SOLVING LINEAR PROGRAMMING PROBLEM WITH FUZZY COEFFICIENTS BY A MODIFIED TWO-STAGE DIFFERENTIAL EVOLUTION

The applications of linear programming with fuzzy constraint coefficients are numerous and various over the past years. This paper proposes a new approach, a modified two-stage differential evolution (DE) algorithm, to solve linear programming with fuzzy constraint coefficients approximately. In the first stage of the proposed DE, the generation of fuzzy numbers for each imprecise coefficient is simulated. The interval value that stands for an imprecise coefficient is to be equally divided into 10 or 15 partitions. Each partition denotes a piece of that interval value which is initially assigned a random real value between 0 and 1. The real values in each partition are then evolved and the final real values in all partitions represent a membership grade of fuzzy number. Using the final real values to perform some calculations, the estimated values of the fuzzy constraint coefficients are obtained. The second stage of the proposed DE is to solve the defuzzified linear programming, using a signed-distance ranking method, to obtain the optimal solution to the original fuzzy problem. To illustrate the efficiency of the proposed DE, two numerical examples are solved and the results obtained are discussed.