应用正弦型拓展函数求解整数规划问题

To Solve the Integer Programming Problem by Introducing a Type of Sine Extensive Function

整数规划等有关离散变量的优化问题由于它的不连续和非光滑劣性,一直是最优化问题的一个难点.本文通过引入具有良好光滑性的正弦波型函数、增加约束条件以消除整数限制,把整数规划问题转化为无整数约束的一般非线性规划问题.新问题可以采用一般解决连续可微问题的方法,如Lagrange乘子法、Ja-cobian法或建立Kuhn-Tucker条件的方法求解.作为实例,本文应用已经发展的新方法求解了一个简单的整数规划问题以证实方法的有效性.

The optimization problem related to discrete variables such as integer programming is always a difficulty thanks to its uncontinuousness and unglossiness. In this paper, a type of sine model functions is introduced and a series of constraint condition is acceded in order to remove the integer restraints to the variables. Then the integral programming problem is transformed to the ordinary nonlinear programming problem without integer constraints. The new problem may be solved by the ways fit for usual continuous and differential problem, such as Lagrangers multiplier algorithm, Jacobian＇s way, and/or establishing Kuhn-Tucker condition. In the end of this paper, a simple integral programming problem is solved by the developed way as an example in which the integer restraints to some variables are removed.