Large-Scale Topology Optimization Using Parameterized Boolean Networks

Abstract

A novel parameterization concept for structural truss topology optimization is presented in this article that enables the use of evolutionary algorithms in design of large-scale structures. The representational power of Boolean networks is used here to parameterize truss topology. A genetic algorithm then operates on parameters that govern the generation of truss topologies using this random network instead of operating directly on design variables. A genetic algorithm implementation is also presented that is congruent with the local rule application of the random network. The primary advantage of using a Boolean random network representation is that a relatively large number of ground structure nodes can be used, enabling successful exploration of a large-scale design space. In the classical binary representation of ground structures, the number of optimization variables increases quadratically with the number of nodes, restricting the maximum number of nodes that can be considered using a ground structure approach. The Boolean random network representation proposed here allows for the exploration of the entire topology space in a systematic way using only a linear number of variables. The number of nodes in the design domain, therefore, can be increased significantly. Truss member geometry and size optimization is performed here in a nested manner where an inner loop size optimization problem is solved for every candidate topology using sequential linear programming with move-limits. The Boolean random network and nested inner-loop optimization allows for the concurrent optimization of truss topology, geometry, and size. The effectiveness of this method is demonstrated using a planar truss design optimization benchmark problem.