Higher and lower-level knowledge discovery from Pareto-optimal sets

Abstract

Innovization (innovation through optimization) is a relatively new concept in the field of multi-objective engineering design optimization. It involves the use of Pareto-optimal solutions of a problem to unveil hidden mathematical relationships between variables, objectives and constraint functions. The obtained relationships can be thought of as essential properties that make a feasible solution Pareto-optimal. This paper proposes two major extensions to innovization, namely higher-level innovization and lower-level innovization. While the former deals with the discovery of common features among solutions from different Pareto-optimal fronts, the latter concerns features commonly occurring among solutions that belong to a specified (or preferred) part of the Pareto-optimal front. The knowledge of such lower-level information is extremely beneficial to a decision maker, since it focuses on a preferred set of designs. On the other hand, higher-level innovization reveals interesting knowledge about the general problem structure. Neither of these crucial aspects concerning multi-objective designs has been addressed before, to the authors' knowledge. We develop methodologies for handling both levels of innovization by extending the authors' earlier automated innovization algorithm and apply them to two well-known engineering design problems. Results demonstrate that the proposed methodologies are generic and are ready to be applied to other engineering design problems.