Multi-objective optimal evolutionary algorithms (MOEAs) are a kind of new effective algorithms to solve Multi-objective optimal problem (MOP). Because ranking, a method which is used by most MOEAs to solve MOP, has some shortcoming s, in this paper, we proposed a new method using tree structure to express the relationship of solutions. Experiments prove that the method can reach the Pare to front, retain the diversity of the population, and use less time.
In many real world problems there are several criteria which have to be considered in order to evaluate the quality of an individual. Only on the basis of the comparison of these several criteria or objectives (thus multi-objective) can a decision be made as to the superiority of one individual over another. Then, as in single-objective problems, an order of individuals within the population can be established from these reciprocal comparisons - multi-objective ranking. After this order has been established the single-objective ranking methods from the subsection 3.1 can be used to convert the order of the individuals to corresponding fitness values.

Multi-objective fitness assignment (and with it multi-objective optimization ) is concerned with the simultaneous minimization of NObj criteria fr, with r = 1, ..., NObj. The values fr are determined by the objective function, which in turn is dependent on the variables of the individuals (the decision variables).

A straightforward example should serve as the motivation for the following considerations. When objects are produced, the production costs should be kept low and the objects should be produced quickly. Various solutions can be developed during production planning which may differ regarding the number and type of the machines employed, as well as regarding the number of workers. The criteria production costs f1 and production time f2, both of which are determined by the objective function, serve as evaluation criteria for each solution.