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Language: English
Keywords: TSP, LKH, Optimization, Python, Heuristic Algorithm
Overview:
This article provides a practical guide to optimizing delivery routes using the Traveling Salesman Problem (TSP) and the Lin-Kernighan-Helsgaun (LKH) algorithm. It begins by highlighting the importance of efficient algorithms and contrasting naive approaches with more sophisticated methods like the simplex algorithm. The author then introduces the TSP, emphasizing its NP-hard nature and the need for heuristic solutions. The core of the article focuses on the LKH algorithm, explaining its theory, implementation in Python using the elkai library, and application to a real-world route optimization scenario. The author concludes by discussing the limitations of LKH and alternative approaches, while advocating for its elegance and efficiency in finding near-optimal solutions for the TSP.
Section Summaries:
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1. LKH’s Theory: The LKH algorithm is an efficient method for solving the Traveling Salesman Problem, scaling well to a large number of cities. It iteratively improves a random tour by replacing connections and accepting changes that reduce the total distance. While not guaranteeing optimality, LKH often converges to near-optimal solutions in practice.
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2. LKH’s Code: The author uses Folium to display points on a 2D map and the
elkailibrary to implement the LKH algorithm in Python. TheTaxiDriverclass is created to encapsulate the route optimization process, taking a JSON file for boundary box and a folder to store the output maps. The code generates random points within the specified boundaries and saves the optimized route as an interactive HTML file. -
3. LKH’s applications: The LKH algorithm is applied to find the shortest path among a set of randomly generated cities. The algorithm efficiently finds a near-optimal route, avoiding the need to explore all possible paths. The optimized route is displayed using the
display_optimized_routefunction, showcasing the effectiveness of the LKH algorithm. -
4. LKH’s limitations: While LKH is a good TSP solution, Dynamic Programming guarantees an optimal solution but is more expensive. The main issue of LKH is its static nature, as it doesn’t account for real-world factors like traffic and road conditions. Dijkstra’s Algorithm and Machine Learning methods are more suitable for dynamic environments.
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5. Conclusions: The article recaps the exploration of the Traveling Salesman Problem and the application of the LKH algorithm. It emphasizes the importance of efficient algorithms, describes the TSP and LKH algorithm, and discusses LKH’s limitations. The author also provides links to his LinkedIn, newsletter, Medium profile, and Upwork profile.
Related Tools:
- Folium: https://python-visualization.github.io/folium/latest/
- elkai: https://github.com/fikisipi/elkai
References:
- LKH Documentation: http://webhotel4.ruc.dk/~keld/research/LKH/
- LKH Original Paper: http://webhotel4.ruc.dk/~keld/research/LKH/LKH-2.0/DOC/LKH_REPORT.pdf
- Simplex Algorithm: https://en.wikipedia.org/wiki/Simplex_algorithm
- Dynamic Programming: https://www.geeksforgeeks.org/travelling-salesman-problem-using-dynamic-programming/
- Genetic Algorithms: https://medium.com/aimonks/traveling-salesman-problem-tsp-using-genetic-algorithm-fea640713758
- Reinforcement Learning: https://ekimetrics.github.io/blog/2021/11/03/tsp/
- Dijkstra’s Algorithm: https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
Original Article Link: https://towardsdatascience.com/hands-on-delivery-routes-optimization-tsp-with-ai-using-lkh-and-python-9078768068cc/