中文说明:
0-1整数规划有很广泛的应用背景,比如指派问题,背包问题等等,实际上TSP问题也是一个0-1问题,当然这些问题都是NP问题,对于规模较大的问题用穷举法是没有办法在可接受的时间内求得最优解的,本程序只不过是一个练习,得意之处是用递归法把所有解都排列出来。另:胡运权所著的《运筹学基础及应用(第三版)》第97页的例3,我用本程序求解得到的结果是:最优解是x*=(1,0, 0, 0, 0),最优值是f(x*)=8,但书求得最优解是x*=(1,0, 1, 0, 0),最优值是f(x*)=4,是不是书中写错了,请大家验证。以下是源程序,大家可以任意使用无版权问题,另外,如果大家有大规模的0-1规划的问题也希望提供给我,谢谢。变量个数至少是3个。
English Description:
0-1 integer programming has a wide range of application backgrounds, such as assignment problem, knapsack problem, etc. in fact, TSP problem is also a 0-1 problem. Of course, these problems are NP problems. For large-scale problems, there is no way to obtain the optimal solution in an acceptable time by using the exhaustive method. This program is just an exercise. The pride is that all solutions are arranged by using the recursive method. In addition, in example 3 on page 97 of the fundamentals and applications of operations research (Third Edition) written by Hu Yunquan, the result obtained by using this program is: the optimal solution is x*= (1,0, 0, 0), the optimal value is f (x*) =8, but the optimal solution obtained in the book is x*= (1,0, 1, 0, 0), and the optimal value is f (x*) =4. Please verify whether it is wrong in the book. The following is the source program. You can use it without copyright. In addition, if you have a large-scale 0-1 planning problem, you also want to provide it to me. Thank you. The number of variables must be at least 3 p>