Optimizing nonlinear steel trusses using enhanced differential evolution with linear population reduction

Sizing optimization of nonlinear inelastic steel truss structures poses significant challenges due to computational intensity from repeated nonlinear analyses and limitations of existing metaheuristic algorithms in handling high-dimensional problems with geometric and material nonlinearities. This paper proposes LEpDE, an enhanced differential evolution algorithm tailored for this task. LEpDE integrates: (1) a pbest mutation scheme balancing local and global searches, (2) a linear population size reduction (LPSR) transitioning from large to small populations for improved initial diversity and final convergence, (3) novel formulas for scale factor (F) and crossover (CR), and (4) an earlier constraint evaluation stop (ECES) to efficiently reduce unnecessary structural analyses. LEpDE's performance was evaluated on three examples (planar 10-bar truss, 47-bar power line truss, and planar 39 bar truss) against EpDE, Rao, a success-history-based parameter adaptation for DE (SHADE), and a LPSR application for SHADE (LSHADE). LEpDE consistently achieved superior best, worst, average, and standard deviation results, with statistical significance confirmed by Student's t-test. Despite a modest 7–10% increase in computation time over EpDE, the substantial gains in solution quality justify this trade-off. These findings establish LEpDE as a robust and efficient tool for nonlinear structural optimization with broad engineering applications.