The location of the distribution facilities and the routing of the vehicles from these facilities are interdependent in many distribution systems. Such a concept recognizes the interdependence; attempts to integrate these two decisions have been limited. Multi-objective location-routing problem (MLRP) is combined with the facility location and the vehicle routing decision and satisfied the different objectives. Due to the problem complexity, simultaneous solution methods are limited, which are given in different objectives with conflicts in functions satisfied. Two kinds of optimal mathematical models are proposed for the solution of MLRP. Three methods have been emphatically developed for MLRP. MGA architecture makes it possible to search the solution space efficiently, which provides a path for searching the solution with two-objective LRP. At last the practical proof is given by random analysis for regional distribution with nine cities.