In this chapter the recently introduced multi-Multi-Objective Optimization Problem (m-MOOP) is described and a new evolutionary approach is suggested for its solution. The m-MOOP is a problem, which may be defined as a result of a demand to find solutions for several different multi-objective problems that are to share components. It is argued and explained here, why posing the m-MOOP as a common MOOR is not an option and other approaches should be considered. The previously introduced Evolutionary Multi-Multi Objective Optimization (EMMOO) algorithms, which solve m-MOOPs, including the sequential, and the simultaneous one, are compared here with a new approach. The comparison is based on the loss of optimality measure.
In the chapter another extension to the suggested EMMOOs is considered and posed as a challenge. It is associated with a local search, which should be most important to the problem in hand both for improving results as well as for guarantying robustness. The chapter concludes with a discussion on the generic nature of the m-MOOP and on some possible extensions of the suggested EMMOOs to other fields of interest.