基于动态规划法求解动态0-1背包问题

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.%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. The results of simulation computation show that the exact algorithm is an efficient algorithm for solving RTVKP.