Heuristic approach and its application to solve NP-complete traveling salesman problem
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Deonarain Brijlall
Abstract
Since long ago, a suitable solution to the traveling salesman problem in different scenarios has always been a popular problem for research. Various heuristic and evolutionary approaches have been designed for it. We developed a simple heuristic approach to identify n optimal routes from nC2 routes abiding a degree constraint, where only those routes are selected in the set of feasible routes (Hx), which have a degree less than or equal to 2. We implemented the present tactic on the milk delivery problem, that is, to determine the best route for a milk van supplying milk to (i) 10 houses and (ii) 20 houses, in an area including dairy. For (i), out of 45 possible routes, 10 optimal routes of Hamiltonian cycle length 188 have been selected in 0.1344 s. Similarly, for (ii), 20 optimal routes of Hamiltonian cycle length 328 have been selected in 0.2488 s from 190 total routes. In this way, the time complexity of the proposed heuristic approach is O(n2 log2n), where its solution always lies in the right neighborhood of 0.
Abstract
Since long ago, a suitable solution to the traveling salesman problem in different scenarios has always been a popular problem for research. Various heuristic and evolutionary approaches have been designed for it. We developed a simple heuristic approach to identify n optimal routes from nC2 routes abiding a degree constraint, where only those routes are selected in the set of feasible routes (Hx), which have a degree less than or equal to 2. We implemented the present tactic on the milk delivery problem, that is, to determine the best route for a milk van supplying milk to (i) 10 houses and (ii) 20 houses, in an area including dairy. For (i), out of 45 possible routes, 10 optimal routes of Hamiltonian cycle length 188 have been selected in 0.1344 s. Similarly, for (ii), 20 optimal routes of Hamiltonian cycle length 328 have been selected in 0.2488 s from 190 total routes. In this way, the time complexity of the proposed heuristic approach is O(n2 log2n), where its solution always lies in the right neighborhood of 0.
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- Machine learning-enabled techniques for speech categorization 1
- Comprehensive study of cybersecurity issues and challenges 21
- An energy-efficient FPGA-based implementation of AES algorithm using HSTL IO standards for new digital age technologies 41
- A comparative study on security issues and clustering of wireless sensor networks 55
- Heuristic approach and its application to solve NP-complete traveling salesman problem 69
- Assessment of fake news detection from machine learning and deep learning techniques 87
- Spam mail detection various machine learning methods and their comparisons 119
- Cybersecurity threats in modern digital world 137
- Mechanism to protect the physical boundary of organization where the private and public networks encounter 149
- By combining binary search and insertion sort, a sorting method for small input size 167
- Index 179
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- Machine learning-enabled techniques for speech categorization 1
- Comprehensive study of cybersecurity issues and challenges 21
- An energy-efficient FPGA-based implementation of AES algorithm using HSTL IO standards for new digital age technologies 41
- A comparative study on security issues and clustering of wireless sensor networks 55
- Heuristic approach and its application to solve NP-complete traveling salesman problem 69
- Assessment of fake news detection from machine learning and deep learning techniques 87
- Spam mail detection various machine learning methods and their comparisons 119
- Cybersecurity threats in modern digital world 137
- Mechanism to protect the physical boundary of organization where the private and public networks encounter 149
- By combining binary search and insertion sort, a sorting method for small input size 167
- Index 179
