Solving the Traveling Salesperson Problem with Precedence Constraints by Deep Reinforcement Learning

This work presents solutions to the Traveling Salesperson Problem with precedence constraints (TSPPC) using Deep Reinforcement Learning (DRL) by adapting recent approaches that work well for regular TSPs. Common to these approaches is the use of graph models based on multi-head attention (MHA) layers. One idea for solving the pickup and delivery problem (PDP) is using heterogeneous attentions to embed the different possible roles each node can take. In this work, we generalize this concept of heterogeneous attentions to the TSPPC. Furthermore, we adapt recent ideas to sparsify attentions for better scalability. Overall, we contribute to the research community through the application and evaluation of recent DRL methods in solving the TSPPC.Comment: This preprint has not undergone peer review or any post-submission improvements or corrections. The Version of Record of this contribution is published in KI 2022: Advances in Artificial Intelligence, and is available online at https://doi.org/10.1007/978-3-031-15791-2_1

Optimal Design and Operation of WHO-EPI Vaccine Distribution Chains

Vaccination has been proven to be the most effective method to prevent infectious diseases and in 1974 the World Health Organization (WHO) established the Expanded Programme on Immunization (EPI) to provide universal access to all important vaccines for all children, with a special focus on underserved low- and middle-income countries. However, there are still roughly 20 million infants worldwide who lack access to routine immunization services and remain at risk, and millions of additional deaths could be avoided if global vaccination coverage could improve. The broad goal of this research is to optimize the design and operation of the WHO-EPI vaccine distribution chain in these underserved low- and middle-income countries. We first present a network design problem for a general WHO-EPI vaccine distribution network by developing a mathematical model that formulates the network design problem as a mixed integer program (MIP). We then present three algorithms for typical problems that are too large to be solved using commercial MIP software. We test the algorithms using data derived from four different countries in sub-Saharan Africa and show that with our final algorithm, high-quality solutions are obtained for even the largest problems within a few minutes. We then discuss the problem of outreach to remote population centers when resources are limited and direct clinic service is unavailable. A set of these remote population centers is chosen, and over an appropriate planning period, teams of clinicians and support personnel are sent from a depot to set up mobile clinics at these locations to vaccinate people there and in the immediate surrounding area. We formulate the problem of designing outreach efforts as an MIP that is a combination of a set covering problem and a vehicle routing problem. We then incorporate uncertainty to study the robustness of the worst-case solutions and the related issue of the value of information. Finally, we study a variation of the outreach problem that combines Set Covering and the Traveling Salesmen Problem and provides an MIP formulation to solve the problem. Motivated by applications where the optimal policy needs to be updated on a regular basis and where repetitively solving this via MIP can be computationally expensive, we propose a machine learning approach to effectively deal with this problem by providing an opportunity to learn from historical optimal solutions that are derived from the MIP formulation. We also present a case study on outreach operations and provide numerical results. Our results show that while the novel machine learning based mechanism generates high quality solution repeatedly for problems that resemble instances in the training set, it does not generalize as well on a different set of optimization problems. These mixed results indicate that there are promising research opportunities to use machine learning to achieve tractability and scalability

Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instances

For the traveling salesman problem (TSP), the existing supervised learning based algorithms suffer seriously from the lack of generalization ability. To overcome this drawback, this paper tries to train (in supervised manner) a small-scale model, which could be repetitively used to build heat maps for TSP instances of arbitrarily large size, based on a series of techniques such as graph sampling, graph converting and heat maps merging. Furthermore, the heat maps are fed into a reinforcement learning approach (Monte Carlo tree search), to guide the search of high-quality solutions. Experimental results based on a large number of instances (with up to 10,000 vertices) show that, this new approach clearly outperforms the existing machine learning based TSP algorithms, and significantly improves the generalization ability of the trained model