A simple pipeline for Multi-Objective and Multi-Modal optimization problems

This work proposes a pipeline and a dedicated algorithm for exploring multimodal solutions in multi-objective optimization (MOO). The approach is based on the premise that, after approximating a Pareto front, the decision-maker can define a trade-off of interest and specify thresholds for equivalence in the objective space and distinctiveness in the decision space. A second algorithm, based on Differential Evolution, then searches for alternative decision variable configurations achieving equivalent objective performance. The proposed method was validated on a classic beam design problem through 51 independent runs, analyzing the algorithm's sensitivity to hyperparameter settings. Results demonstrate the algorithm's ability to identify diverse solutions with equivalent performance, enhancing the decision-making process by offering alternatives for practical implementation.