The traveling salesman problem is a traditional issue that has to do with making the most efficient use of resources while at the same time expending the least amount of energy in that utilization. The designation for this type of problem hails back to the days of the traveling salesman, who often wished to arrange travel in a manner that allowed for visiting the most towns without having to double back and cross into any given town more than once.
In a wider sense, the traveling salesman problem is considered to be a classic example of what is known as a tour problem. Essentially, any type of tour problem involves making a series of stops along a designated route and making a return journey without ever making a second visit to any previous stop. Generally, a tour problem is present when there is concern on making the most of available resources such as time and mode of travel to accomplish the most in results. Finding a solution to a tour problem is sometimes referred to as discovering the least-cost path, implying that the strategic planning of the route will ensure maximum benefit with minimum expenditure incurred.
The concept of the traveling salesman problem can be translated into a number of different disciplines. For example, the idea of combinatorial optimization has a direct relationship to the traveling salesman model. As a form of optimization that is useful in both mathematical and computer science disciplines, combinatorial optimization seeks to team relevant factors and apply them in a manner that will yield the best results with repeated usage.
In a similar manner, discrete optimization attempts to accomplish the same goal, although the term is sometimes employed to refer to tasks or operations that occur on a one-time basis rather than recurring. Discrete optimization also is helpful in computer science and mathematical disciplines. In addition, discrete optimization has a direct relationship to computational complexity theory and is understood to be of use in the development of artificial intelligence.
While the imagery associated with a traveling salesman problem may seem an oversimplification of these types of detailed options for optimization, the idea behind the imagery helps to explain a basic fundamental to any type of optimization that strives for efficiency. The traveling salesman problem that is solved will yield huge benefits in the way of maximum return for minimum investment of resources.