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This paper presents the results of a study on trusses which are need to satisfy optimal conditions, i.e. the lowest Cost possible cost with maximal performance. The trusses considered were statically indeterminate steel structures with a multi-system loading. The cost is represented by the material volume of the structure and the maximal performance is reflected by the high working stresses reflect the maximum performance within allowable stress limits. The material strength was modeled as a random variable with a Log Normal distribution. The structures are also required to meet a failure probability of Pf =10 -3 , which may occur locally within the elements as well as globally on the structure as a whole. The complexity of optimization problems depends in general on the number of the considered variables. The larger the number of variables considered, the more complicated becomes the solution process. Therefore, cases of single variable elements such as multi variables ones were considered in this study. Optimization problems are usually solved by applying iterative procedures, frequently resorting to mathematical programming. In these procedures the process usually converges to unreliable solutions; it even may completely bogged down with no solution. To circumvent this problem, iteration was carried out by applying Genetic Algorithms where the process proceeds in a stochastic manner.

Truss structure optimization for two design variable elements using Genetic Algorithm with stress and failure probability constraints