Structural topology optimization using a genetic algorithm with a morphological geometric representation scheme

This paper describes a versatile methodology for solving topology design optimization problems using a genetic algorithm (GA). The key to its effectiveness is a geometric representation scheme that works by specifying a skeleton which defines the underlying topology/connectivity of a structural continuum together with segments of material surrounding the skeleton. The required design variables are encoded in a chromosome which is in the form of a directed graph that embodies this underlying topology so that appropriate crossover and mutation operators can be devised to recombine and help preserve any desirable geometry characteristics of the design through succeeding generations in the evolutionary process. The overall methodology is first tested by solving ‘target matching’ problems—simulated topology optimization problems in each of which a ‘target’ geometry is first created and predefined as the optimum solution, and the objective of the optimization problem is to evolve design solutions to converge towards this target shape. The methodology is then applied to design two path-generating compliant mechanisms—large-displacement flexural structures that undergo some desired displacement paths at some point when given a straight line input displacement at some other point—by an actual process of topology/shape optimization.