Investigating the Significance of “One-to-Many” Mappings in Multiobjective Optimization

Significant research has focused on multiobjective design optimization and negotiating trade-offs between conflicting objectives. Many times, this research has referred to the possibility of attaining similar performance from multiple, unique design combinations. While such occurrences may allow for greater design freedom, their significance has yet to be quantified for trade-off decisions made in the design space (DS). In this paper, we computationally explore which regions of the performance space (PS) exhibit “one-to-many” mappings back to the DS, and examine the behavior and validity of the corresponding region associated with this mapping. Regions of interest in the PS and DS are identified and generated using indifference thresholds to effectively “discretize” both spaces. The properties analyzed in this work are a mapped region’s location in the PS and DS and the total hypervolume of the mappings. Our proposed approach is demonstrated on two different multiobjective engineering problems. The results indicate that one-to-many mappings occur in engineering design problems, and that while these mappings can result in significant design space freedom, they often result in notable performance sacrifice.