How does a delivery driver find the shortest possible route to visit a list of 20 different addresses? This is the classic formulation of the Traveling Salesman Problem (TSP): given a list of cities and the distances between each pair, what is the shortest possible route that visits each city exactly once and returns to the origin city? While it sounds simple, the TSP is famously "NP-hard," meaning the number of possible routes explodes as you add more cities, making it impossible to solve by brute force for all but the smallest lists.
🔍 The Discovery
Name of the Technology: The Traveling Salesman Problem (TSP)
Original Creator/Institution: The problem was first formulated in the 1800s, but it gained prominence in the 1930s and has been studied extensively by mathematicians at institutions like the RAND Corporation.
Year of Origin: circa 1930s (modern formulation)
License: A fundamental, public domain problem in combinatorial optimization.
Because finding the absolute perfect solution is so hard, a huge amount of research has gone into creating "heuristic" algorithms that find very good, near-optimal solutions quickly. These methods, like "nearest neighbor" or more advanced techniques like "simulated annealing" and "genetic algorithms," are the real "sleeping giants." They work by starting with a random route and then iteratively making small, smart improvements—like swapping the order of two cities—to gradually find shorter and shorter paths until a good-enough solution is found.
🛠️ Ready for Today: Why This Isn't Just Theory
The TSP is one of the most intensely studied problems in computer science and operations research. While finding the perfect solution is a famous challenge, the powerful approximation algorithms developed to tackle it are used every day to solve massive logistical problems, saving companies millions of dollars in fuel and time.
Status: The problem is in the public domain, as are the many algorithms used to solve it.
Implementations: High-quality TSP solvers are available in many optimization libraries.
Python: Google's
OR-Toolsis a powerful, open-source library with a highly optimized constraint solver that can handle TSP and other routing problems efficiently.Concorde: The "Concorde TSP Solver" is a specialized, state-of-the-art academic solver that can find the exact optimal solution for surprisingly large numbers of cities.
Academic/Specialized: Many other solvers exist, often tailored for specific variations of the problem (e.g., with time windows).
💡 Creative Applications (Ideas To Get You Thinking)
Any problem that can be framed as "finding the cheapest sequence to perform a set of tasks" can be modeled as a TSP.
Idea 1 (A "Manufacturing" Robot Arm Optimizer): On a circuit board assembly line, a robotic arm has to place components at hundreds of different locations. The time it takes to move between locations is a major bottleneck. By treating the component locations as "cities," a TSP solver could calculate the optimal path for the robot arm to follow, minimizing its travel time and significantly speeding up the manufacturing process.
Idea 2 (A "Genome Sequencing" Assembler): In DNA sequencing, scientists end up with millions of tiny, overlapping fragments of a genome. The process of assembling them into the correct full sequence can be modeled as a TSP. Each fragment is a "city," and the "distance" between them is a measure of their overlap. Finding the shortest path is equivalent to finding the most likely order of the fragments to reconstruct the original genome.
Idea 3 (A "Telescope" Observation Scheduler): An astronomical observatory has a list of hundreds of stars and galaxies it needs to observe in a single night. Moving the telescope from one target to the next takes time. A TSP solver could determine the optimal order in which to observe the targets, minimizing the total time the telescope spends slewing across the sky and maximizing the time it spends collecting valuable scientific data.
🐰 The Rabbit Hole
Dive Deeper: The "Minute Math" YouTube channel has a great video called "The Traveling Salesman Problem Explained in Under 5 Minutes" that has a very intuitive explanation of the TSP using graph theory.
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Till next time,