Dimensionality Reduction of Objectives and Constraints in Multi-objective Optimization Problems: A System Design Perspective

The notion of Optimal System Design [12] holds that in order to 'truly' maximize/minimize an objective function, the feasible set needs to be optimized. Inspired by it, the attempt in our recent work [11] was to incorporate constraint-reduction in our earlier proposed procedures on dimensionality reduction of objectives [4], [10]. In that, while targetting constrained single-objective optimization problems (SOPs), we could arrive at a critical set of constraints and also their importance based rank-ordering. This information was used to study the shift from the constrained to the unconstrained optima. The methodology above was based on treating the a priori stated constraints as objectives besides the original-objective, and on applying [4], [10] to this combined objective set-but-without constraints. In this work, the endeavor is to extend the above notion to the realm of multi-objective optimization problems (MOPs). Towards it, while we hire much from the above methodology, we make a fundamental shift, in that, we retain the a priori stated constraints, while evaluating the combined objective set. The motivation for this shift lies, in that, it allows more effective realization of the notion of System Design than the approach in [11]. Reasonable effort has been spent on establishing this argument. Incorporating this change, a procedure for simultaneous reduction in objectives and constraints (for both SON, MOPs) is proposed, which also defines a realizable path towards Optimal System Design. Finally, the procedure is demonstrated on two test problems and one real world problem.