Abstract:

Traditional solutions of 0-1 programming problems belong mostly to direct discrete solving methods. A strict conversion for the problem and approximate continuous solution are proposed in this paper which have three steps: (1) 0-1 discrete variables were expressed as continuous variables on the interval [0, 1] by means of a step function; (2) Objective function is approximated to take more near smooth polish function to approach tradeoff step function, and every constraint function is approximated to take linear polish function to approach tradeoff step function, then 0-1 programming problem is transformed to continuous optimization model from discrete problem; (3) The model is solved by using the method with high smoothness solution. This method breaks certain solving method applies only to certain types of 0-1 programming, so it can solve more general problems. During the solving process, a sinusoidal polish function is taken to obtain very good computational results.

Key words: step function, 0-1 programming, discrete, continuous, tradeoff step function, smooth polish function, sinusoidal polish function