Combinatorial optimization underpins applications in artificial intelligence, logistics, and network design, yet classical techniques such as greedy search and dynamic programming struggle to balance ...

For example, when there are eight cities, there are 5040 routes connecting this. One solution is " Greedy Algorithm A way of thinking about moving from one city to the nearest city all the time.

The traveling salesman problem is one of the basic problems that many theoretical computer scientists have been working on. Many scientists think that there is no algorithm for the traveling salesman ...

We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors ...