Due to dynamic network conditions, routing is the most critical part in WMNs and needs to be optimised. The routing strategies developed for WMNs must be efficient to make it an operationally self configurable network. Thus we need to resort to near shortest path evaluation. This lays down the requirement of some soft computing approaches such that a near shortest path is available in an affordable computing time. This paper proposes a Fuzzy Logic based integrated cost measure in terms of delay, throughput and jitter. Based upon this distance (cost) between two adjacent nodes we evaluate minimal shortest path that updates routing tables. We apply two recent soft computing approaches namely Big Bang Big Crunch (BB-BC) and Biogeography Based Optimization (BBO) approaches to enumerate shortest or near short paths. BB-BC theory is related with the evolution of the universe whereas BBO is inspired by dynamical equilibrium in the number of species on an island. Both the algorithms have low computational time and high convergence speed. Simulation results show that the proposed routing algorithms find the optimal shortest path taking into account three most important parameters of network dynamics. It has been further observed that for the shortest path problem BB-BC outperforms BBO in terms of speed and percent error between the evaluated minimal path and the actual shortest path.