Reactive GRASP for the prize-collecting covering tour problem

This paper presents a greedy randomized adaptive search procedure (GRASP) for the prize-collecting covering tour problem, which is the problem of finding a route for traveling teams that provide services to communities geographically distant from large urban locations. We devised a novel hybrid heuristic by combining a reactive extension of the GRASP with Random Variable Neighborhood Search (VND) meta-heuristic for the purpose of solving the PCCTP. Computational experiments were conducted on a PCCTP benchmark from the literature, and the results demonstrate our approach provides a significant improvement in solving PCCTP and comparable with the state-of-the-art, mainly regarding the computational processing time.

Two meta-heuristics for solving the multi-vehicle multi-covering tour problem with a constraint on the number of vertices

In this work we deal with a generalized variant of the multi-vehicle covering tour problem (m-CTP). The m-CTP consists of minimizing the total routing cost and satisfying the entire demand of all customers, without the restriction of visiting them all, so that each customer not included in any route is covered. In the m-CTP, only a subset of customers is visited to fulfill the total demand, but a restriction is put on the length of each route and the number of vertices that it contains. This paper tackles a generalized variant of the m-CTP, called the multi-vehicle multi-covering Tour Problem (mm-CTP), where a vertex must be covered several times instead of once. We study a particular case of the mm-CTP considering only the restriction on the number of vertices in each route and relaxing the constraint on the length (mm-CTP-p). A hybrid metaheuristic is developet by combining Genetic Algorithm (GA), Variable Neighborhood Descent method (VND), and a General Variable Neighborhood Search algorithm (GVNS) to solve the problem. Computational experiments show that our approaches are competitive with the Evolutionary Local Search (ELS) and Genetic Algorithm (GA), the methods proposed in the literature.

Iterative Column Generation Algorithm for Generalized Multi-Vehicle Covering Tour Problem

The multi-vehicle covering tour problem ([Formula: see text]-CTP) is defined on a graph [Formula: see text], where [Formula: see text] is a set of vertices that can be visited and [Formula: see text] is a set of vertices that must be covered but cannot be visited. The objective of the [Formula: see text]-CTP is to obtain a set of total minimum cost tours on subset of [Formula: see text], while covering all [Formula: see text] by up to [Formula: see text] vehicles. In this paper, we first generalize the original [Formula: see text]-CTP by adding a realistic constraint, and then propose an algorithm for the generalized [Formula: see text]-CTP using a column generation approach. Computational experiments show that our algorithm performs well and outperforms the existing algorithms.

A generalized model and a heuristic algorithm for the large-scale covering tour problem

The covering tour problem (CTP) is defined on a graph, where there exist two types of vertices. One is called visited vertex, which can be visited. The other is called covered vertex, which must be covered but cannot be visited. Each visited vertex covers a subset of covered vertices, and the costs of edges between visited vertices are given. The objective of the CTP is to obtain a minimum cost tour on a subset of visited vertices while covering all covered vertices. In this paper, we deal with the large-scale CTPs, which are composed of tens of thousands of vertices; in the previous studies, the scales of the instances in the experiments are at most a few hundred vertices. We propose a heuristic algorithm using local search techniques for the large-scale CTP. With computational experiments, we show that our algorithm outperforms the existing methods.