Minimum constraint perturbation method for system topology optimization

An algorithm is presented for system topology optimization in which constraints are defined in terms of the state variables. A parametric optimization problem is first formulated with positive side constraints defined in terms of a scalar parameter. Then the optimal solution is conceived as a function of the parameter and a sequence of the optimal solutions is traced with respect to the parameter. Since the optimal topology is found by decreasing the parameter to null and by removing the variables corresponding to the active side constraints, difficulties due to the deteriorated state equations are successfully overcome. Conditions for uniqueness of the solution are discussed and a procedure is presented to find the boundary of a continuous set of optimal solutions. Efficiency of the proposed method is demonstrated in the examples of problems with eigenvalue constraints and the typical characteristics of the sequence of the solutions are discussed.