Deflation constraints for global optimization of composite structures

Abstract

The study presents deflation constraints that enable a systematic exploration of the design space during the design of composite structures. By incorporating the deflation constraints, gradient-based optimizers become able to find multiple local optima over the design space. The study presents the idea behind deflation using a simple sine function, where all roots within an interval can be systematically found. Next, the novel deflation constraints are presented: hypersphere, hypercube and hypercuboid; consisting of a combination of Gaussian and sigmoid functions. As a test case, the developed constraints are applied to the optimization of a double-cosine function, where all the 13 minima points could be found with 24 deflation constraints. It is shown that a new optimum is encountered after each deflation constraint is added, with the optimization subsequently re-started from the same initial point, or resumed from the last found minimum, being the latter the recommended approach. The new deflation constraints are then used in heuristic-based direct search methods, where a genetic algorithm optimizer is able to find new optimum individuals for straight-fiber composites. Lastly, variable-stiffness composites were designed with the deflation constraints applied to the multimodal optimization problem of recovering fiber orientations from a set of optimum lamination parameters.