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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. [ABSTRACT FROM AUTHOR]

The utilization of cloud computing environments is highly popular for carrying out workflow executions due to its ability to provide clients with immediate access to computing resources. Among the various workflow scheduling problems in the cloud, deadline-constrained workflow scheduling has garnered increasing attention in recent years. This paper introduces a hybrid scheduling algorithm known as Partial Critical Path–Ant Colony Optimization (PCP–ACO), which aims to minimize the execution cost of a workflow while ensuring that it meets the user-defined deadline in cloud environments. PCP–ACO is a list scheduling algorithm that combines the PCP heuristic algorithm with the meta-heuristic ACO to achieve faster convergence. The list scheduling algorithm consists of two phases: task ordering and resource selection. In the case of PCP–ACO, the first step involves calculating a topological sort of the workflow tasks to assign priority to each task. Subsequently, the ACO meta-heuristic is employed to allocate the appropriate resource to each task of the workflow, based on their respective sub-deadlines that are computed using the PCP heuristic. In order to evaluate the effectiveness of the proposed algorithm, several experiments were conducted using five real scientific workflows. The results demonstrate that PCP–ACO outperforms the IC-PCP, L-ACO, and HP-GA algorithms in terms of average execution cost, achieving reductions of 19%, 17.3%, and 21.5%, respectively. [ABSTRACT FROM AUTHOR]