The basic principle and method of genetic algorithm and an updating genetic algorithm-elitist non-dominated sorting genetic algorithm——elitist non-dominated sorting genetic algorithm (NSGA-Ⅱ) are introduced.

In this algorithm, the Pareto non-dominated sorting mechanism is integrated with the differential evolution algorithm;meanwhile the individual crowding mechanism and the mutation strategy are improved to cope with the premature convergence and the search bias.

In multi objective-decision making problems,satisfactory solution often need to be searched in non-inferior solution set.

For example, the well-known weighting method is time-consuming and also easy to leave out some part of total non-inferior solution set.

From the fact that multiobjective programming with indefinite phases has usually only noninferior solutions, the concepts of the noninferior compound matrix of phase return and the recurrence matrix for multiobjective programming with indefinite phases were put forward.

The noninferior solution of mutiobjective decision problem is discussed based on a proposed simple mathematical model of city bus planning.

A genetic algorithm is developed for calculating noninferior solutions of multiobjective optimization in this paper It shows that the method is efficient in a numerical experiment.