Early forecasting of vehicle flow speeds is crucial for sustainable traffic development and establishing Traffic Speed Forecasting (TSF) systems for each country. While online mapping services offer significant benefits, dependence on them hampers the development of domestic alternative platforms, impeding sustainable traffic management and posing security risks. There is an urgent need for research to explore sustainable solutions, such as leveraging Global Positioning System (GPS) probe data, to support transportation management in urban areas effectively. Despite their vast potential, GPS probe data often present challenges, particularly in urban areas, including interference signals and missing data. This paper addresses these challenges by proposing a process for handling anomalous and missing GPS signals from probe vehicles on parallel multilane roads in Vietnam. Additionally, the paper investigates the effectiveness of techniques such as Particle Swarm Optimization Long Short-Term Memory (PSO-LSTM) and Genetic Algorithm Long Short-Term Memory (GA-LSTM) in enhancing LSTM networks for TSF using GPS data. Through empirical analysis, this paper demonstrates the efficacy of PSO-LSTM and GA-LSTM compared to existing methods and the state-of-the-art LSTM approach. Performance metrics such as Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Median Absolute Error (MDAE) validate the proposed models, providing insights into their forecasting accuracy. The paper also offers a comprehensive process for handling GPS outlier data and applying GA and PSO algorithms to enhance LSTM network quality in TSF, enabling researchers to streamline calculations and improve supposed model efficiency in similar contexts.