An improved multi-objective Runge-Kutta Sinh Cosh optimizer for stochastic design of reinforced concrete cantilever retaining wall considering uncertainty

• A novel stochastic-metaheuristic framework is recommended for the optimal design of reinforced concrete cantilever retaining walls • Using a new multi-objective improved Sinh-Cosh optimization (MOISCHO) enhanced by a solution quality strategy integrated with Runge-Kutta method • A Monte Carlo simulation integrated with the K-Means clustering algorithm is used to generate and reduce uncertainty scenarios In this study, a novel stochastic-metaheuristic framework is recommended for the optimal design of reinforced concrete cantilever retaining walls (DRCCRW), incorporating a new multi-objective improved optimizer that accounts for uncertainties in the friction angle of retained soil, backfill slope, and surcharge load. Four cases are explored to evaluate the proposed framework: Case I aims to minimize cost while maximizing the factor of safety (FOS); Case II aims to minimize weight while maximizing the FOS; Case III is an extension of Case I that incorporates uncertainty; and Case IV extends Case II with uncertainty considerations. The study applies a new multi-objective improved Sinh-Cosh optimization (MOISCHO) enhanced by a solution quality strategy integrated with Runge-Kutta method to optimize the DRCCRW and strengthening the exploration and exploitation capabilities. Additionally, a Monte Carlo simulation integrated with the K-Means clustering algorithm is used to generate and reduce uncertainty scenarios. The simulation results for Cases I and II demonstrate that MOISCHO achieves the lower cost and weight values while also to maximize the FOS compared to conventional MOSCHO algorithm, and also the well-established multi-objective particle swarm Optimization (MOPSO) and multi-objective exponential distribution optimizer (MOEDO). Additionally, MOISCHO outperforms the other techniques as it yields a Pareto optimal set of solutions with greater convergence and bigger C index, reflecting the superiority of its solutions. In addition, the stochastic results reflect the beneficial impact by taking into account the uncertainty in soil friction angle but adverse impacts for uncertainties in the backfill slope and surcharge load on cost, weight, and FOS in Cases III and IV. These effects arise from the inherent uncertainties and the defined uncertainty scenarios.