The optimal base of a matroid/with tree-type constraints

Let M be a matroid defined on a weighted finite set E=(e_1,…,e_n).l(e) is the weight of e∈E.P (X_1,…,X_m) is a set of subsets of E.X_i,X_j∈P,if X_i∩X_j≠(the empty set),then either X_i X_j or X_jX_i.For each X_i∈P,there are two associate nonnegative integers a_i and b_i with o_i≤b_i≤|X_i|.We call a base T of M a feasible base with respect to P(or simply call it a feasible base of M),if X_i∈P,a_i≤|X_i∩T|≤b_i.A base T' is called optimal if:i) This feasible,In this paper we present a polynomial algorithm to solve the optimal base problem.