The Stability and Computational Complexity Analysis of Tree-seed Algorithm for Frequency-Constrained 10-bar Truss Problem

Optimization studies in truss problems produce different results according to different optimization conditions, which leads to significant changes in the results obtained. This paper presents a comprehensive analysis of the Tree-Seed Algorithm (TSA) in solving the frequency-constrained 10-bar truss optimization problem, a well-known benchmark in structural engineering characterized by its complex, non-linear, and multi-modal design space. The TSA, inspired by natural processes of tree growth and seed dispersion, is evaluated in the truss problem for its stability, computational efficiency, and ability to find optimal solutions. Through rigorous testing involving 51 independent runs, the TSA consistently achieves optimal solutions with a mean objective function value of 554.4549 and a standard deviation of 1.4049. The algorithm demonstrates rapid convergence, typically within 100 iterations. The design parameters of the frequency-constrained 10-bar truss optimization problem were found by TSA within stability. These findings highlight the TSA's effectiveness and reliability, establishing it as a robust tool for tackling complex engineering optimization problems and suggesting its potential for broader applications in structural optimization.