## 1 Introduction  
The rapid growth of digital commerce and the increasing complexity of logistics operations have intensified the demand for efficient sales route optimization. In competitive distribution environments, companies seek to minimize operational costs while improving service quality. Effective route planning not only reduces fuel consumption and delivery delays but also enhances customer satisfaction and fleet productivity. At its core, the problem of sales route optimization is combinatorial in nature and is closely related to well-known NP-hard problems such as the Traveling Salesman Problem (TSP) and the Vehicle Routing Problem (VRP) [1, 2, 3]. Traditional approaches to these problems--such as integer linear programming or dynamic programming--offer precise solutions but are computationally infeasible for large-scale, real-time scenarios. As a result, researchers have increasingly turned to metaheuristic techniques like genetic algorithms (GA), Ant Colony Optimization (ACO), and Tabu Search (TS), which balance solution quality with computational tractability [4, 5, 6]. However,standard GA implementations often suffer from the premature convergence, limited adaptability, and inefficient handling of dynamic factors such as traffic congestion and weather variability [7]. In recent years, research has advanced toward hybrid models that combine metaheuristics with machine learning techniques to address these limitations. For instance, [PERSON] et al. [8] developed a mobile application that integrates GA with the Google Maps API for route optimization. Although their solution improved route planning efficiency, it lacked real-time adaptability and scalability. Other efforts have demonstrated the value of enhancing GAs with local refinement mechanisms; for example, [PERSON] et al. [9] combined GA with Tabu Search to improve convergence and escape local optima. Adaptive variants, such as those introduced by [PERSON] et al. [7], have also proven effective in time-constrained routing problems by dynamically adjusting mutation rates. Recent contributions further emphasize deep learning and hybridization as key enablers of intelligent routing. [PERSON] et al. [10] proposed a deep learning model to predict urban travel times based on historical traffic data, while [PERSON] et al. [11] classified neural approaches to solving the TSP, highlighting their potential for generalizing to complex routing contexts. Hybrid strategies, like the salp swarm model proposed by [PERSON] and [PERSON] [12] and crossover-enhanced GAs explored by [PERSON] et al. [13], continue to push the frontier of route optimization. Moreover, sustainability-driven approaches have emerged, such as those by [PERSON] et al. [14] and [PERSON] et al. [15], addressing multi-objective constraints including environmental impact and emergency logistics. Despite these innovations, real-time adaptability remains a major challenge in the design of robust and scalable routing systems. Existing models often lack mechanisms for continuous reoptimization in the face of uncertain and dynamic conditions. This paper addresses these limitations by introducing a hybrid solution that combines a genetic algorithm with adaptive mutation and Tabu Search for improved search diversification and local refinement. To incorporate real-time adaptability, the method integrates a Long Short-Term Memory (LSTM) neural network trained to predict travel time under dynamic traffic conditions. This combination enables intelligent, scalable, and responsive route planning, capable of adapting in real time. The main contributions of this work are threefold. First, we present a Hybrid Genetic Algorithm (HGA) enhanced with adaptive mutation and Tabu Search for robust optimization. Second, we incorporate a deep learning model (LSTM) to predict travel times, improving route decisions in dynamic contexts. Third, we demonstrate the practical benefits of our system through comprehensive experiments, showcasing its effectiveness over standard and adaptive GA baselines.