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.

Key words: NP-hard problem, 0-1 knapsack problem, Dynamic optimization, Time-varying knapsack problems, Dynamic programming