中文摘要：

给出了一种求解一般二次整数背包问题（quadratic integer knapsack problem,QIKP）的新算法.该方法把占优的概念与分支定界思想结合,旨在寻求全局最优解.对QIKP给出了占优的定义,通过变量系数之间的关系,很容易找到占优组和极小占优组,从而删除可行域中那些非最优点.新的占优定义对凹的二次函数尤其有效.在理论证明的基础上,设计相应的算法,并进行了数值计算.结果显示,在随机产生的例子中,该算法是有效的,并且与传统的分支定界算法相比,得到了更好的最优解,最优值有了较大的提升.

英文摘要：

A new algorithm for solving quadratic integer knapsack problems（QIKP） is presented.The concept of the dominance of general quadratic integer knapsack problems is defined,and a simple way to identify domination tuples is described.A new algorithm is designed to delete dominated feasible solutions and to solve quadratic integer knapsack problems.The numerical results show that the algorithm is effective.Compared with the traditional branch-and-bound algorithm,the optimal values have been greatly improved.