A Metaheuristic Approach to Solving the Generalized Vertex Cover Problem

AMS Subj. Classification: 90C27, 05C85, 90C59The topic is related to solving the generalized vertex cover problem (GVCP) by genetic algorithm. The problem is NP-hard as a generalization of well-known vertex cover problem which was one of the first problems shown to be NP-hard. The definition of the GVCP and basics of genetic algorithms are described. Details of genetic algorithm and numerical results are presented in [8]. Genetic algorithm obtained high quality solutions in a short period of time

Combining statistical learning with metaheuristics for the multi-depot vehicle routing problem with market segmentation

In real-life logistics and distribution activities it is usual to face situations in which the distribution of goods has to be made from multiple warehouses or depots to the nal customers. This problem is known as the Multi-Depot Vehicle Routing Problem (MDVRP), and it typically includes two sequential and correlated stages: (a) the assignment map of customers to depots, and (b) the corresponding design of the distribution routes. Most of the existing work in the literature has focused on minimizing distance-based distribution costs while satisfying a number of capacity constraints. However, no attention has been given so far to potential variations in demands due to the tness of the customerdepot mapping in the case of heterogeneous depots. In this paper, we consider this realistic version of the problem in which the depots are heterogeneous in terms of their commercial o er and customers show di erent willingness to consume depending on how well the assigned depot ts their preferences. Thus, we assume that di erent customer-depot assignment maps will lead to di erent customer-expenditure levels. As a consequence, market-segmentation strategies need to be considered in order to increase sales and total income while accounting for the distribution costs. To solve this extension of the MDVRP, we propose a hybrid approach that combines statistical learning techniques with a metaheuristic framework. First, a set of predictive models is generated from historical data. These statistical models allow estimating the demand of any customer depending on the assigned depot. Then, the estimated expenditure of each customer is included as part of an enriched objective function as a way to better guide the stochastic local search inside the metaheuristic framework. A set of computational experiments contribute to illustrate our approach and how the extended MDVRP considered here diré in terms of the proposed solutions from the traditional one.Peer ReviewedPreprin

The Multi-Vehicle Probabilistic Covering Tour Problem

This paper introduces the Multi-Vehicle Probabilistic Covering Tour Problem (MVPCTP) which extends the Covering Tour Problem (CTP) by incorporating multiple vehicles and probabilistic coverage. As in the CTP, total demand of customers is attracted to the visited facility vertices within the coverage range. The objective function is to maximize the expected customer demand covered. The MVPCTP is first formulated as an integer non-linear programming problem, and then a linearization is proposed, which is strengthened by several sets of valid inequalities. An effective branch-and-cut algorithm is developed in addition to a local search heuristic based on Variable Neighborhood Search to obtain upper bounds. Extensive computational experiments are performed on new benchmark instances adapted from the literature