The Least Absolute Shrinkage and Selection Operator (LASSO) is used to tackle both the multicollinearity issue and the variable selection concurrently in the linear regression model. The Least Angle Regression (LARS) algorithm has been used widely to produce LASSO solutions. However, this algorithm is unreliable when high multicollinearity exists among regressor variables. One solution to improve the estimation of regression parameters when multicollinearity exists is adding preliminary information about the regression coefficient to the model as either exact linear restrictions or stochastic linear restrictions. Based on this solution, this article proposed a generalized version of the stochastic restricted LARS algorithm, which combines LASSO with existing stochastic restricted estimators. Further, we examined the performance of the proposed algorithm by employing a Monte Carlo simulation study and a numerical example.