This work analyses the application of heuristic algorithms in the transmission network expansion planning problem using the Hybrid Linear Model (HLM). The HLM is a relaxed model which still has not been fully explored. The work presents a detailed study of a constructive heuristic algorithm for the HLM and proposes an extension of the model and a solution technique for multi-stage planning. Quality evaluation of solutions found by HLM and the possibilities of application of the model for transmission system planning are also discussed. Finally, tests with the most known systems of the specialized literature are presented.