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

Peter Simov, Scott Ferguson
2010 Volume 1: 36th Design Automation Conference, Parts A and B   unpublished
SIMOV, PETER RANGELOV. Investigating the Significance of "One-to-many" Mappings in Multiobjective Optimization. (Under the direction of Scott Michael Ferguson.) 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. These occurrences allow for greater design freedom. Their significance has
more » ... ir significance has not been used to quantify trade-off decisions made in the design space (DS). The current thesis computationally explores which regions of the performance space (PS) exhibit "one-to-many" mappings back to the DS, examines the behavior and validity of the corresponding regions associated with this mapping. The research investigates the performances from two different sets of designs. One set contains Pareto-optimal designs, generated using multiobjective genetic algorithm. The second set of designs is generated using Latin Hypercube sampling over the design domain to obtain dominated performances. Mappings are generated from the PS of each set to the DS using indifference thresholds to effectively "discretize" both spaces. A mappings's location in the PS and its mapped design bounds are analyzed. The total design hypervolume of the mappings contribute to design freedom. The thesis demonstrates the method on three 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.
doi:10.1115/detc2010-28689 fatcat:eo3654qjunh67bveqoztqt3vx4