  A minimum Manhattan distance (MMD) approach to multiple criteria decision
making in multiobjective optimization problems (MOPs) is proposed. The approach
selects the final solution corresponding with a vector that has the MMD from a
normalized ideal vector. This procedure is equivalent to the knee selection
described by a divide and conquer approach that involves iterations of pairwise
comparisons. Being able to systematically assign weighting coefficients to
multiple criteria, the MMD approach is equivalent to a weighted-sum (WS)
approach. Because of the equivalence, the MMD approach possesses rich geometric
interpretations that are considered essential in the field of evolutionary
computation. The MMD approach is elegant because all evaluations can be
performed by efficient matrix calculations without iterations of comparisons.
While the WS approach may encounter an indeterminate situation in which a few
solutions yield almost the same WS, the MMD approach is able to determine the
final solution discriminately. Since existing multiobjective evolutionary
algorithms aim for a posteriori decision making, i.e., determining the final
solution after a set of Pareto optimal solutions is available, the proposed MMD
approach can be combined with them to form a powerful solution method of
solving MOPs. Furthermore, the approach enables scalable definitions of the
knee and knee solutions.
