In this paper we address the Swap-Body Vehicle Routing Problem, a variant of the Truck and Trailer Routing Problem. It was introduced in the VeRoLog Challenge 2014. We develop a solution approach that we coin Relax-and-Repair. It consists in solving a relaxed version of the SB-VRP and deriving a feasible solution by repairing the relaxed one. We embed this approach within a population-based heuristic. During computation we store all feasible routes in order to derive better solutions by solving a set-partitioning problem. In order to take advantages of nowadays multi-core machines, our algorithm is designed as a collaborative parallel population-based heuristic. Experimental results show that our relax-and-repair algorithm is very competitive and point the impact of each phase on the quality of the obtained solutions. The advantage of our approach is that it can be adapted to solve complex industrial routing problems.