The cutting plane method is an augmentative constrained optimization procedure that is often used with continuous-domain optimization techniques such as linear and convex programs. We investigate the viability of a similar idea within message passing -- which produces integral solutions -- in the context of two combinatorial problems: 1) For Traveling Salesman Problem (TSP), we propose a factor-graph based on Held-Karp formulation, with an exponential number of constraint factors, each of which has an exponential but sparse tabular form. 2) For graph-partitioning (a.k.a., community mining) using modularity optimization, we introduce a binary variable model with a large number of constraints that enforce formation of cliques. In both cases we are able to derive surprisingly simple message updates that lead to competitive solutions on benchmark instances. In particular for TSP we are able to find near-optimal solutions in the time that empirically grows with N^3, demonstrating that augmentation is practical and efficient.
Fuzhou University（福州大学）；Université d’Angers（昂热大学）；Huazhong University of Science and Technology（华中科技大学）
The Clustered Traveling Salesman Problem (CTSP) is a variant of the popular Traveling Salesman Problem (TSP) arising from a number of real-life applications. In this work, we explore a transformation approach that solves the CTSP by converting it to the well-studied TSP. For this purpose, we first investigate a technique to convert a CTSP instance to a TSP and then apply powerful TSP solvers (including exact and heuristic solvers) to solve the resulting TSP instance. We want to answer the following questions: How do state-of-the-art TSP solvers perform on clustered instances converted from the…
University of Technology and Engineering, Vietnam National University（越南国立大学工程技术大学）；Interuniversitary Research Centre on Entreprise Networks, Logistics and Transportation (CIRRELT)（企业网络、物流与运输校际研究中心（CIRRELT））；Polytechnique Montréal（蒙特利尔理工学院）
The Clustered Traveling Salesman Problem with a Prespecified Order on the Clusters, a variant of the well-known traveling salesman problem is studied in literature. In this problem, delivery locations are divided into clusters with different urgency levels and more urgent locations must be visited before less urgent ones. However, this could lead to an inefficient route in terms of traveling cost. This priority-oriented constraint can be relaxed by a rule called d-relaxed priority that provides a trade-off between transportation cost and emergency level. Our research proposes two approaches to…
With applications to many disciplines, the traveling salesman problem (TSP) is a classical computer science optimization problem with applications to industrial engineering, theoretical computer science, bioinformatics, and several other disciplines. In recent years, there have been a plethora of novel approaches for approximate solutions ranging from simplistic greedy to cooperative distributed algorithms derived from artificial intelligence. In this paper, we perform an evaluation and analysis of cornerstone algorithms for the Euclidean TSP. We evaluate greedy, 2-opt, and genetic algorithms.…
Institute for Advanced Studies（高等研究院）；Aeronautics Institute of Technology（航空技术学院）
Using an enhanced Self-Organizing Map method, we provided suboptimal solutions to the Traveling Salesman Problem. Besides, we employed hyperparameter tuning to identify the most critical features in the algorithm. All improvements in the benchmark work brought consistent results and may inspire future efforts to improve this algorithm and apply it to different problems.
We present a self-learning approach that combines deep reinforcement learning and Monte Carlo tree search to solve the traveling salesman problem. The proposed approach has two advantages. First, it adopts deep reinforcement learning to compute the value functions for decision, which removes the need of hand-crafted features and labelled data. Second, it uses Monte Carlo tree search to select the best policy by comparing different value functions, which increases its generalization ability. Experimental results show that the proposed method performs favorably against other methods in small-to-…
Tay Bac University（西北大学）；Hanoi University of Science and Technology（河内科技大学）；Le Quy Don Technical University（黎魁盾技术大学）
Traveling salesman problem (TSP) is a well-known in computing field. There are many researches to improve the genetic algorithm for solving TSP. In this paper, we propose two new crossover operators and new mechanism of combination crossover operators in genetic algorithm for solving TSP. We experimented on TSP instances from TSP-Lib and compared the results of proposed algorithm with genetic algorithm (GA), which used MSCX. Experimental results show that, our proposed algorithm is better than the GA using MSCX on the min, mean cost values.
