A revisited branch-and-cut algorithm for large-scale orienteering problems

The orienteering problem is a route optimization problem which consists of finding a simple cycle that maximizes the total collected profit subject to a maximum distance limitation. In the last few decades, the occurrence of this problem in real-life applications has boosted the development of many heuristic algorithms to solve it. However, during the same period, not much research has been devoted to the field of exact algorithms for the orienteering problem. The aim of this work is to develop an exact method which is able to obtain the optimum in a wider set of instances than with previous methods, or to improve the lower and upper bounds in its disability. We propose a revisited version of the branch-and-cut algorithm for the orienteering problem which includes new contributions in the separation algorithms of inequalities stemming from the cycle problem, in the separation loop, in the variables pricing, and in the calculation of the lower and upper bounds of the problem. Our proposal is compared to three state-of-the-art algorithms on 258 benchmark instances with up to 7397 nodes. The computational experiments show the relevance of the designed components where 18 new optima, 76 new best-known solutions and 85 new upper-bound values were obtained

Two-Stage Robust Optimization for the Orienteering Problem with Stochastic Weights

In this paper, the two-stage orienteering problem with stochastic weights is studied, where the first-stage problem is to plan a path under the uncertain environment and the second-stage problem is a recourse action to make sure that the length constraint is satisfied after the uncertainty is realized. First, we explain the recourse model proposed by Evers et al. (2014) and point out that this model is very complex. Then, we introduce a new recourse model which is much simpler with less variables and less constraints. Based on these two recourse models, we introduce two different two-stage robust models for the orienteering problem with stochastic weights. We theoretically prove that the two-stage robust models are equivalent to their corresponding static robust models under the box uncertainty set, which indicates that the two-stage robust models can be solved by using common mathematical programming solvers (e.g., IBM CPLEX optimizer). Furthermore, we prove that the two two-stage robust models are equivalent to each other even though they are based on different recourse models, which indicates that we can use a much simpler model instead of a complex model for practical use. A case study is presented by comparing the two-stage robust models with a one-stage robust model for the orienteering problem with stochastic weights. The numerical results of the comparative studies show the effectiveness and superiority of the proposed two-stage robust models for dealing with the two-stage orienteering problem with stochastic weights

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

The Team Orienteering Problem with Overlaps : An Application in Cash Logistics

The team orienteering problem (TOP) aims at finding a set of routes subject to maximum route duration constraints that maximize the total collected profit from a set of customers. Motivated by a real-life automated teller machine cash replenishment problem that seeks for routes maximizing the number of bank account holders having access to cash withdrawal, we investigate a generalization of the TOP that we call the team orienteering problem with overlaps (TOPO). For this problem, the sum of individual profits may overestimate the real profit. We present exact solution methods based on column generation and a metaheuristic based on large neighborhood search to solve the TOPO. An extensive computational analysis shows that the proposed solution methods can efficiently solve synthetic and real-life TOPO instances. Moreover, the proposed methods are competitive with the best algorithms from the literature for the TOP. In particular, the exact methods can find the optimal solution of 371 of the 387 benchmark TOP instances, 33 of which are closed for the first time

An evolutionary algorithm for online, resource constrained, multi-vehicle sensing mission planning

Mobile robotic platforms are an indispensable tool for various scientific and industrial applications. Robots are used to undertake missions whose execution is constrained by various factors, such as the allocated time or their remaining energy. Existing solutions for resource constrained multi-robot sensing mission planning provide optimal plans at a prohibitive computational complexity for online application [1],[2],[3]. A heuristic approach exists for an online, resource constrained sensing mission planning for a single vehicle [4]. This work proposes a Genetic Algorithm (GA) based heuristic for the Correlated Team Orienteering Problem (CTOP) that is used for planning sensing and monitoring missions for robotic teams that operate under resource constraints. The heuristic is compared against optimal Mixed Integer Quadratic Programming (MIQP) solutions. Results show that the quality of the heuristic solution is at the worst case equal to the 5% optimal solution. The heuristic solution proves to be at least 300 times more time efficient in the worst tested case. The GA heuristic execution required in the worst case less than a second making it suitable for online execution.Comment: 8 pages, 5 figures, accepted for publication in Robotics and Automation Letters (RA-L