Multi-objective optimization of reinforced concrete cantilever retaining wall: a comparative study

This paper investigates the performance of four multi-objective optimization algorithms, namely non-dominated sorting genetic algorithm II (NSGA-II), multi-objective particle swarm optimization (MOPSO), strength Pareto evolutionary algorithm II (SPEA2), and multi-objective multi-verse optimization (MVO), in developing an optimal reinforced concrete cantilever (RCC) retaining wall. The retaining wall design was based on two major requirements: geotechnical stability and structural strength. Optimality criteria were defined as reducing the total cost, weight, CO2 emission, etc. In this study, two sets of bi-objective strategies were considered: (1) minimum cost and maximum factor of safety, and (2) minimum weight and maximum factor of safety. The proposed method's efficiency was examined using two numerical retaining wall design examples, one with a base shear key and one without a base shear key. A sensitivity analysis was conducted on the variation of significant parameters, including backfill slope, the base soil’s friction angle, and surcharge load. Three well-known coverage set measures, diversity, and hypervolume were selected to compare the algorithms’ results, which were further assessed using basic statistical measures (i.e., min, max, standard deviation) and the Friedman test with a 95% level of confidence. The results demonstrated that NSGA-II has a higher Friedman rank in terms of coverage set for both cost-based and weight-based designs. SPEA2 and MOPSO outperformed both cost-based and weight-based solutions in terms of diversity in examples without and with the effects of a base shear key, respectively. However, based on the hypervolume measure, NSGA-II and MVO have a higher Friedman rank for examples without and with the effects of a base shear key, respectively, for both the cost-based and weight-based designs.