A fuzzy multi-objective enhanced arithmetic optimization algorithm for stochastic design of reinforced concrete cantilever retaining wall using unscented transformation

• A fuzzy tri-objective design method is proposed for RCRW optimization. • Enhanced AOA with Elite Archive improves efficiency and solution quality. • Unscented Transformation models surcharge load uncertainty effectively. • Four cases compare two-objective, tri-objective, and stochastic designs. • EAOA outperforms other optimizers in HV, GD, and SP, ensuring balance. In the study, a new stochastic design approach based on fuzzy tri-objective optimization and unscented transformation (UT) is proposed for reinforced concrete cantilever retaining walls (RCRW) considering minimizing the cost, and weight as well as maximizing the safety factor (SF) incorporating surcharge load uncertainty. A new enhanced arithmetic optimization algorithm (EAOA) is recommended to find the optimal decision variables of the designing problem based on the Elite Archive Mechanism ensuring a balanced and efficient search process throughout its execution. The UT is utilized to model the uncertainty and solving the stochastic designing problem integrating the multi-objective EAOA. The simulations are implemented in four cases I) two-objective considering cost and SF, II) two-objective considering weight and SF III) tri-objective design considering cost, weight, and SF, IV) tri-objective stochastic design considering cost, weight, and SF via UT. The impact of tri-objective optimization and also incorporating surcharge load uncertainty using the UT is evaluated on the design problem and values of cost, weight, and SF. The results showed multi-objective EAOA algorithm yields an optimal compromise, achieving a balanced trade-off between minimizing cost and weight while maintaining a high safety factor. While two-objective cases showed the best value in one objective, they did not achieve the desired value in the other objectives. Moreover, when uncertainty in surcharge load is considered, the cost and weight increase slightly, by 3.9% and 3.0%, respectively. This increase is due to the additional material requirements to support the increased load, which results in a more robust design. Simultaneously, the safety factor decreases by 5.3%, which is a result of the increased stress on the retaining wall. In comparison of the optimizers, the proposed multi-objective EAOA provides the highest Hypervolume (HV) and the lowest Generational Distance (GD) and Spread (SP) compared to the well-known algorithms. This shows that even with the added uncertainty, the EAOA algorithm continues to offer diverse and well-distributed solutions across the three objectives, ensuring an optimal balance between cost, weight, and safety factor.