TSP is an important task in transport logistics

In the modern world, it is not uncommon for specialists to solve long-standing and sometimes ancient problems. The case of TSP (“traveling salesman problem”) belongs to the category of such examples. In order to understand the importance of TSP in today’s life and how you can use some traveler salesman problem solver to solve it, we invite you to read our short review about this theme.

Let’s start

So, we have before us a traveling merchant or traveling salesman (TS), who moves from one settlement to another and offers people to buy from him the necessary, and sometimes unnecessary goods. Let’s try to imagine how a merchant, loaded with goods, leaves his house; goes around settlement after settlement, selling goods, and returns home again. Its activity is like constant natural phenomena – cyclical and almost continuous.

His task is to get as much profit as possible, spending as little time as possible on it. This means that he must plan in advance for himself the most profitable route. One of the evaluation criteria in this case will be the total time that he can spend on the road. Consequently, the shorter his local paths are, the less time he will spend on overcoming them; and the more profitable his route will be. But after all, he needs to visit each settlement, without entering them twice; but at the same time, without missing a single one of them. Is it possible to plan a route this way? Let’s figure it out.

Suppose a traveling salesman needs to visit 3 – 5 settlements. When planning his path, he can simply go through all the options for routes between settlements; also taking into account the route from his home to any settlement and back. With this approach, it is quite possible to choose the most optimal path option. And most likely this is how the ancient merchants planned their routes.

Old problem new

Now let’s try to extrapolate this solution to the modern tasks of transport logistics. At the same time, the problem remains the same – finding the optimal route for any movement between several locations in the shortest possible time. The difficulty lies in the fact that the number of locations, in this case, can significantly exceed the number that is acceptable for the method of simple enumeration of options. And this means that the number of analyzed options will increase many times over. So if you need to analyze 100 locations, the number of options will be a value consisting of 158 digits. Therefore, this method is not suitable for use in most cases of motion planning.

Alas, there is no doubt that both this algorithm for solving TSP and other similar algorithms with an increasing amount of data make this solution practically impossible. And in this context, the following conclusion suggests itself – the search for an exact solution of the TSP is irrational. And if this is so, then it would be more correct to focus our efforts on calculations that are not exact but bring the final result to it as close as possible. There is no need to be afraid of approximate solutions. Due to the fact that they are very close to the exact solution, for such an important problem as TSP; they are also extremely useful.
Common sense, intuition; and the results of observations of various natural processes come to the rescue in the search for approximate solutions of TSP.

The methods for solving TSP

Such a conclusion is based on the well-known heuristic rule: “If an approximate solution of a problem is required; it is necessary to model the natural process that can solve a similar problem in natural conditions.”
Since the goal of solving the TSP is to find the optimal route; the problem itself will be included in the total number of combinatorial optimization problems.
There are several methods for solving problems of combinatorial optimization, and hence TSP. Their analysis is the topic of a separate article.

Here we restrict ourselves to a simple enumeration of the most famous of them. It:

• gradient descent method;
• annealing simulation method;
• method of branches and boundaries;
• Hungarian method;
• ant algorithm;
• nearest neighbor method, etc.

Afterword

What is the practical application of the TSP solution? Being a kind of marker; TSP shows the ways to calculate the most efficient routes for absolutely any transport and logistics systems; contributes to the improvement of calculation systems for modern navigators; and ultimately contributes to significant progress in the field of cargo transportation, movement and delivery of goods around the world.