The New Approaches Based on Ant Colony Optimization and Greedy Search Algorithm for Solving Hierarchical Chinese Postman Problem with Stochastic Travel Times

Hierarchical Chinese postman problem (HCPP), a variant of the Chinese postman problem, aims to find the shortest tour or tours by passing through the arcs classified according to precedence relationship. HCPP, which has a wide application area in real-life problems such as shovel snow and routing patrol vehicles where precedence relations are important, belongs to the NP-hard problem class. In real-life problems, travel time between the two locations in city traffic varies due to reasons such as traffic jam, weather conditions, etc. Therefore travel times are uncertain. In this study, HCPP is handled with the chance-constrained stochastic programming approach, and a new type of problem, hierarchical Chinese postman problem with stochastic travel times, is introduced. Due to the NP-hard nature of the problem, the developed mathematical model with stochastic parameter values cannot find proper solutions in large size problems within the appropriate time interval. Therefore, two new solution approaches, a heuristic method based on the Greedy Search (GSA) algorithm and a meta-heuristic method based on ant colony optimization (ACO) are proposed in this study. These new algorithms were tested on modified benchmark instances and randomly generated problem instances with as many as 817 edges. The performance of algorithms was compared in terms of solution quality and computational time.

On the periodic hierarchical Chinese postman problem

This paper presents a mathematical formulation and a heuristic approach for a new variant of the Hierarchical Chinese Postman Problem (HCPP). Indeed, we introduce the concept of periodicity, and we define and solve, for the first time, the Periodic-HCPP, denoted as P-HCPP. Given that the resulting integer programming model makes use of a big number of binary variables and given the extended time horizon considered, 30 days in our case, the problem is characterized by a high level of complexity. However, our developed heuristic is able to solve instances having up to 40 nodes, 520 arcs and 5 hierarchies, whereas a general-purpose solver like Gurobi was not able to provide solutions for instances having more than 10 nodes. While the collected results are very encouraging, we provide at the end of this paper a set of possible future extensions of this work.

A Parallel Bioinspired Algorithm for Chinese Postman Problem Based on Molecular Computing

The Chinese postman problem is a classic resource allocation and scheduling problem, which has been widely used in practice. As a classical nondeterministic polynomial problem, finding its efficient algorithm has always been the research direction of scholars. In this paper, a new bioinspired algorithm is proposed to solve the Chinese postman problem based on molecular computation, which has the advantages of high computational efficiency, large storage capacity, and strong parallel computing ability. In the calculation, DNA chain is used to properly represent the vertex, edge, and corresponding weight, and then all possible path combinations are effectively generated through biochemical reactions. The feasible solution space is obtained by deleting the nonfeasible solution chains, and the optimal solution is solved by algorithm. Then the computational complexity and feasibility of the DNA algorithm are proved. By comparison, it is found that the computational complexity of the DNA algorithm is significantly better than that of previous algorithms. The correctness of the algorithm is verified by simulation experiments. With the maturity of biological operation technology, this algorithm has a broad application space in solving large-scale combinatorial optimization problems.

Optimized Route to Clear Diverging Diamond Interchange Using Discrete Optimization Method

Interchanges and intersections are the most complex part of a roadway network and are very challenging for snow plowing operators. The objective of the study is to test if the empirical best plowing route to clear a Diverging Diamond Interchange (DDI) recommended by Clear Roads is also mathematically optimized. A discrete optimization method was employed to find the shortest route. In the study, the DDI is represented as a directed graph model. The task of clearing all lanes is treated as the well-known directed Chinese postman problem, which was then solved by an existing network optimization algorithm upon appropriate modification. The results showed that the best practice plowing route recommended by Clear Roads is one of the computed optimal routes with the Efficiency Index of 2/3. The approach proposed in the study can also be applied to other complex intersections and interchanges and help agencies achieve cost-effective snow control operations.