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| 求解多目标最小生成树问题的改进算法 |
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陈国龙1,2, 郭文忠2, 涂雪珠2, 陈火旺1
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1.国防科学技术大学计算机学院,湖南,长沙,410073;2.福州大学数学与计算机科学学院,福建,福州,350002
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| 摘要: |
| 多目标最小生成树问题是典型的NP问题,Zhou和Gen提出了一种用于计数多目标最小生成树问题的所有非劣最优最小生成树的算法,但该算法无法保证能够找到所有非劣最优最小生成树.针对此问题,提出一种改进的计数算法,并定性说明改进算法能够找到问题的所有非劣最优最小生成树.改进算法在进行子树剔除时增加了一些条件.模拟实验结果表明,改进后的计数算法能够找到所有的非劣最优解.这也说明该算法具有应用的潜力. |
| 关键词: 最小生成树 非劣最优解 |
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| 基金项目:Supported by the National Natural Science Foundation of China under Grant No.60172017(国家自然科学基金);the Natural Science Foundation of Fujian Province of China under Grant No.A0410010(福建省自然科学基金);the Natural Science Foundation of Fujian Provincial Educational Commission of China under Grant No.K03012(福建省教育厅科技三项科研项目) |
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| An Improved Algorithm to Solve the Multi-Criteria Minimum Spanning Tree Problem |
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CHEN Guo-Long,GUO Wen-Zhong,TU Xue-Zhu,CHEN Huo-Wang
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| Abstract: |
| The multi-criteria minimum spanning tree (mc-MST) problem is a typical NP-hard problem. An algorithm to enumerate the set of Pareto optimal spanning trees on some mc-MST instances was put forward by Zhou and Gen, but it does not guarantee returning all the Pareto optimal solutions. To settle this problem, an improved algorithm is developed and also proved to be able to find all the true Pareto optimal solutions in this paper. The new algorithm adds some conditions in the elimination of subtrees. Simulation results show that the new algorithm can find all the Pareto optimal solutions and also show that the new algorithm has potential usage in practice. |
| Key words: minimum spanning tree Pareto optimal |
