基于模运算的新颖离散差分演化算法求解多背包问题

多背包问题（MKP）是一个求解难度极大的背包问题。为了基于差分演化（DE）求解MKP，首先建立了MKP的整数规划模型，在利用模运算构造简单且有效的新型传递函数基础上，提出了一个新颖离散差分演化算法MODDE；基于贪心策略提出了消除MKP不可行解的一个有效算法GROA，由此利用MODDE给出了求解MKP的一种新方法。最后，利用MODDE求解30个国际通用的MKP实例，通过与四个代表性演化算法的比较表明，MODDE不仅计算结果优，而且算法的稳定性强，是求解MKP的一个高效算法。

Novel discrete differential evolution algorithm based on modulo operation for solving multiple knapsack problem

The multiple knapsack problem(MKP) is a special knapsack problem with great difficulty. In order to solve MKP by differential evolution(DE), this paper firstly established the integer programming model of MKP. Based on a simple and efficient new transfer function based on modulo operation, it proposed a novel discrete differential evolution algorithm MODDE. Then, the method used an efficient algorithm GROA to eliminate the unfeasible solution of MKP by greedy strategy. Therefrom, this paper proposed a new method for solving MKP based on MODDE. Finally, it used MODDE to solve 30 international instances of MKP. Comparing with 4 representative evolution algorithms shows that MODDE not only has better calculation results, but also has stronger stability. It is indeed an efficient algorithm for solving MKP.