This paper describes a technique on an optimization of tree-structure data by of multi-objective evolutionary algorithm, or multi-objective genetic programming. GP induces bloat of the tree structure as one of the major problem. The cause of bloat is that the tree structure obtained by the crossover operator grows bigger and bigger but its evaluation does not improve. To avoid the risk of bloat, a partial sampling operator is proposed as a mating operator. The size of the tree and a structural distance are introduced into the measure of the tree-structure data as the objective functions in addition to the index of the goodness of tree structure. GP is defined as a three-objective optimization problem. SD is also applied for the ranking of parent individuals instead to the crowding distance of the conventional NSGA-II. When the index of the goodness of tree-structure data is two or more, the number of objective functions in the above problem becomes four or more. We also propose an effective many-objective EA applicable to such the many-objective GP. We focus on NSGA-II based on Pareto partial dominance (NSGA-II-PPD). NSGA-II-PPD requires beforehand a combination list of the number of objective functions to be used for Pareto partial dominance (PPD). The contents of the combination list greatly influence the optimization result. We propose to schedule a parameter r meaning the subset size of objective functions for PPD and to eliminate individuals created by the mating having the same contents as the individual of the archive set.