Different methods were presented for shape and topology optimization. One of them is adaptive biological growth (ABG) method. Through fast computation, higher accuracy and less cost, this method has been used successfully in structural optimization. Adaptive biological growth method is inspired from behavior of nature and specifically from trees. One of important principles in behavior of trees is the adaptive biological growth principle. The principle expresses that growth of biological structure is commensurate by biological load. i.e. parts of structure which are subjected to more loading and stress have more cross section or are made from stronger and harder materials. In this paper, two different optimization algorithms have been applied to structures. Using the finite element method, the algorithms can be simply implemented and applied to the optimization problems. The first algorithm is applied to a shape optimization problem. To achieve the optimum shape, the stresses should be as uniform as possible or the stress concentration regions should be removed. To accomplish this, the nominal dimensions having a higher stress are increased and those having a lower stress are decreased. The second algorithm is the soft kill option (SKO) that is applied to a cone cantilever beam as well as a beam with variable cross section where the optimum topology of them are sought. The algorithm is based on the Young\\\'s modulus of elements. In fact the Young's modulus of each element is taken as a function of its stress. To achieve an optimum topology, elements having less stress are deleted or become inactive and those with a higher stress remain in the structure. The results show that these algorithms can give the optimum shape and topology of the structural components effectively.

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