Background: In the context of genomic selection in animal breeding, animportant objective is to look for explicative markers for a phenotype understudy. The challenge of this study was to propose a model, based on a smallnumber of markers, to predict a quantitative trait. To deal with a high number ofmarkers, we propose using combinatorial optimization to perform variableselection, associated with a multiple regression model in a first approach and amixed model in a second, to predict the phenotype.Results:The efficiency of our two approaches, the first assuming that animals areindependent and the second integrating familial relationships, was evaluated onreal datasets. This reveals the importance of taking familial relationships intoaccount as the performances of the second approach were better. For example,on PIC data the correlation is around 0.15 higher using our approach takingfamilial relationships into account than with the Lasso bounded to 96 selectedmarkers. We also studied the importance of familial relationships on phenotypeswith different heritabilities. Finally, we compared our approaches with classicapproaches and obtained comparable results, sometimes better.Conclusion: This study shows the relevance of combining combinatorialoptimization with a regression model to propose a predictive model based on areasonable number of markers. Although this implies more parameters to beestimated and, therefore, takes longer to execute, it seems interesting to use amixed model in order to take familial relationships between animals into account.