A data scientist at a national logistics company is tasked with optimizing daily delivery routes for its fleet. Each route involves a truck starting from a central depot, visiting approximately 50 unique customer locations, and returning to the depot. The goal is to minimize the total distance traveled, which is a classic Traveling Salesman Problem (TSP). Given the number of locations, which approach provides a practical and efficient solution for finding a near-optimal route for daily operational use?
Implement a brute-force search by enumerating all possible permutations of the 50 locations to guarantee the shortest path.
Construct a Minimum Spanning Tree (MST) that connects the depot and all customer locations to define the route.
Formulate the problem as an integer linear program and solve for the optimal tour using the simplex method.
Employ a heuristic algorithm, such as 2-opt or Simulated Annealing, to find an approximate solution.
A local-search heuristic or meta-heuristic (for example, 2-opt, Lin-Kernighan, Simulated Annealing, or a Genetic Algorithm) is the most pragmatic choice.
Brute-force enumeration grows as (n − 1)!/2 and becomes infeasible long before 50 stops.
An integer-programming or branch-and-cut solver such as Concorde can in fact find the exact optimum for 50 cities in seconds, but it requires specialized software and maintenance; implementing such a solver from scratch is rarely justified for a daily, on-the-fly routing pipeline, especially when late orders or traffic incidents require rapid re-optimization.
A Minimum Spanning Tree connects all nodes with minimum cost but is a tree (no cycle), so it does not satisfy the TSP tour requirement.
Heuristic methods, by contrast, are lightweight to code, deliver solutions within a few percent of optimal in milliseconds, and can be rerun easily when the distance matrix changes-making them the most practical tool in day-to-day delivery operations.
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