Constraint-Aware and Economic Optimization of Riverbank Retaining Walls Using Metaheuristic Algorithms

The optimal design of riverbank retaining walls requires a careful balance between structural safety, constructability, and economic efficiency. In this study, a constraint-aware optimization framework is developed for the design of concrete gravity retaining walls by explicitly incorporating stability, serviceability, and geometric feasibility constraints. Several metaheuristic algorithms are comparatively evaluated under identical computational conditions using 30 independent runs, a population size of 50, and 1000 iterations. The results demonstrate that enforcing geometric constraints is essential to prevent non-physical designs and to ensure engineering realism. Quantitative analysis shows that the Flower Fertilization Optimization (FFO) algorithm yields the minimum wall weight, reducing material usage by approximately 19% compared to more conservative solutions. In contrast, the adaptive exploration artificial bee colony (AEABC) algorithm exhibits the most robust and repeatable convergence behavior with low statistical dispersion across independent runs. An economic assessment based on concrete volume further confirms the direct impact of material efficiency on construction cost. The proposed framework highlights the importance of constraint-aware optimization for achieving reliable and economically efficient retaining wall designs.