Branch-Price-and-Cut for the Soft-Clustered Capacitated Arc-Routing Problem

The soft-clustered capacitated arc-routing problem (SoftCluCARP) is a variant of the classical capacitated arc-routing problem. The only additional constraint is that the set of required edges, that is, the streets to be serviced, is partitioned into clusters, and feasible routes must respect the soft-cluster constraint, that is, all required edges of the same cluster must be served by the same vehicle. In this article, we design an effective branch-price-and-cut algorithm for the exact solution of the SoftCluCARP. Its new components are a metaheuristic and branch-and-cut-based solvers for the solution of the column-generation subproblem, which is a profitable rural clustered postman tour problem. Although postman problems with these characteristics have been studied before, there is one fundamental difference here: clusters are not necessarily vertex-disjoint, which prohibits many preprocessing and modeling approaches for clustered postman problems from the literature. We present an undirected and a windy formulation for the pricing subproblem and develop and computationally compare two corresponding branch-and-cut algorithms. Cutting is also performed at the master-program level using subset-row inequalities for subsets of size up to five. For the first time, these nonrobust cuts are incorporated into MIP-based routing subproblem solvers using two different modeling approaches. In several computational studies, we calibrate the individual algorithmic components. The final computational experiments prove that the branch-price-and-cut algorithm equipped with these problem-tailored components is effective: The largest SoftCluCARP instances solved to optimality have more than 150 required edges or more than 50 clusters.

Genetic Algorithm for the Capacitated Chinese Postman Problem on Mixed Networks

The genetic algorithm is used to investigate the Chinese postman problem with the constraints of working time span and load capacity for postman on mixed networks. In course of chromosome encoding, the priority-based encoding for serving edges set is used, and the priority and the strategy of “serve while going” in the shortest path is integrated to use in course of decoding. A genetic scheme is designed to solve the capacitated Chinese postman problem without translating arc routing problem into node routing problem. The simulation experiments show that the methods is feasible and efficient, it can easily solve the capacitated Chinese postman problems on all kinds of complex networks.