Multi-objective functional analysis for product portfolio optimization

Product portfolio optimization requires that one identify a few designs that provide for the widest variety of functions while minimizing product variety. This requires one to identify groupings of products that meet different functional tradeoffs. Here we propose to use multi-objective optimization for estimating the non-dominated sets of designs, and mapping these to the design space reveals that the good designs are often restricted to a few patches on a low-dimensional manifold, thus resulting in significant dimensionality reductions for the design decision space. We model function in a design family in terms of a phenomenological description, leading to a set of performative behaviours at the functional level, which are determined using set of performance metrics specific to a given embodiment. The non-dominated designs are clustered in the design space in an unsupervised manner to obtain candidate product groupings which the designer may inspect to arrive at portfolio decisions.We demonstrate this process on two different designs (faucets and springs), involving both continuous and discrete design variables. The effect of numerical stability in the process is investigated empirically, and the conditions under which the results would scale to large dimensional spaces are also explored.