Keywords: genetic algorithm, ant colony optimization, travel salesman problem.

Structural optimum design algorithms find the best values for design variables such that the performance and the strength of the structure are acceptable. Although most optimization techniques have been developed for continuous design variables, in most design cases the design variables are discrete, and so, in the recent decade different computing techniques have been also developed for discrete variables. One of these methods is the genetic algorithm in which the search method has been inspired from the natural and genetic selection procedure. Dorigo et al. [1,2,3,4] presented a new computational optimization method called the "ant colony optimization (ACO)" algoritm which tries to model the basic capabilities of ant behaviour as a combined search algorithm. The ant colony is able to find the shortest path between the ants' nest and the food resources using a complex system based on the pheromones effect.

In this paper a design procedure has been developed for optimum design of space trusses using ACO techniques. The objective function is the cost of the truss, and the allowable stresses and displacements are the constraints. The design variables are the cross sectional areas of the members which are selected from a discrete input data set. The design of the truss with discrete cross sectional areas has been modelled as a modified travelling salesman problem (TSP). The TSP indicates that the configuration of the truss and the length that has resulted from the TSP shows its weight. The number of the paths between the nodes refers to the number of the input discrete values of the cross sectional areas of the members. In the design process of the ACO, a penalty function has been used for constraint satisfaction. The truss has been analyzed under earthquake loading and the displacements of the nodes and the stresses in the members have been calculated and whenever they have exceeded the allowable values, the penalty function has been activated. For dynamic analysis of the structure, the acceleration of Bam earthquake has been used for the critical case of the structure. Each cycle of the algorithm will be completed when one ant of the ant colony allocates a cross sectional area to each member, or to each member group. So, as many different truss designs will be produced as the number of the colony ants. At the end of each cycle all the different designs will be compared and the truss with the least weight which also satisfies the constraints will be found. The algorithm converges to the final result when the truss with the less weight in several consequent cycles remains the same.

The capability of the method comparing to the other methods has been indicated through several numerical examples at the end of this paper.

1

M. Dorigo, V. Maniezzo, and A. Colorni, "Distributed Optimization By Ant colonies", Proc., 1st European Conf. on Artificial Life, MIT Press, Cambridge, Mass., pp. 134-142, 1991a.

2

M. Dorigo, V. Maniezzo, and A. Colorni, "Positive feedback as a search strategy", Tech. Rep. No. 91-016, Politecnico di Milano, Italy, 1991b.

3

M. Dorigo, V. Maniezzo, and A. Colorni, "An investigation of some properties of an ant algorithm", Proc., 1992 Parallel Problem Solving from Nature Conf., Elsevier, Amsterdam, pp. 509-520, 1992.

4

M. Dorigo, V. Maniezzo, and A. Colorni, "The ant system: Optimization by a colony of cooperating agents", IEEE Trans. Syst. Man Cybern., 26(1), 29-41, 1996. doi:10.1109/3477.484436

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