Weight Induced Norm Approach to Group Decision Making for Multiobjective Optimization Problems in Systems Engineering

A final solution must be selected from a set of Pareto optimal solutions in the end when a multiobjective optimization problem is solved. Such selection becomes much more complicated for systems engineering when it involves multiple decision makers (DMs). This article proposes a weight induced norm (WIN) approach to group decision making from a systems engineering perspective. The importance of DMs and their preferences on objectives are associated with weighting coefficients using existing transformations. The weights are used to define a norm, introducing the concept of distance. Solution quality is assessed in the objective space. The final solution is the one that corresponds with the vector closest to a normalized ideal vector. Theoretical analysis is conducted to show a number of superior features of the WIN approach: backward compatibility, weighted-sum equivalence, Pareto compliance, invariability in normalization, and pairwise consistency. Numerical analysis illustrates that the WIN approach can produce a final solution reflecting the DMs' importance and their preferences adequately; the WIN approach to solution selection can be interpreted using geometrical or algebraic arguments, which facilitates the DMs' understanding of the decision process; it can readily distinguish the best solution from the remaining ones to avoid ambiguity.