Hybrid truss layout optimization for generating multiple design alternatives

Abstract

As of writing this thesis little research has been done in truss layout optimization for multiple design alternatives. A hybrid scheme is proposed in which the fast gradient-based search of the Ground Structure Method (GSM) is employed for the search of optimal topology and size, while a population-based meta-heuristic algorithm explores the non-convex parameter space of geometry optimization. The scheme works by employing a meta-heuristic algorithm to optimize the nodal coordinates of a truss structure where for each iteration and each member of the population a small-scale (i.e. problems with a small number of degrees of freedom) GSM is performed, in order to obtain the optimal topology for the given nodal locations. Three variants of the scheme based on three different meta-heuristic algorithms are developed: Firstly, an Artificial Bee Colony (ABC) and Particle Swarm Optimization (PSO) variant are developed in combination with an original topology identification method, to extract design alternatives from the solutions found throughout the optimization process. The developed topology identification method identifies different design alternatives based on topological differences by making use of existing graph isomorphism testing algorithms from graph theory. Additionally, the topology identification method employs a multi-step filtering process to prevent members which are non-critical to the performance of the structure to influence the design alternative selection process. Finally, a Multi-Species Particle Swarm optimization (MSPSO) variant is developed without the need for a topology identification method. For all methods convergence speed in terms of number of iterations, topological variety and computation time per iteration have been evaluated and are compared. Of the developed methods, the ABC variant converges fastest towards a single good solution, however the topological variety is lacking. The slower converging MSPSO variant produces solutions with moderate topological variety, as well as reasonable material volumes. The PSO variant requires the least computation time per iteration of the developed methods. Its produced topological variety is closer to that of the ABC than the MSPSO variant and it has a slightly faster convergence speed than the MSPSO variant. Direct usage of the MOSEK API is made instead of the more commonly used CVXPY API which reduces GSM problem setup times for small-scale (28 degrees of freedom) problems by a factor of 13. Computation times for the hybrid method, from start to finish, for 3D structures with 4 to 8 movable nodes (12 to 24 geometric degrees of freedom) range from 15 to 50 seconds on standard desktop PC hardware. Because of the multiple design alternative nature of the hybrid method, and consequently the end-user does not require fast back-to-back optimization runs, these computation times are deemed acceptable. It is concluded that while in its current state the methods based on the hybrid scheme are unlikely to be suitable for usage in practice, further developments in methods to distinguish design alternatives could make the hybrid scheme, in particular the ABC variant, useful in the design of more material efficient truss structures.