The quality of the initial population is a critical factor in the convergence speed and overall performance of an optimization algorithm. A well-structured initial population can significantly enhance the exploration capabilities of the algorithm, allowing it to more efficiently traverse the solution space and converge more quickly and reliably towards optimal or near-optimal solutions. In this paper, we present the Circle Group Heuristic (CGH), a spatially structured initialization method, for generating high-quality initial populations to enhance the convergence speed of the Discrete Bacterial Memetic Evolutionary Algorithm (DBMEA) in solving the Traveling Salesman Problem (TSP) and related combinatorial optimization problems. This work extends the CGH beyond the TSP to a broader class of routing problems. The results show that the integration of CGH into DBMEA demonstrated consistent performance improvements on the TSP, the Traveling Repairman Problem (TRP), and the Traveling Salesman Problem with Time Window (TSPTW) instances of varying sizes. In particular, CGH provided high-quality starting points that accelerated convergence and reduced computational cost. In all tested scenarios, DBMEA enhanced with CGH and consistently preserved the best-known solution quality while reducing execution time.