This article introduces a new method to estimate the least absolutes linear regression model's parameters, which considers optimization problems based on the weighted aggregation operators of ordered least absolute deviations. In the optimization problem, weighted aggregation of orderd fitted least absolute deviations provides data analysis to identify the outliers while considering different fitting functions simultaneously in the modeling problem. Accordingly, this approach is not affected by outlier observations and in any problem proportional to the number of potential outliers selects the best model estimator with the optimal break-down point among a set of other candidate estimators. The performance and the goodness-of-fit of the proposed approach are investigated, analyzed and compared in modeling analytical dataset and a real value dataset in hydrology engineering at the presence of outliers. Based on the results of the sensitivity analysis, the properties of unbiasedness and efficiency of the estimators are obtained.