This paper considers a multi-objective version of the Multiple Traveling Salesman Problem (MOmTSP). In particular, two objectives are considered: the minimization of the total traveled distance and the balance of the working times of the traveling salesmen. The problem is formulated as an integer multi-objective optimization model. A non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve the MOmTSP. The solution scheme allows one to find a set of ordered solutions in Pareto fronts by considering the concept of dominance. Tests on real world instances and instances adapted from the literature show the effectiveness of the proposed algorithm.

This paper proposes a metaheuristic algorithm to solve the Multi-Depot Vehicle Routing Problem with a Heterogeneous Fleet (MDHFVRP). The problem consists of determining the customers and the vehicles to be assigned to each used depot and the routes to be performed to fulfill the demands of a set of customers. The objective is to minimize the sum of the fixed cost associated with the used vehicles and of the variable traveling costs related to the performed routes. The proposed approach is based on a modified genetic algorithm, which generates an initial population with heuristic solutions obtained from the well-known (LKH) heuristic algorithm for the TSP together with the solution of a mathematical model for the shortest path problem. In addition, two recombination methods and a mutation operator are considered. Computational experiments on benchmark instances show that the proposed algorithm can obtain high-quality solutions within short computing times.

This paper presents the implementation of an efficient modified genetic algorithm for solving the multi-traveling salesman problem (mTSP). The main characteristics of the method are the construction of an initial population of high quality and the implementation of several local search operators which are important in the efficient and effective exploration of promising regions of the solution space. Due to the combinatorial complexity of mTSP, the proposed methodology is especially applicable for real-world problems. The proposed algorithm was tested on a set of six benchmark instances, which have from 76 and 1002 cities to be visited. In all cases, the best known solution was improved. The results are also compared with other existing solutions procedure in the literature.

In this article, a hybrid algorithm is proposed to solve the Vehicle Scheduling Problem with Multiple Depots. The proposed methodology uses a genetic algorithm, initialized with three specialized constructive procedures. The solution generated by this first approach is then refined by means of a Set Partitioning (SP) model, whose variables (columns) correspond to the current itineraries of the final population. The SP approach possibly improves the incumbent solution which is then provided as an initial point to a well-known MDVSP model. Both the SP and MDVSP models are solved with the help of a mixed integer programming (MIP) solver. The algorithm is tested in benchmark instances consisting of 2, 3 and 5 depots, and a service load ranging from 100 to 500. The results obtained showed that the proposed algorithm was capable of finding the optimal solution in most cases when considering a time limit of 500 seconds. The methodology is also applied to solve a real-life instance that arises in the transportation system in Colombia (2 depots and 719 services), resulting in a decrease of the required fleet size and a balanced allocation of services, thus reducing deadhead trips.

El problema de programación de rutas en una empresa de transporte generalmente considera varios escenarios de distribución de bienes los cuales, a su vez, constituyen diferentes grados de complejidad en su programación. Un escenario común consiste en establecer la ruta más corta para la distribución de un conjunto de productos a través de un único vehículo. Sin embargo, existen escenarios mucho más complejos de modelar, en donde se consideran varios vehículos partiendo desde diferentes puntos a fin de distribuir los bienes a un conjunto amplio de clientes, ventanas de tiempo, entrega y recogida simultánea y entrega primero y recogida al regreso. En este libro se presenta un conjunto de problemáticas propias de la programación óptima de rutas, cuyos modelos han sido estudiados, definidos, propuestos y evaluados en el desarrollo del proyecto titulado: Herramienta computacional para la programación óptima de rutas en una empresa de transporte de carga, considerando diferentes estrategias de distribución de productos con código 6-19-5, realizado con el apoyo de la universidad Tecnológica de Pereira y su vicerrectoría de Investigaciones, Innovación y Extensión. Estos modelos son concatenados de forma pedagógica y gradual, con el objetivo de transitar fácilmente desde el modelo simple del TSP hasta el OLRP, pasando por el MTSP, CVRP y MCVRP. El aspecto pedagógico consiste en que la presentación de los problemas debe permitir apreciar el crecimiento gradual del modelo clásico del TSP, a través de restricciones, parámetros y variables adicionales, así como modificaciones a la función objetivo, hasta convertirse en los problemas subsecuentes. De esta forma, un estudiante de maestría, doctorado, o en general cualquier lector interesado, podría experimentar con la inclusión y exclusión de restricciones en el modelo para visualizar el impacto sobre los resultados obtenidos.