Saturday 08 March 2025
A team of researchers has developed a new algorithm that can solve complex traveling salesman problems (TSPs) more efficiently than previous methods. The TSP is a classic problem in computer science and operations research, where a salesman must visit a set of cities and return to the starting point while minimizing travel distance.
The new algorithm, called DualOpt, uses a combination of two strategies: a grid-based divide-and-conquer procedure and a path-based divide-and-optimize procedure. This approach allows it to solve large-scale TSPs with thousands of nodes in a fraction of the time it would take other methods.
One of the key challenges in solving TSPs is that they are inherently hard problems, meaning that there is no known efficient solution algorithm for all instances of the problem. As a result, most algorithms rely on heuristics or approximations to find good but not necessarily optimal solutions.
DualOpt addresses this challenge by breaking down the problem into smaller sub-problems and solving them recursively. The grid-based procedure partitions the TSP into smaller grids, which are then solved independently using a neural network solver. This approach allows DualOpt to quickly identify promising regions of the search space and focus on those areas.
The path-based procedure takes the solutions from the grid-based procedure and further optimizes them by dividing the paths into sub-paths and solving each one separately. This approach helps to reduce the number of possible solutions and makes it easier for the algorithm to find the optimal solution.
In tests, DualOpt was able to solve large-scale TSPs with thousands of nodes in a fraction of the time it would take other methods. For example, it was able to solve a 100,000-node instance in just over 8 minutes, compared to several hours or even days for other algorithms.
The implications of this work are significant, as TSPs have applications in many fields, including logistics, transportation, and telecommunications. By developing more efficient algorithms like DualOpt, researchers hope to make it possible to solve complex problems that were previously unsolvable.
One potential application of DualOpt is in optimizing delivery routes for companies like UPS or FedEx. Currently, these companies use heuristics to plan their routes, which can lead to inefficiencies and increased costs. With a more efficient algorithm like DualOpt, they could potentially reduce their fuel consumption and lower their emissions.
Another potential application is in solving complex problems in fields like medicine and biology.
Cite this article: “Efficient Algorithm Solves Complex Traveling Salesman Problems”, The Science Archive, 2025.
Traveling Salesman Problem, Algorithm, Optimization, Computer Science, Operations Research, Logistics, Transportation, Telecommunications, Neural Network, Heuristics
