Keywords: multi-objective optimisation, genetic algorithm, Pareto front, multi-population, self-adaptive, composite structures.

Structural applications of composite materials have been growing due to their excellent specific stiffness, low weight, and reduced energy consumption. One design approach to decrease costs is to adopt a hybrid construction where expensive and high-stiffness material is used together with inexpensive and low-stiffness material. The optimisation problem of topology associated with material/stacking sequence design of hybrid composites is very complex when sizing variables, as ply angle and layer thickness are simultaneously considered. Furthermore, since the balance between weight/cost and stiffness is important in hybrid laminate construction the use of multi-objective design procedures are necessary.

A methodology for structural robust design that simultaneously considers minimum weight/cost and minimum strain energy related with maximum performance is presented in this paper. The trade-off between performance target, depending on given stress, displacement and buckling constraints imposed on composite structures, against minimum weight/cost, is searched. The Pareto-optimal front is built using the concept of Pareto dominance to assign scalar fitness values to individuals. Such a challenge is performed here using a hierarchical genetic algorithm with co-evolution of multi-populations [1]. A self-adaptive genetic search incorporating Pareto dominance is presented. The search adopts an elitist strategy storing the non-dominated solutions found during the evolutionary process. Adaptive rules will perform using additional information related to the behaviour of state and design variables of the structural problem. The introduction of adaptive rules occurs at selection, mutation, crossover and migration operators [1,2,3]. Self-adaptation has proved to be highly beneficial in automatically adjusting evolutionary parameters.

The problem of stacking sequence design of composite structures is well known for having many local optima, and so, dominated solutions are expected. The approach proposed in this work uses a mixture of developed techniques and new techniques in order to find multiple Pareto-optimal solutions in parallel. The principal aspects are: the storage of the Pareto-optimal solutions found, the use of the concept of Pareto dominance to assign scalar fitness values to individuals, and the clustering through the co-evolution of sub-populations to reduce the number of non-dominated solutions stored without destroying the characteristics of the Pareto-optimal front. A numerical example showing these benefits is presented.

1

C.A. Conceição António, "A hierarchical genetic algorithm with age structure for multimodal optimal design of hybrid composites", Structural and Multidisciplinary Optimization, 31, 280-294, 2006. doi:10.1007/s00158-005-0570-9

2

C.A. Conceição António, "A study on synergy of multiple crossover operators in a hierarchical genetic algorithm applied to structural optimization", Structural and Multidisciplinary Optimization, 38(2), 117-135, 2009. doi:10.1007/s00158-008-0268-x

3

C. Conceição António, "Self-adaptation procedures in genetic algorithms applied to the optimal design of composite structures", International Journal of Mechanics and Materials in Design, 5(3), 289-302, 2009. doi:10.1007/s10999-009-9102-x

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