Application of Gröbner bases and quantifier elimination for insightful engineering design

Abstract

Engineering design is a process of generating a design solution satisfying customers' various requirements. As the design proceeds, more and more parameters are introduced to define the design solution. As more design parameters come into design consideration, designers face increasing difficulties in gaining insights into the relationships among these parameters. This research aims at overcoming the above difficulties by applying techniques of Grobner basis (GB) and quantifier elimination (QE). The new constraint-solving methods derived from these techniques help designers in gaining important insights during engineering design. These constraint-solving methods have been evaluated through case studies of multidisciplinary engineering design. The evaluation results have illustrated these constraint-solving methods are useful for gaining insights that help designers in making informed design decisions.