A multi-objective model for microarray based on analytic hierarchy process is built.A heuristic algorithm improved from UMDA called MOEDA is to solve the model.Both classification accuracy and number of genes are the objectives.The classification accuracy is treated absolutely important than the number of genes.It always gets high accuracy with small number of genes on microarray data. Microarray data has significant potential in clinical medicine, which always owns a large quantity of genes relative to the samples' number. Finding a subset of discriminatory genes (features) through intelligent algorithms has been trend. Based on this, building a disease prognosis expert system will bring a great effect on clinical medicine. In addition, the fewer the selected genes are, the less cost the disease prognosis expert system is. So the small gene set with high classification accuracy is what we need. In this paper, a multi-objective model is built according to the analytic hierarchy process (AHP), which treats the classification accuracy absolutely important than the number of selected genes. And a multi-objective heuristic algorithm called MOEDA is proposed to solve the model, which is an improvement of Univariate Marginal Distribution Algorithm. Two main rules are designed, one is 'Higher and Fewer Rule' which is used for evaluating and sorting individuals and the other is 'Forcibly Decrease Rule' which is used for generate potential individuals with high classification accuracy and fewer genes. Our proposed method is tested on both binary-class and multi-class microarray datasets. The results show that the gene set selected by MOEDA not only results in higher accuracies, but also keep a small scale, which cannot only save computational time but also improve the interpretability and application of the result with the simple classification model. The proposed MOEDA opens up a new way for the heuristic algorithms applying on microarray gene expression data.