The expected variable nature of future access network structures calls for network providers to adapt accordingly in order to facilitate loss free networks supported with the developing IP infrastructure. To this end, a routing optimization mechanism applicable to randomly shaped all-IP access networks must be developed. In this paper, Multi-Plane Routing (MPR) that consolidates various aspects in all-IP infrastructure as a whole is redesigned and reformulated to provide a comprehensive solution in consideration of the randomness of future access networks. We prove the offline Routing Plane (RP) construction problem as being the generalization of the Minimum Set Cover (MSC) problem which is NP and also NP-complete. To this end, we propose a novel MSC-based paths-diverse offline TE algorithm which is comprehensively applicable to random wireless access network structures. Our simulation results demonstrate the constructed RPs for complex random networks of different sizes and sparseness (i.e. meshing). Hence, the comprehensive applicability of our novel approach is verified. Moreover, we propose a new optimization framework along with a dynamic cost function (considering capacity and correlation of paths) that formally describe our novel offline TE mechanism for future randomly shaped wireless IP access networks.