Optimal pivot path of the simplex method for linear programming based on reinforcement learning
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| Publicado en: | Science China. Mathematics vol. 67, no. 6 (Jun 2024), p. 1263 |
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| Autor principal: | |
| Otros Autores: | , , , |
| Publicado: |
Springer Nature B.V.
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| Acceso en línea: | Citation/Abstract Full Text - PDF |
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| 045 | 2 | |b d20240601 |b d20240630 | |
| 100 | 1 | |a Li, Anqi |u University of Chinese Academy of Sciences, School of Mathematical Sciences, Beijing, China (GRID:grid.410726.6) (ISNI:0000 0004 1797 8419) | |
| 245 | 1 | |a Optimal pivot path of the simplex method for linear programming based on reinforcement learning | |
| 260 | |b Springer Nature B.V. |c Jun 2024 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a Based on the existing pivot rules, the simplex method for linear programming is not polynomial in the worst case. Therefore, the optimal pivot of the simplex method is crucial. In this paper, we propose the optimal rule to find all the shortest pivot paths of the simplex method for linear programming problems based on Monte Carlo tree search. Specifically, we first propose the SimplexPseudoTree to transfer the simplex method into tree search mode while avoiding repeated basis variables. Secondly, we propose four reinforcement learning models with two actions and two rewards to make the Monte Carlo tree search suitable for the simplex method. Thirdly, we set a new action selection criterion to ameliorate the inaccurate evaluation in the initial exploration. It is proved that when the number of vertices in the feasible region is Cnm, our method can generate all the shortest pivot paths, which is the polynomial of the number of variables. In addition, we experimentally validate that the proposed schedule can avoid unnecessary search and provide the optimal pivot path. Furthermore, this method can provide the best pivot labels for all kinds of supervised learning methods to solve linear programming problems. | |
| 653 | |a Linear programming | ||
| 653 | |a Apexes | ||
| 653 | |a Simplex method | ||
| 653 | |a Monte Carlo simulation | ||
| 653 | |a Supervised learning | ||
| 653 | |a Searching | ||
| 653 | |a Polynomials | ||
| 700 | 1 | |a Guo, Tiande |u University of Chinese Academy of Sciences, School of Mathematical Sciences, Beijing, China (GRID:grid.410726.6) (ISNI:0000 0004 1797 8419) | |
| 700 | 1 | |a Han, Congying |u University of Chinese Academy of Sciences, School of Mathematical Sciences, Beijing, China (GRID:grid.410726.6) (ISNI:0000 0004 1797 8419) | |
| 700 | 1 | |a Li, Bonan |u University of Chinese Academy of Sciences, School of Mathematical Sciences, Beijing, China (GRID:grid.410726.6) (ISNI:0000 0004 1797 8419) | |
| 700 | 1 | |a Li, Haoran |u University of Chinese Academy of Sciences, School of Mathematical Sciences, Beijing, China (GRID:grid.410726.6) (ISNI:0000 0004 1797 8419) | |
| 773 | 0 | |t Science China. Mathematics |g vol. 67, no. 6 (Jun 2024), p. 1263 | |
| 786 | 0 | |d ProQuest |t Science Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3275301848/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3275301848/fulltextPDF/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |