In summary, we study effective potentials for description of the mud + p and mup+ d scattering. In this work we use integral potential surfaces which have recently been reported. Such potentials have been written for Jacobi coordinates. At first, the potential functions are simplified and then are optimized using differential evolution method. The s-wave cross-sections at the mud(1s)+p scattering are estimated at low-energies. For precise assessment of the reliability of the method, the lowest state of the pdmu molecule is estimated and compared with those previously reported. Our results agree good with those previously reported.