). https://doi.org/10.1007/s00158-004-0498-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-004-0498-5