An alternating active-phase algorithm for multi-material topology optimization

The alternating active-phase algorithm has recently been used to solve multi-material topology optimization (TO) problems. The algorithm splits the multi-material problem into several two-material problems that are inexactly solved in a sequential way, using a nonlinear programming method. The coupling of the solutions is done using a Gauss-Seidel scheme, which means that, form materials, m(m - 1)/2 subproblems need to be solved at each iteration, resulting in a high computational cost when the problem is very large. Besides, algorithm convergence depends on reducing the filter radius, which can also increase computational cost. In this work, we propose a new alternating active-phase algorithm for solving multi-material TO problems. The new algorithm solves m subproblems with one material per iteration, using the non-monotonic spectral projected gradient method. This combination greatly reduces the overall time required to solve the problem. Furthermore, the convergence of the proposed algorithm does not depend on reducing the filter radius. The efficiency of the new method is supported by experiments with some classical topological optimization problems.