运筹学中若干离散规划问题的相对差分搜索解法

运筹学中有很多离散规划问题。其中的线性规划通常用分枝定界法或割平面法，还有图上作业法求解。不论哪种方法工作量都不小，而且效率低；至于非线性规划大都是用动态规划法求解，也很麻烦、耗时。对于大规模问题，不论线性或非线性离散规划，现有解法都受到问题规模的限制；还有资源分配和背包问题至今没有见到解决方法。本文就是为了解决这些问题，提出了相对差分搜索算法。通过5个算例和其它文献中的一些算例计算验证了本法简单、快速、有效和精确，尤其不受问题规模的限制是其最大的优点。

Relative Difference Search Algorithm for Some Nonlinear Discrete Programming Problems in Operations Research

There are many discrete programming problems,in which generally the branch and bound,cutting plan or graphical operation methods are adopted to solve the linear discrete programs.No matter what method is used,much labor should be used,and the efficiency is lower.For the nonlinear discrete programs the dynamic programming method is used generally,and much time have to be consumed.For the large scale problems,whether linear or nonlinear discrete programs are solved,the existing methods are all restricted to the scale of problems.In addition,the methods for solving the resources allocation and knapsack problems haven't been found now.In order to solve the above problems,the paper presents a relative difference search algorithm.Calculation of five examples in this paper and other examples in other papers show that the algorithm is simple,rapid,effective and accurate.Especially the nonrestriction to the scale of problems is its main merit.