A novel framework for generating tunable and scalable benchmark problems for multimodal multiobjective optimization

This study advances performance analysis, evaluation, and comparison of multimodal multiobjective optimization (MMO) methods. It introduces a novel procedure for systematically generating scalable and tunable MMO problems (MMOPs) from standard multiobjective optimization problems (MOPs). The procedure can simulate various challenges associated with MMO, some of which are difficult, if not impossible, to model using existing benchmark generators. Five composite problems are suggested, each based on a widely used standard MOP. This study also proposes a novel parametric performance indicator, called the Inverted Generational Effective Distance (IGED), which jointly considers convergence and diversity in both the objective and decision spaces. A control parameter within the indicator allows adjusting the relative importance of convergence and diversity in both spaces. Controlled simulations investigate the necessity and impact of this parameter. Finally, the performance of several promising MMO methods is assessed on the proposed MMOPs using IGED, serving as a reference point for future research.