Highly Efficient Feasible Direction Method (HEFDiM) for Structural Topology Optimization

Feasible Direction Method (FDM) is a concise yet rigorous mathematical method for structural topology optimization, which can be easily applied to different types of problems with less modification. In addition, the FDM always converges to a near optimum rapidly. However, the problem of inefficiency stays unsolved. In this work, we advance the state-of-the-art by proposing a highly efficient feasible direction method (HEFDiM), which substantially improves the efficiency of the FDM with negligible loss of accuracy. The proposed method can benefit us in at least four aspects: 1) Analytical gradient projection; 2) Fewer heuristics and clear physical meaning; 3) Negligible memory and time-cost for updating; 4) Directly applied to different problems without extra efforts. In particular, we address problems including 1) Efficient determination of effective constraints for gradient projection; 2) Acceleration of null-space projection calculation; 3) Avoidance of time costing 1-D searching; 4) Elimination of split-stepping and zig-zag problems. Benchmark problems, including the MBB, the force inverter mechanism, and the 3D cantilever beam are used to validate the effectiveness of the method. Specifically, the results show that the updating speed of the HEFDiM is approximately 10 times higher (even faster for larger-scale optimization problems) with lower objective value than that of the classical efficient 88-line MATLAB code (Andreassen et, al. 2011). The HEFDiM is implemented in MATLAB which is open-sourced for educational usage.