Epsilon-continuation approach for truss topology optimization

A so-called epsilon-continuation approach is proposed for the solution of singular optimum in truss topology optimization problems. This approach is an improved version of the epsilon-relaxed approach. In the proposed approach, we start the optimization process from a relaxation parameter with a relatively large value and obtain a solution by applying the epsilon-relaxed approach. Then we decrease the value of the relaxation parameter by a small amount and choose the optimal solution from the previous optimization process as the initial design for the next optimization. This continuation process is continued until a small termination value of the relaxation parameter is reached. Convergence analysis of the proposed approach is also presented. Numerical examples show that this approach can alleviate the dependence of the final solution on the initial choice of the design variable and enhance the probability of finding the singular optimum from rather arbitrary initial designs.