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.
This paper presents a powerful genetic algorithm(GA) to solve the traveling salesman problem (TSP). To construct a powerful GA, I use edge swapping(ES) with a local search procedure to determine good combinations of building blocks of parent solutions for generating even better offspring solutions. Experimental results on well studied TSP benchmarks demonstrate that the proposed GA is competitive in finding very high quality solutions on instances with up to 16,862 cities.
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…
North University Baia Mare（北巴亚马雷大学）；Babes-Bolyai University（巴贝什-博尧伊大学）
A well known N P-hard problem called the Generalized Traveling Salesman Problem (GTSP) is considered. In GTSP the nodes of a complete undirected graph are partitioned into clusters. The objective is to find a minimum cost tour passing through exactly one node from each cluster. An exact exponential time algorithm and an effective meta-heuristic algorithm for the problem are presented. The meta-heuristic proposed is a modified Ant Colony System (ACS) algorithm called Reinforcing Ant Colony System (RACS) which introduces new correction rules in the ACS algorithm. Computational results are report…
Generalized traveling salesman problem (GTSP) is an extension of classical traveling salesman problem (TSP), which is a combinatorial optimization problem and an NP-hard problem. In this paper, an efficient discrete state transition algorithm (DSTA) for GTSP is proposed, where a new local search operator named \textit{K-circle}, directed by neighborhood information in space, has been introduced to DSTA to shrink search space and strengthen search ability. A novel robust update mechanism, restore in probability and risk in probability (Double R-Probability), is used in our work to escape from l…
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…
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 …
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…
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…
Isfahan University of Technology（伊斯法罕理工大学）；Simon Fraser University（西蒙弗雷泽大学）
The Generalized Traveling Salesman Problem (GTSP) is an extension of the well-known Traveling Salesman Problem (TSP), where the node set is partitioned into clusters, and the objective is to find the shortest cycle visiting each cluster exactly once. In this paper, we present a new hybrid Ant Colony System (ACS) algorithm for the symmetric GTSP. The proposed algorithm is a modification of a simple ACS for the TSP improved by an efficient GTSP-specific local search procedure. Our extensive computational experiments show that the use of the local search procedure dramatically improves the perfor…
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.…
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) usi…
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…
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…
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…
This article presents a new algorithm which is a modified version of the elite ant system (EAS) algorithm. The new version utilizes an effective criterion for escaping from the local optimum points. In contrast to the classical EAC algorithms, the proposed algorithm uses only a global updating, which will increase pheromone on the edges of the best (i.e. the shortest) route and will at the same time decrease the amount of pheromone on the edges of the worst (i.e. the longest) route. In order to assess the efficiency of the new algorithm, some standard traveling salesman problems (TSPs) were st…
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））
In this paper we use marker method and propose a new mutation operator that selects the nearest neighbor among all near neighbors solving Traveling Salesman Problem.
In this paper a highly abstracted view on the historical development of Genetic Algorithms for the Traveling Salesman Problem is given. In a meta-data analysis three phases in the development can be distinguished. First exponential growth in interest till 1996 can be observed, growth stays linear till 2011 and after that publications deteriorate. These three phases are examined and the major milestones are presented. Lastly an outlook to future work in this field is infered.
The Traveling Salesman Problem (TSP) is one of the most famous optimization problems. Greedy crossover designed by Greffenstette et al, can be used while Symmetric TSP (STSP) is resolved by Genetic Algorithm (GA). Researchers have proposed several versions of greedy crossover. Here we propose improved version of it. We compare our greedy crossover with some of recent crossovers, we use our greedy crossover and some recent crossovers in GA then compare crossovers on speed and accuracy.
Traveling Salesman Problem (TSP) is one of the most common studied problems in combinatorial optimization. Given the list of cities and distances between them, the problem is to find the shortest tour possible which visits all the cities in list exactly once and ends in the city where it starts. Despite the Traveling Salesman Problem is NP-Hard, a lot of methods and solutions are proposed to the problem. One of them is Genetic Algorithm (GA). GA is a simple but an efficient heuristic method that can be used to solve Traveling Salesman Problem. In this paper, we will show a parallel genetic alg…
NeuFACO: Neural Focused Ant Colony Optimization for Traveling Salesman Problem
College of Engineering and Computer Science, VinUniversity（工程与计算机科学学院，Vin大学）；School of Information and Communications Technology, Hanoi University of Science and Technology（信息与通信技术学院，河内科学技术大学）；University of Engineering and Technology, Vietnam National University（工程大学，越南国家大学）
Grad. School of Info. Science；Technology Hokkaido University Sapporo, Japan \ .；Technology Hokkaido University Sapporo, Japan；Information Initiative Center Hokkaido University Sapporo, Japan
In this paper, we propose a two-stage optimization strategy for solving the Large-scale Traveling Salesman Problems (LSTSPs) named CCPNRL-GA. First, we hypothesize that the participation of a well-performed individual as an elite can accelerate the convergence of optimization. Based on this hypothesis, in the first stage, we cluster the cities and decompose the LSTSPs into multiple subcomponents, and each subcomponent is optimized with a reusable Pointer Network (PtrNet). After subcomponents optimization, we combine all sub-tours to form a valid solution, this solution joins the second stage o…
Self Organizing Migrating Algorithm (SOMA) is a meta-heuristic algorithm based on the self-organizing behavior of individuals in a simulated social environment. SOMA performs iterative computations on a population of potential solutions in the given search space to obtain an optimal solution. In this paper, an Opportunistic Self Organizing Migrating Algorithm (OSOMA) has been proposed that introduces a novel strategy to generate perturbations effectively. This strategy allows the individual to span across more possible solutions and thus, is able to produce better solutions. A comprehensive an…
Genetic algorithm includes some parameters that should be adjusting so that the algorithm can provide positive results. Crossover operators play very important role by constructing competitive Genetic Algorithms (GAs). In this paper, the basic conceptual features and specific characteristics of various crossover operators in the context of the Traveling Salesman Problem (TSP) are discussed. The results of experimental comparison of more than six different crossover operators for the TSP are presented. The experiment results show that OX operator enables to achieve a better solutions than other…
Nowadays swarm intelligence-based algorithms are being used widely to optimize the dynamic traveling salesman problem (DTSP). In this paper, we have used mixed method of Ant Colony Optimization (AOC)and gradient descent to optimize DTSP which differs with ACO algorithm in evaporation rate and innovative data. This approach prevents premature convergence and scape from local optimum spots and also makes it possible to find better solutions for algorithm. In this paper, we are going to offer gradient descent and ACO algorithm which in comparison to some former methods it shows that algorithm has…
We consider the bicriteria asymmetric traveling salesman problem (bi-ATSP). Optimal solution to a multicriteria problem is usually supposed to be the Pareto set, which is rather wide in real-world problems. We apply to the bi-ATSP the axiomatic approach of the Pareto set reduction proposed by V. Noghin. We identify series of "quanta of information" that guarantee the reduction of the Pareto set for particular cases of the bi-ATSP. An approximation of the Pareto set to the bi-ATSP is constructed by a new multi-objective genetic algorithm. The experimental evaluation carried out in this paper sh…
The Traveling salesman problem (TSP) is proved to be NP-complete in most cases. The genetic algorithm (GA) is one of the most useful algorithms for solving this problem. In this paper a conventional GA is compared with an improved hybrid GA in solving TSP. The improved or hybrid GA consist of conventional GA and two local optimization strategies. The first strategy is extracting all sequential groups including four cities of samples and changing the two central cities with each other. The second local optimization strategy is similar to an extra mutation process. In this step with a low probab…
