Keywords: geometric crossover, phenotype building block, partial fitness, topology optimisation, genetic algorithm, structural optimisation.

It is well recognised that the efficiency of a genetic algorithm in exploration and exploitation of the solution space can be improved by incorporating domain-specific knowledge into the algorithm. In many real-world applications, the physics of the problem suggests heuristics that can be incorporated into the search and selection procedures. Whenever genetic algorithms are applied to such problems, knowledge about the domain of application should be considered in the design of the reproduction operators as well as the representation and selection. Domain knowledge has been broadly incorporated in selection and reproduction operators. Heuristics or knowledge-augmented operators are tailored for individual applications.

Phenotype building blocks (PBBs) contain information at the phenotype level. PBBs are either the components of a multi-component system, or different parts of a continuous system with different design qualities and, or evaluation measures. Using PBBs can lead to enhancement of the search efficiency by utilising problem specific search operators and heuristics applied on the PBBs. In order to preserve, propagate and recombine good building blocks efficiently, building blocks should have a low probability of being disrupted by crossover. Therefore, the crossover operation should be designed at the phenotype level. Geometric crossover (GCO) is applied on the phenotype rather than the genotype.

By identifying PBBs and using GCO, partial fitness can be defined and employed to improve the performance of the search algorithm. It is shown that these concepts can be applied to a wide range of structural optimisation problems with different characteristics. These concepts can be applied to both, discrete and continuous structures. PBBs may or may not have sharp boundaries. PBB can be defined as a combination of genotype building blocks of a discrete system or it can be identified based on different functions of different segments of a continuous system. Partial fitness can be defined based on either the individual assessment criteria or some new assessment criteria. There is no restriction on the type of the design variables involved in the problem (indexed, real value, integer, distributed, single value, continuous and discrete). Another advantage of using GCO is as result of its ease of application to non-fixed-length and variable-length chromosomes. Variable-length chromosomes are a common feature of topology optimisation problems when using genetic algorithms. Hence, GCO can be easily applied to structural optimisation problems including topology optimisation without predefining a grid.

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