Mixed approaches to handle limitations and execute mutation in the genetic algorithm for truss size, shape and topology optimization

Abstract

A high-performance genetic algorithm for the optimal synthesis of trusses in discrete search spaces is developed. The main feature of the proposed computational procedure is the possibility of obtaining effective solutions without the violation of any constraint. In general, a varying of cross-sectional areas of bars, coordinates of nodes and topology system is provided. A group of individuals in the population can be accepted for further consideration only if all specified limitations have been fulfilled. Penalties that significantly change an objective function are introduced for other individuals. This mechanism of handling limitations provides for correction of inaccuracies that can introduce penalty functions for satisfying the problem conditions. Both a random change to the entire set of admissible values and a random choice of values among adjacent elements in this set can be performed during the mutation stage. Standard test examples for benchmark mathematical functions and trusses show high efficiency of the considered iterative procedure in terms of solution accuracy.