Representation of topology by boundary cycle and its application to structural optimization (A formulation to combine algebraic topology with genetic algorithm

This paper deals with structural optimization in view of topology. The numerical examples are concerned with the partition of a certain area into equal parts of prescribed number with the shortest boundary line. The problem is to find the nodes and boundaries which satisfy these conditions. The boundary cycles are utilized to represent the topology of the area partition, and the genetic, algorithm is used in the process to find the optimal boundary cycles in order to minimize the total length of the boundaries, which is given as a function of the nodal coordinates and curvatures of the boundary lines. The examples verify the validity of the proposed method.