The Team Orienteering Arc Routing Problem

The team orienteering arc routing problem (TOARP) is the extension to the arc routing setting of the team orienteering problem. In the TOARP, in addition to a possible set of regular customers that have to be serviced, another set of potential customers is available. Each customer is associated with an arc of a directed graph. Each potential customer has a profit that is collected when it is serviced, that is, when the associated arc is traversed. A fleet of vehicles with a given maximum traveling time is available. The profit from a customer can be collected by one vehicle at most. The objective is to identify the customers that maximize the total profit collected while satisfying the given time limit for each vehicle. In this paper we propose a formulation for this problem and study a relaxation of its associated polyhedron. We present some families of valid and facet-inducing inequalities that we use in the implementation of a branch-and-cut algorithm for the resolution of the problem. Computational experiments are run on a large set of benchmark instances.The authors thank the reviewers for their comments that helped to provide an improved and clearer version of this paper. Angel Corberan, Isaac Plana, and Jose M. Sanchis wish to thank the Ministerio de Ciencia e Innovacion [Project MTM2009-14039-C06-02] and the Ministerio of Economia y Competitividad [Project MTM2012-36163-C06-02] of Spain for their support.Archetti, C.; Speranza, MG.; Corberan, A.; Sanchís Llopis, JM.; Plana, I. (2014). The Team Orienteering Arc Routing Problem. Transportation Science. 48(3):442-457. https://doi.org/10.1287/trsc.2013.0484S44245748

A matheuristic for the Team Orienteering Arc Routing Problem

In the Team OrienteeringArc Routing Problem (TOARP) the potential customers are located on the arcs of a directed graph and are to be chosen on the basis of an associated profit. A limited fleet of vehicles is available to serve the chosen customers. Each vehicle has to satisfy a maximum route duration constraint. The goal is to maximize the profit of the served customers. We propose a matheuristic for the TOARP and test it on a set of benchmark instances for which the optimal solution or an upper bound is known. The matheuristic finds the optimal solutions on all, except one, instances of one of the four classes of tested instances (with up to 27 vertices and 296 arcs). The average error on all instances fo rwhich the optimal solution is available is 0.67 percent.Angel Corberan, Isaac Plana and Jose M. Sanchis wish to thank the Ministerio de Economia y Competitividad (project MTM2012-36163-C06-02) of Spain and the Generalitat Valenciana (project GVPROMETEO2013-049) for their support.Archetti, C.; Corberan, A.; Plana, I.; Sanchís Llopis, JM.; Speranza, MG. (2015). A matheuristic for the Team Orienteering Arc Routing Problem. European Journal of Operational Research. 245(2):392-401. https://doi.org/10.1016/j.ejor.2015.03.022S392401245

The Vehicle Routing Problem with Service Level Constraints

We consider a vehicle routing problem which seeks to minimize cost subject to service level constraints on several groups of deliveries. This problem captures some essential challenges faced by a logistics provider which operates transportation services for a limited number of partners and should respect contractual obligations on service levels. The problem also generalizes several important classes of vehicle routing problems with profits. To solve it, we propose a compact mathematical formulation, a branch-and-price algorithm, and a hybrid genetic algorithm with population management, which relies on problem-tailored solution representation, crossover and local search operators, as well as an adaptive penalization mechanism establishing a good balance between service levels and costs. Our computational experiments show that the proposed heuristic returns very high-quality solutions for this difficult problem, matches all optimal solutions found for small and medium-scale benchmark instances, and improves upon existing algorithms for two important special cases: the vehicle routing problem with private fleet and common carrier, and the capacitated profitable tour problem. The branch-and-price algorithm also produces new optimal solutions for all three problems

Profitable mixed capacitated arc routing and related problems

Mixed Capacitated Arc Routing Problems (MCARP) aim to identify a set of vehicle trips that, starting and ending at a depot node, serve a given number of links, regarding the vehicles capacity, and minimizing a cost function. If both profits and costs on arcs are considered, the Profitable Mixed Capacitated Arc Routing Problem (PMCARP) may be defined. We present compact flow based models for the PMCARP, where two types of services are tackled, mandatory and optional. Adaptations of the models to fit into some other related problems are also proposed. The models are evaluated, according to their bounds quality as well as the CPU times, over large sets of test instances. New instances have been created from benchmark ones in order to solve variants that have been introduced here for the first time. Results show the new models performance within CPLEX and compare, whenever available, the proposed models against other resolution methods.info:eu-repo/semantics/publishedVersio

An Optimal Control Theory for the Traveling Salesman Problem and Its Variants

We show that the traveling salesman problem (TSP) and its many variants may be modeled as functional optimization problems over a graph. In this formulation, all vertices and arcs of the graph are functionals; i.e., a mapping from a space of measurable functions to the field of real numbers. Many variants of the TSP, such as those with neighborhoods, with forbidden neighborhoods, with time-windows and with profits, can all be framed under this construct. In sharp contrast to their discrete-optimization counterparts, the modeling constructs presented in this paper represent a fundamentally new domain of analysis and computation for TSPs and their variants. Beyond its apparent mathematical unification of a class of problems in graph theory, the main advantage of the new approach is that it facilitates the modeling of certain application-specific problems in their home space of measurable functions. Consequently, certain elements of economic system theory such as dynamical models and continuous-time cost/profit functionals can be directly incorporated in the new optimization problem formulation. Furthermore, subtour elimination constraints, prevalent in discrete optimization formulations, are naturally enforced through continuity requirements. The price for the new modeling framework is nonsmooth functionals. Although a number of theoretical issues remain open in the proposed mathematical framework, we demonstrate the computational viability of the new modeling constructs over a sample set of problems to illustrate the rapid production of end-to-end TSP solutions to extensively-constrained practical problems.Comment: 24 pages, 8 figure