In this chapter, we describe an additional tool for the study of Pareto optimal points (POPs) in comparison to ones considered in Sect. 4.1 : the algorithm A7 for the fusion of sets of POPs . We also propose the algorithm A8, which constructs the set of POPs for bi-criteria optimization of matchings in trees relative to two weight functions. In the end of the chapter, we discuss the notion of a totally optimal matching (optimal relative to two weight functions simultaneously) and show how we can recognize the existence of totally optimal matchings using multi-stage and bi-criteria optimization algorithms. This chapter contains some revised results from the conference paper .