Weighted k-NNC: An Efficient Computation Reduction Method for Metaheuristic-Based Structural Optimization

Structural optimization is essential for finding optimal designs in practical engineering tasks. Metaheuristic algorithms have been widely applied in structural optimization problems in recent years, especially when dealing with discrete design variables, the nonlinearity of the objective function and constraints. Unlike gradient-based algorithms, which rely on the slope variation of a function, metaheuristic algorithms do not require derivative calculations and thus avoid being trapped in local optimum. However, metaheuristic algorithms often require numerous function evaluations, involving costly structural analyses, thus increasing computational load considerably. This paper investigates a method to reduce computational load, specifically by reducing the number of function evaluations for metaheuristic-based structural optimization problems. The proposed strategy is based on eliminating unpromising designs during the optimization process. For each newly generated solution, an early assessment through its k nearest neighbors, named k-nearest neighbor comparison (k-NNC), is applied, acting as a filter. If a solution is deemed less promising, it is eliminated without going through the function evaluation step. Conversely, if a solution is deemed good, it is retained for the next comparison and selection step. This paper presents the implementation sequence of k-NNC, highlighting its disadvantages in terms of efficiency and accuracy. From this, a new method, the distance-weighted k-nearest neighbor comparison (wkNNC), has been developed. In wkNNC, the distance from the k neighbors to the solution under consideration is used as the weight for comparison. Furthermore, an archive of infeasible solutions and the potential solution refinement are introduced for enhancing the accuracy and efficiency of wkNNC. The superiority of wkNNC is demonstrated in the sizing optimization of some benchmark discrete cross-section truss structures. The wkNNC method, combined with the Best-Worst-Random (BWR) algorithm, achieves a computational load reduction of over 80 percent.