Auxiliary algorithm to approach a near-global optimum of a multi-objective function in acoustical topology optimization

In this study, an auxiliary algorithm is proposed to avoid local optima in solving an acoustical topology optimization problem by using a gradient-based optimizer. A local optimum convergence issue often occurs in the multi-objective function problem because the sub-objective functions are non-convex in general. In order to overcome this issue and find a near-global optimum, the sign change of sensitivity is heuristically conducted based on the objective function difference at every step of design variable updating. An acoustical topology optimization problem is formulated for improving a noise attenuation performance of a muffler. The heuristic-based auxiliary algorithm is combined with a well-known optimization algorithm to solve the topology optimization problem for a single target frequency as well as a multi-target frequency. Diverse optimal topologies were successfully obtained for various design conditions. Comparison of the optimized solutions by the proposed method and the previous methods strongly supported the validity of the proposed auxiliary algorithm. The application of the proposed method to a suction muffler design problem showed the industrial applicability of the method.