Multidimensional Knapsack Problem Based on Uncertain Measure

The research of classical multidimensional knapsack problem always assumes that the weights, the values and the capacities are constant values. However, in the real-life industrial engineering applica- tions, the multidimensional knapsack problem often comes with uncertainty for lacking of the information about these parameters. This paper investigates a constrained multidimensional knapsack problem under uncertain environment, in which the relevant parameters are assumed to be uncertain variables. Within the framework of uncertainty theory, two types of uncertain programming models with discount con- straints are constructed for the problem with di erent decision criteria, i.e., the expected value criterion and the critical value criterion. Taking full advantage of the operational law for uncertain variables, the proposed models can be transformed into their corresponding deterministic models. After theoretically investigating the properties of the models, we do some numerical experiments. The numerical results illustrate that the proposed models are feasible and ecient for solving the constrained multidimensional knapsack problem with uncertain parameters.