Local and global Pareto dominance applied to optimal design and material selection of composite structures

The optimal design of hybrid composite structures considering sizing, topology and material selection is addressed in a multi‐objective optimization framework. The proposed algorithm, denoted by Multi‐objective Hierarchical Genetic Algorithm (MOHGA), searches for the Pareto‐optimal front enforcing population diversity by using a hierarchical genetic structure based on co‐evolution of multi‐populations. An age structured population is used to store the ranked solutions aiming to obtain the Pareto front. A self‐adaptive genetic search incorporating Pareto dominance and elitism is presented. Two concepts of dominance are used: the first one denoted by local non‐dominance is implemented at the isolation stage of populations and the second one called global non‐dominance is considered at age structured population. The age control emulates the human life cycle and enables to apply the species conservation paradigm. A new mating and offspring selection mechanisms considering age control and dominance are adopted in crossover operator applied to age‐structured population. Application to hybrid composite structures requiring the compromise between minimum strain energy and minimum weight is presented. The structural integrity is checked for stress, buckling and displacement constraints considered in the multi‐objective optimization. The design variables are ply angles and ply thicknesses of shell laminates, the cross section dimensions of beam stiffeners and the variables associated with the material distribution at laminate level and structure level. The properties of the proposed approach are discussed in detail.