Multiobjective and multi-physics topology optimization using an updated smart normal constraint bi-directional evolutionary structural optimization method
To date the design of structures using topology optimization methods has mainly focused on single-objective problems. Since real-world design problems typically involve several different objectives, most of which counteract each other, it is desirable to present the designer with a set of Pareto optimal solutions that capture the trade-off between these objectives, known as a smart Pareto set. Thus far only the weighted sums and global criterion methods have been incorporated into topology optimization problems. Such methods are unable to produce evenly distributed smart Pareto sets. However, recently the smart normal constraint method has been shown to be capable of directly generating smart Pareto sets. Therefore, in the present work, an updated smart Normal Constraint Method is combined with a Bi-directional Evolutionary Structural Optimization (SNC-BESO) algorithm to produce smart Pareto sets for multiobjective topology optimization problems. Two examples are presented, showing that the Pareto solutions found by the SNC-BESO method make up a smart Pareto set. The first example, taken from the literature, shows the benefits of the SNC-BESO method. The second example is an industrial design problem for a micro fluidic mixer. Thus, the problem is multi-physics as well as multiobjective, highlighting the applicability of such methods to real-world problems. The results indicate that the method is capable of producing smart Pareto sets to industrial problems in an effective and efficient manner.
KeywordsMultiobjective optimization Multi-physics optimization Normal constraint method BESO Pareto
D.J. Munk thanks the Australian government for their financial support through the Endeavour Fellowship scheme.
The authors would like to thank Dr Tiziano Ghisu for producing the data displayed in Fig. 14.
- Boyce NO, Mattson CA (2008) Reducing computational time of the normal constraints method by eliminating redundant optimization runs. In: 12th AIAA/ISSMO multidisciplinary analysis and optimization conference. AIAAGoogle Scholar
- Das I (1999) An improved technique for choosing parameters for Pareto surface generation using normal-boundary intersection. University of Buffalo, Center for Advanced Design, BuffaloGoogle Scholar
- Haddock ND, Mattson CA, Knight DC (2008) Exploring direct generation of smart Pareto sets. In: 12th AIAA/ISSMO multidisciplinary analysis and optimization conference. AIAAGoogle Scholar
- Ismail-Yahaya A, Messac A (2002) Effective generation of the Pareto frontier using the normal constraint method. In: 40th AIAA aerospace sciences meeting & exhibit. AIAAGoogle Scholar
- Martinez JSM, Blasco X, Salceo JV (2009a) A new perspective on multiobjective optimization by enhanced normalized normal constraint method. Struct Multidiscip Optim 36:537–546Google Scholar
- Martinez M, Garcia-Nieto S, Sanchis J, Blasco X (2009b) Genetic algorithms optimization for normalized normal constraint method under Pareto construction. Adv Eng Softw 40:260–267Google Scholar
- Messac A, Sukam CP, Melachrinoudis E (2000a) Aggregate objective functions and Pareto frontiers: required relationships and practical implications. Optim Eng 1:171–188Google Scholar
- Messac A, Sundararaj GJ, Tappeta RV, Renaud JE (2000b) Ability of objective functions to generate points on nonconvex Pareto frontiers. AIAA J 38:1084–1091Google Scholar
- Munk D, Vio G, Kipouros T, Parks G (2016a) Computational design for micro fluidic devices using a tightly coupled Lattice Boltzmann and level set-based optimization algorithm. In: Proceedings of the 11th ASMO UK/ISSMO conference on engineering design optimization. ASMO, UKGoogle Scholar
- Munk DJ, Kipouros T, Vio GA, Parks GT, Steven GP (2016b) Topology optimization of micro fluidic mixers considering fluid-structure interactions with a coupled Lattice Boltzmann method. J Comput Phys Under reviewGoogle Scholar
- Pareto V (1964) Cour deconomie politique (the first edition in 1896) edn. Librarie Droz-Geneve, GenevaGoogle Scholar
- Prager W, Rozvany GIN (1977) Optimization of the structural geometry. In: Bednarek A, Cesari L (eds) Dynamical systems. Academic Press, pp 265–293Google Scholar
- Proos KA, Steven GP, Querin OM, Xie YM (2001a) Multicriterion evolutionary structural optimization using the weighting and the global criterion methods. AIAA J 39(10):2006–2012Google Scholar
- Proos KA, Steven GP, Querin OM, Xie YM (2001b) Stiffness and inertia multicriteria evolutionary structural optimization. Eng Comput 18:1031–1054Google Scholar
- Rozvany GIN, Lewinski T (eds) (2013) Topology optimization in structural and continuum mechanics, 1st edn. Springer, DordrechtGoogle Scholar
- Rynne B (2007) Linear functional analysis, 1st edn. Springer, New YorkGoogle Scholar
- Tanaka M, Watanabe H, Furukawa Y, Tanino T (1995) GA-based decision support system for multicriteria optimization. In: 1995 IEEE international conference on systems, man, and cybernetics, vol 2. IEEE, pp 1556–1561Google Scholar