Automated Graph Theoretic Force Method and its Application in Optimal Design of Frame Structures

In this study, the graph-theoretic force method is applied to the optimal design of frame structures and systematically compared with the conventional displacement method. The optimization is performed using the Water Strider Algorithm (WSA), a recently developed bio-inspired metaheuristic, whose population-based search strategy is integrated with both analysis approaches. To ensure reproducibility, all key WSA parameters are reported, and large-scale highly indeterminate frame examples (up to 292 members) are tested, extending beyond previous benchmark studies. In addition, a counterexample with DKI < DSI is included, demonstrating that the relative efficiency of the two methods is problem-dependent rather than universal. The results show that for large-scale highly indeterminate frames, the graph-theoretic force method combined with WSA significantly reduces computational time while maintaining accuracy comparable to the displacement method. These findings highlight both the scalability and the limitations of the graph-theoretic force method, offering a balanced perspective for its practical application in structural optimization.