School of Computer Science, Huazhong University of Science and Technology（华中科技大学计算机科学与技术学院）；Institute of Artificial Intelligence, Huazhong University of Science and Technology（华中科技大学人工智能研究院）；MIS, University of Picardie Jules Verne（皮卡第儒勒-凡尔纳大学MIS实验室）
We address the Traveling Salesman Problem (TSP), a famous NP-hard combinatorial optimization problem. And we propose a variable strategy reinforced approach, denoted as VSR-LKH, which combines three reinforcement learning methods (Q-learning, Sarsa and Monte Carlo) with the well-known TSP algorithm, called Lin-Kernighan-Helsgaun (LKH). VSR-LKH replaces the inflexible traversal operation in LKH, and lets the program learn to make choice at each search step by reinforcement learning. Experimental results on 111 TSP benchmarks from the TSPLIB with up to 85,900 cities demonstrate the excellent per…
The efficiency and dynamism of Unmanned Aerial Vehicles (UAVs), or drones, present substantial application opportunities in several industries in the last years. Notably, the logistic companies gave close attention to these vehicles envisioning reduce delivery time and operational cost. A variant of the Traveling Salesman Problem (TSP) called Flying Sidekick Traveling Salesman Problem (FSTSP) was introduced involving drone-assisted parcel delivery. The drone is launched from the truck, proceeds to deliver parcels to a customer and then is recovered by the truck in a third location. While the d…
The Traveling Salesman Problem is one of the most intensively studied combinatorial optimization problems due both to its range of real-world applications and its computational complexity. When combined with the Set Covering Problem, it raises even more issues related to tractability and scalability. We study a combined Set Covering and Traveling Salesman problem and provide a mixed integer programming formulation to solve the problem. Motivated by applications where the optimal policy needs to be updated on a regular basis and repetitively solving this via MIP can be computationally expensive…
Qatar Environment and Energy Research Institute (QEERI), Hamad bin Khalifa University（哈马德·本·哈利法大学卡塔尔环境与能源研究所）；State University of Novi Pazar（新帕扎尔州立大学）；University of Hamburg（汉堡大学）；Pontificia Universidad Católica de Valparaíso（瓦尔帕莱索天主教大学）
In this paper we present a new population based metaheuristic called the fixed set search (FSS). The proposed approach represents a method of adding a learning mechanism to the greedy randomized adaptive search procedure (GRASP). The basic concept of FSS is to avoid focusing on specific high quality solutions but on parts or elements that such solutions have. This is done through fixing a set of elements that exist in such solutions and dedicating computational effort to finding near optimal solutions for the underlying subproblem. The simplicity of implementing the proposed method is illustra…
Nanyang Technological University（南洋理工大学）；Singapore Institute of Manufacturing Technology（新加坡制造技术研究院）
We present NeuroLKH, a novel algorithm that combines deep learning with the strong traditional heuristic Lin-Kernighan-Helsgaun (LKH) for solving Traveling Salesman Problem. Specifically, we train a Sparse Graph Network (SGN) with supervised learning for edge scores and unsupervised learning for node penalties, both of which are critical for improving the performance of LKH. Based on the output of SGN, NeuroLKH creates the edge candidate set and transforms edge distances to guide the searching process of LKH. Extensive experiments firmly demonstrate that, by training one model on a wide range …
This paper further defines the class of fragment constructive heuristics used to compute feasible solutions for the Traveling Salesman Problem into arc-greedy and node-greedy subclasses. Since these subclasses of heuristics can create subtours, two known methodologies for subtour elimination on symmetric instances are reviewed and are expanded to cover asymmetric problem instances. This paper introduces a third novel methodology, the Greedy Tracker, and compares it to both known methodologies. Computational results are generated across multiple symmetric and asymmetric instances. The results d…
Word embeddings are one of the most fundamental technologies used in natural language processing. Existing word embeddings are high-dimensional and consume considerable computational resources. In this study, we propose WordTour, unsupervised one-dimensional word embeddings. To achieve the challenging goal, we propose a decomposition of the desiderata of word embeddings into two parts, completeness and soundness, and focus on soundness in this paper. Owing to the single dimensionality, WordTour is extremely efficient and provides a minimal means to handle word embeddings. We experimentally con…
Steiner Traveling Salesman Problem with Quantum Annealing
Department of Mechanical, Energy and Management Engineering, University of Calabria（机械、能源与管理工程系，卡塔尔大学）；TECNALIA, Basque Research and Technology Alliance (BRTA)（TECNALIA，巴斯克研究与技术联盟（BRTA））
Recent works using deep learning to solve the Traveling Salesman Problem (TSP) have focused on learning construction heuristics. Such approaches find TSP solutions of good quality but require additional procedures such as beam search and sampling to improve solutions and achieve state-of-the-art performance. However, few studies have focused on improvement heuristics, where a given solution is improved until reaching a near-optimal one. In this work, we propose to learn a local search heuristic based on 2-opt operators via deep reinforcement learning. We propose a policy gradient algorithm to …
