基于数论的纯整数规划问题的解法研究  

Research on the Solution of Pure Integer Programming Problem Based on Number Theory

作　　者：周斌 Zhou Bin(Sanming Medical and Polytechnic Vocational College,Sanming,Fujian 365001,China)

机构地区：[1]三明医学科技职业学院,福建三明365001

出　　处：《大理大学学报》2023年第6期14-19,共6页Journal of Dali University

基　　金：三明医学科技职业学院校级教科研课题(2017KY020)。

摘　　要：为避免求解纯整数规划问题过程中需要考虑松弛线性规划问题,使用数论中的不定方程理论,结合不等式方程求解的估算法提出了一种高效的纯整数规划问题的新解法。通过两个定理的推导证明新解法求解纯整数规划问题的可行性,并以纯整数规划问题为例子,分别用割平面法、分枝定界法和提出的新解法进行求解。结果表明,与割平面法、分枝定界法相比,新解法对于简单的纯整数规划问题的求解过程更简单。In order to avoid the need to consider the relaxation linear programming problem in solving pure integer programming problem,an efficient new solution method for pure integer programming problem is proposed by using the indefinite equation theory in number theory and the estimation method for solving inequality equations.Through the derivation of two theorems,it is proved that the new solution method is feasible to solve pure integer programming problems.Taking the pure integer programming problem as an example,the cutting-plane method,the branch-and-bound method and the new solution method proposed are used to solve it respectively.The results show that compared with the cutting-plane method and branch-and-bound method,the new method is simpler for solving simple pure integer programming problems.

关 键 词：纯整数规划 数论 不定方程理论 线性规划 

分 类 号：O221[理学—运筹学与控制论]