Author(s)： Hitoshi Yanami

J. Math-for-Ind. 1B (2009) 149-156.

• File： JMI2009B-8.pdf (367KB)

Abstract
We propose a new approach to tackling multi-objective optimization problems. Our method uses symbolic computation called quantifier elimination. From experimental data we first make an approximated polynomial model　for each objective function and then solve a first-order formula related to those functions to find the feasible region, which contains information on the Pareto optimal front. Our approach has an advantage over classical numerical optimization methods that return only one optimal point at a time. Furthermore, by introducing into a formula an adjusting point and a new variable that restricts the parameter ranges we can visualize how the objective functions locally behave. This idea leads us to a new criterion for measuring the robustness against production tolerance. We also show how our methods are applied to the design problem of a hard disk slider.

Keyword(s).　 symbolic computation, quantifier elimination, multi-objective optimization