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| 基于动态规划法求解动态o-1背包问题 | |
| 引用本文： | 贺毅朝,田海燕,张新禄,王志威,高锁刚. 基于动态规划法求解动态o-1背包问题[J]. 计算机科学, 2012, 39(7): 237-241 |
| 作者姓名： | 贺毅朝 田海燕 张新禄 王志威 高锁刚 |
| 作者单位： | 1. 石家庄经济学院信息工程学院 石家庄050031 2. 河北师范大学数学与信息科学学院 石家庄050016;计算数学与应用河北省重点实验室 石家庄050016 3. 河北师范大学数学与信息科学学院 石家庄050016 |
| 基金项目： | 国家自然科学基金，河北省高等学校科学技术研究青年基金 |
| 摘 要： | 随机时变背包问题(RTVKP)是一种动态组合优化问题,也是一种典型的NP-hard问题。由于RTVKP问题中物品的价值、重量和背包载重均是动态变化的,导致问题的求解非常困难。在动态规划法基础上,提出了一种求解背包载重随机变化的RTVKP问题的确定性算法,分析了其复杂度和成功求解需要满足的条件。对两个大规模实例的计算表明,该算法是求解RTVKP问题的一种高效算法。 |
| 关 键 词： | NP-难问题 0-1背包问题 动态优化 时变背包问题 动态规划法 |
Solving Dynamic 0-1 Knapsack Problems Based on Dynamic Programming Algorithm |
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| HE Yi-chao , TIAN Hai-yan , ZHANG Xin-lu , WANG Zhi-wei , GAO Suo-gang. Solving Dynamic 0-1 Knapsack Problems Based on Dynamic Programming Algorithm[J]. Computer Science, 2012, 39(7): 237-241 | |
| Authors: | HE Yi-chao TIAN Hai-yan ZHANG Xin-lu WANG Zhi-wei GAO Suo-gang |
| Affiliation: | 2(Information Engineering School,Shijiazhuang University of Economics,Shijiazhuang 050031,China)1(College of Mathematics and Information Science,Hebei Normal University,Shijiazhuang 050016,China)2(Hebei Key Laboratory of Computational Mathematics and Application,Shijiazhuang 050016,China)3 |
| Abstract: | Random time-varying knapsack problem (RTVKP) is a dynamic combinatorial optimization problem, is a typical NP-hard problem too. Because the value and size of items and the size of knapsack can change along with the time, it causes that solving this problem is more difficult. We proposed an efficient algorithm for solving RTVKP with dynamic size of knapsack based on dynamic programming method, and analyzed the complexity of new algorithm and the condition of its successful executing. I}he results of simulation computation show that the exact algorithm is an efficient algorithm for solving RTVKP. |
| Keywords: | NP-hard problem 0-1 knapsack problem Dynamic optimization Time-varying knapsack problems Dynamic programming |
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