Hybrid pointer networks for traveling salesman problems optimization

In this work, we proposed a hybrid pointer network (HPN), an end-to-end deep reinforcement learning architecture is provided to tackle the travelling salesman problem (TSP). HPN builds upon graph pointer networks, an extension of pointer networks with an additional graph embedding layer. HPN combines the graph embedding layer with the transformer’s encoder to produce multiple embeddings for the feature context. We conducted extensive experimental work to compare HPN and Graph pointer network (GPN). For the sack of fairness, we used the same setting as proposed in GPN paper. The experimental results show that our network significantly outperforms the original graph pointer network for small and large-scale problems. For example, it reduced the cost for travelling salesman problems with 50 cities/nodes (TSP50) from 5.959 to 5.706 without utilizing 2opt. Moreover, we solved benchmark instances of variable sizes using HPN and GPN. The cost of the solutions and the testing times are compared using Linear mixed effect models. We found that our model yields statistically significant better solutions in terms of the total trip cost. We make our data, models, and code publicly available https://github.com/AhmedStohy/Hybrid-Pointer-Networks.

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Neural Network Algorithm for Solving Large Scale Travelling Salesman Problems

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.542-543.1398 ◽

2012 ◽

Vol 542-543 ◽

pp. 1398-1402

Author(s):

Guo Zhong Cheng ◽

Wei Feng ◽

Fang Song Cui ◽

Shi Lu Zhang

Keyword(s):

Neural Network ◽

Time Complexity ◽

Large Scale ◽

Travelling Salesman Problem ◽

Effective Algorithm ◽

Travelling Salesman ◽

Satisfactory Solution ◽

Network Algorithm ◽

The Neural Network ◽

Neural Network Algorithm

This study improves the neural network algorithm that was presented by J.J.Hopfield for solving TSP(travelling salesman problem) and gets an effective algorithm whose time complexity is O(n*n), so we can solve quickly TSP more than 500 cities in microcomputer. The paper considers the algorithm based on the replacement function of the V Value. The improved algorithm can greatly reduces the time and space complexities of Hopfield method. The TSP examples show that the proposed algorithm could efficiently find a satisfactory solution and has a fast convergence speed.

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GPU-based parallel genetic approach to large-scale travelling salesman problem

The Journal of Supercomputing ◽

10.1007/s11227-016-1748-1 ◽

2016 ◽

Vol 72 (11) ◽

pp. 4399-4414 ◽

Cited By ~ 8

Author(s):

Semin Kang ◽

Sung-Soo Kim ◽

Jongho Won ◽

Young-Min Kang

Keyword(s):

Large Scale ◽

Travelling Salesman Problem ◽

Genetic Approach ◽

Travelling Salesman

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EFFICIENT METAHEURISTIC ALGORITHMS FOR THE MULTI-STRIPE TRAVELLING SALESMAN PROBLEM

Journal of Computer Science and Cybernetics ◽

10.15625/1813-9663/36/3/14770 ◽

2020 ◽

Vol 36 (3) ◽

pp. 233-250

Author(s):

Ban Ha Bang

Keyword(s):

Quadratic Assignment Problem ◽

Travelling Salesman Problem ◽

Computation Time ◽

Metaheuristic Algorithms ◽

Neighborhood Search ◽

Quadratic Assignment ◽

Travelling Salesman ◽

Local Optima ◽

Benchmark Instances ◽

Main Components

The Multi-stripe Travelling Salesman Problem (Ms-TSP) is an extension of the Travelling Salesman Problem (TSP). In the \textit{q}-stripe TSP with $q \geq 1$, the objective function sums the costs for travelling from one customer to each of the next \textit{q} customers along the tour. The resulting \textit{q}-stripe TSP generalizes the TSP and forms a special case of the Quadratic Assignment Problem. To solve medium and large size instances, a metaheuristic algorithm is proposed. The proposed algorithm has two main components, which are construction and improvement phases. The construction phase generates a solution using Greedy Randomized Adaptive Search Procedure (GRASP) while the optimization phase improves the solution with several variants of Variable Neighborhood Search, both coupled with a technique called Shaking Technique to escape from local optima. In addition, Adaptive Memory is integrated into our algorithms to balance between the diversification and intensification. To show the efficiency of our proposed metaheuristic algorithms, we extensively experiment on benchmark instances. The results indicate that the developed algorithms can produce efficient and effective solutions at a reasonable computation time.

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Optimal Solution of a Large-scale Travelling Salesman Problem applying DNN and k-opt

The Journal of The Institute of Internet Broadcasting and Communication ◽

10.7236/jiibc.2015.15.4.249 ◽

2015 ◽

Vol 15 (4) ◽

pp. 249-257

Author(s):

Sang-Un Lee

Keyword(s):

Large Scale ◽

Travelling Salesman Problem ◽

Optimal Solution ◽

Travelling Salesman

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Coevolution of structural variation and optimization in sound systems of human language

10.1101/346965 ◽

2018 ◽

Author(s):

Meng-Han Zhang ◽

Tao Gong

Keyword(s):

