Analyzing and Modeling the Maximum Diversity Problem by Zero‐One Programming*
提出一个可量化的多样性概念，建立二次零一模型，证明最大多样性问题是NP难的，并给出两个计算效率更高的等价线性整数规划模型。
ABSTRACT The problem of maximizing diversity deals with selecting a set of elements from some larger collection such that the selected elements exhibit the greatest variety of characteristics. A new model is proposed in which the concept of diversity is quantifiable and measurable. A quadratic zero‐one model is formulated for diversity maximization. Based upon the formulation, it is shown that the maximum diversity problem is NP‐hard. Two equivalent linear integer programs are then presented that offer progressively greater computational efficiency. Another formulation is also introduced which involves a different diversity objective. An example is given to illustrate how additional considerations can be incorporated into the maximum diversity model.