| Grey multi-objective programming is an overlapping field of multi-objective programming and gray system theory. Some practical problems of objective function and constraint conditions show different forms of uncertainty. The gray modeling system idea and the modeling approach enable the effective resolve of such uncertainty expressed as gray parameters, which is otherwisely delt with inconveniently by classical method of multi-objective programming. Grey multi-objective programming is a very complicated combinatorial optimization problem, most of which can not be settled by analytical method. Genetic Algorithm is based on the biological mechanism of natural selection and heredity, leveraging colony searching technology, and is particularly applicable for the resolution of complicated non-linear problems intractable with traditional searching methods. In fact, the genetic algorithm advantage is more effective in the multi-objective programming than in dealing with the one-objective programming. In recent years, the use of genetic algorithms for multi-objective programming algorithm made some progress. To solve the problems of premature convergence and local minima in simple genetic algorithm (SGA), the author proposed a combining algorithm for structural optimization, which is based on genetic algorithm and gradient algorithm. HGA uses gradient algorithm to superpose, get a result, and consequently improves the herd of genetic algorithm with this result, then compares the superior one of genetic algorithm with the root of gradient algorithm, and chooses the best point to be the incipient point of the next step of super position. With this method, it can keep the best root of all the course, and also it can speed up searching, and keep the best global root. Numerical examples show that the combining algorithm possesses both the merit of genetic algorithm on strong global searching ability and gradient algorithm to solve complicated grey multi-objective programming.
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