Modified genetic algorithm for optimal design of truss structures

Truss systems are widely used in engineering practice, mainly due to the economy, simple manufacturing, transportation and storage. These systems form the framework of such constructions as bridges, towers, roof supporting structures, etc. Usually a truss system includes a large number of elements (trusses), which can have different parameters (length, cross-sectional area, shape of crosssection, material). Thus, the optimization of truss systems is relevant problem in engineering. Truss systems can be optimized according several criteria: sizing, shape, and topology [1]. Large number of design parameters makes this problem complex. As the sizing optimization usually does not cause serious computational problems, further we will deal with the topology and shape optimization. In topology optimization the optimal truss placement scheme in the framework of nodes with fixed positions is sought. This problem is discrete; the number of possible variants depends on the number of nodes and is huge even in the case of small-scale structures. Therefore full-search algorithms can not be used for the solution. Instead, different methods and algorithms avoiding the examination of all possible connection combinations are exploited. Thus, in the so-called “ground structure method” [2] the solution begins from an over-connected truss system, and the superfluous trusses are eliminated. Also the simulated annealing method [3], which is the generalization of Monte Carlo method, is used. However, the most natural strategy for topology optimization of truss systems seems to be the use of genetic algorithms (GA), where the solution is adapted to the constraints and objective function [4]. In this paper we solve the topology optimization problems using original modified genetic algorithm, which for this particular class of problems yields better results than the classical GA [5]. In shape optimization the number of nodes and trusses is constant, and only positions of the nodes may vary. Design parameters in this case are the coordinates of certain set of nodes [6]. Thus, the truss system topology must be known prior to the shape optimization. Naturally, in the joint topology/shape optimization the multilevel design strategy can be employed, where in one phase the topology optimization is dealt with, and in the other – the shape optimization [7]. In this paper we also employ this approach; shape optimization is performed using classical GA, thus improving the solution obtained in the topology optimization phase. An additional research was conducted in order to ascertain what strategy can yield better solutions: to carry out the shape optimization following the topology optimization, or simply perform only the topology optimization with increased number of nodes. 2. Problem formulation