Large Scale ◽

Structural Variation ◽

Human Language ◽

Linguistic Typology ◽

Mixed Effect ◽

World Languages ◽

Mixed Effect Models ◽

Gradual Evolution ◽

Vowel Systems ◽

Two Parameters

AbstractEvolution of sound systems of human language is an optimization process to improve communicative effectiveness: The intrinsic structures of sound systems are constantly organized with respect to constraints in speech production and perception. However, there lack sufficient quantitative descriptions of this process, large-scale investigations on universal tendencies in sound systems, and explicit evidence on whether demographic and/or geographic factors can influence linguistic typology of sound systems. Here, we proposed two composite parameters, namely structural variation and optimization, to capture linguistic typology of sound systems, vowel systems in particular. Synchronic comparisons based on a large-scale vowel corpus of world languages revealed a universal negative correlation between the two parameters. Phylogenetic comparative analyses identified a correlated evolution of the two, but with distinct evolutionary modes: a gradual evolution of the structural variation and a punctuated equilibrium of the optimization. Mixed-effect models also reported significant effects of speaker population size and longitude on shaping vowel systems of world languages. All these findings elaborate the intrinsic evolutionary mechanism of sound systems, clarify the extrinsic, non-linguistic effects on shaping human sound systems, and quantitatively describe and interpret the evolution and typology of sound systems.

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OPTIMASI MULTI TRAVELLING SALESMAN PROBLEM (M-TSP) UNTUK DISTRIBUSI PRODUK PADA HOME INDUSTRI TEKSTIL DENGAN ALGORITMA GENETIKA

KLIK - KUMPULAN JURNAL ILMU KOMPUTER ◽

10.20527/klik.v4i2.86 ◽

2017 ◽

Vol 4 (2) ◽

pp. 125

Author(s):

Agung Mustika Rizki ◽

Wayan Firdaus Mahmudy ◽

Gusti Eka Yuliastuti

Keyword(s):

Genetic Algorithm ◽

Textile Industry ◽

Travelling Salesman Problem ◽

Test Results ◽

Travelling Salesman ◽

Fitness Value ◽

Optimal Value ◽

Distribution Process ◽

Optimal Population ◽

The Cost

In the field of textile industry, the distribution process is an important factor that can affect the cost of production. For that we need optimization on the distribution process to be more efficient. This problem is a model in the Multi Travelling Salesman Problem (M-TSP). Much research has been done to complete the M-TSP model. Among several methods that have been applied by other researchers, genetic algorithms are a workable method for solving this model problem. In this article the authors chose the genetic algorithm is expected to produce an optimal value with an efficient time. Based on the results of testing and analysis, obtained the optimal population amount of 120. For the optimal generation amount is 800. The test results related to the number of population and the number of generations are used as input to test the combination of CR and MR, obtained the optimal combination of CR = 0 , 4 and MR = 0.6 with a fitness value of 2.9964.Keywords: Textile Industry, Multi Travelling Salesman Problem (M-TSP), Genetic AlgorithmPada bidang industri tekstil, proses distribusi merupakan satu faktor penting yang dapat berpengaruh terhadap biaya produksi. Untuk itu diperlukan optimasi pada proses distribusi agar menjadi lebih efisien. Masalah seperti ini merupakam model dalam Multi Travelling Salesman Problem (M-TSP). Banyak penelitian telah dilakukan untuk menyelesaikan model M-TSP. Diantara beberapa metode yang telah diterapkan oleh peneiti lain, algoritma genetika adalah metode yang bisa diterapkan untuk penyelesaian permasalahan model ini. Dalam artikel ini penulis memilih algoritma genetika diharapkan dapat menghasilkan nilai yang optimal dengan waktu yang efisien. Berdasarkan hasil pengujian dan analisis, didapatkan jumlah populasi yang optimal sebesar 120. Untuk jumlah generasi yang optimal adalah sebesar 800. Hasil pengujian terkait jumlah populasi dan jumlah generasi tersebut dijadikan masukan untuk melakukan pengujian kombinasi CR dan MR, didapatkan kombinasi yang optimal yakni CR=0,4 dan MR=0,6 dengan nilai fitness sebesar 2,9964.Kata kunci: Industri Tekstil, Distribusi, Multi Travelling Salesman Problem (M-TSP), Algoritma Genetika

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Improving Initial Population for Genetic Algorithm using the Multi Linear Regression Based Technique

Communications - Scientific letters of the University of Zilina ◽

10.26552/com.c.2021.1.e1-e10 ◽

2020 ◽

Vol 23 (1) ◽

pp. E1-E10

Author(s):

Esra'a Alkafaween ◽

Ahmad B. A. Hassanat ◽

Sakher Tarawneh

Keyword(s):

Genetic Algorithm ◽

Genetic Algorithms ◽

Linear Regression ◽

Heuristic Search ◽

Large Scale ◽

Travelling Salesman Problem ◽

Initial Population ◽

Problem Size ◽

Travelling Salesman ◽

Multi Linear Regression

Genetic algorithms (GAs) are powerful heuristic search techniques that are used successfully to solve problems for many different applications. Seeding the initial population is considered as the first step of the GAs. In this work, a new method is proposed, for the initial population seeding called the Multi Linear Regression Based Technique (MLRBT). That method divides a given large scale TSP problem into smaller sub-problems and the technique works frequently until the sub-problem size is very small, four cities or less. Experiments were carried out using the well-known Travelling Salesman Problem (TSP) instances and they showed promising results in improving the GAs' performance to solve the TSP.

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