Propose a heuristic algorithm to solve the Traveling Salesman Problem for a large dataset where exact computation is infeasible. Describe the approach, such as Simulated Annealing, Genetic Algorithms, or Ant Colony Optimization. Provide pseudocode for the algorithm. Discuss the time complexity, the trade-offs between solution quality and computation speed, and potential pitfalls of the chosen heuristic method compared to a brute-force approach.