Inspired by interaction behaviors of individuals in swarm intelligence, a novel algorithm for combinatorial optimization is proposed, which is called as Route-Exchange Algorithm (REA). In the heuristic approach, individuals of a swarm search the state space independently and simultaneously. When one encounters another in the process, they would interact with each other, exchange the information of routes toured, and utilize the more valuable experiences to improve their own search efficiency. In this paper, the algorithm is applied to assignment problem and quadric assignment problem. The experiment results indicate the algorithm can quickly converge to the optimal solution with quite low cost.