Ant Colony Optimization for solving Directed Chinese Postman Problem

The Chinese Postman Problem (CPP) is a well-known optimization problem involving determining the shortest route, modeling the system as an undirected graph, for delivering mail, ensuring all roads are traversed while returning to the post office. The Directed Chinese Postman Problem (DCPP) extends the Chinese Postman Problem (CPP), where the underlying graph representing the system incorporates exclusively directed edges. Similarly to CPP, this problem has plenty of applications in route optimization, interactive system analysis, and circuit design problems. However, due to the added constraint (directionality of edges), DCPP results are more challenging to solve. Although methods to solve it in literature are proposed, typically by using minimum-cost-flow algorithms, the meta-heuristics approaches proposed to deal with it are very limited. In this paper, we propose an innovative meta-heuristic approach to solve DCPP by using an ant colony optimization (ACO) algorithm, i.e., an algorithm that simulates in a simplified way the behavior of some species of ants to solve optimization problems. The efficiency of our ant colony optimization for solving the Directed Chinese Postman Problem (ACO-DCPP) is measured by comparing the ACO outcomes with the results obtained by a recursive algorithm that explores all the possible solutions. Results show that ACO-DCPP is stable and gets the global optimum frequently by using an extremely limited number of solutions explored.