Comparison of heuristics and metaheuristics for topology optimisation in acoustic porous materials

When designing sound packages, often fully filling the available space with acoustic materials is not the most absorbing solution. Better solutions can be obtained by creating cavities of air pockets, but determining the most optimal shape and topology that maximises sound absorption is a computationally challenging task. Many recent topology optimisation applications in acoustics use heuristic methods such as solid-isotropic-material-with-penalisation (SIMP) to quickly find near-optimal solutions. This study investigates seven heuristic and metaheuristic optimisation approaches including SIMP applied to topology optimisation of acoustic porous materials for absorption maximisation. The approaches tested are hill climbing, constructive heuristics, SIMP, genetic algorithm, tabu search, covariance-matrix-adaptation evolution strategy (CMA-ES), and differential evolution. All the algorithms are tested on seven benchmark problems varying in material properties, target frequencies, and dimensions. The empirical results show that hill climbing, constructive heuristics, and a discrete variant of CMA-ES outperform the other algorithms in terms of the average quality of solutions over the different problem instances. Though gradient-based SIMP algorithms converge to local optima in some problem instances, they are computationally more efficient. One of the general lessons is that different strategies explore different regions of the search space producing unique sets of solutions.