Solving a combinatorial problem via self-organizing process: an application of the Kohonen algorithm to the traveling...

Area of Science:

• Computational intelligence
• Artificial neural networks
• Operations research

Background:

• The Traveling Salesman Problem (TSP) is a classic combinatorial optimization challenge.
• Existing TSP solutions often require complex parameter tuning or energy functions.
• There is a need for simpler, yet effective, algorithmic approaches to TSP.

Purpose of the Study:

• To apply the Kohonen algorithm for solving the Traveling Salesman Problem.
• To develop a neural network model of the Kohonen algorithm for TSP.
• To demonstrate the algorithm's efficacy without ad hoc parameter selection.

Main Methods:

• Utilized the Kohonen self-organizing map algorithm.
• Developed a neural network model analogous to the Kohonen algorithm.
• Tested the approach on various numerical examples of the TSP.

Main Results:

• Achieved good suboptimal tours for the Traveling Salesman Problem using solely the Kohonen algorithm.
• The neural network model provided a version of the algorithm closer to traditional neural networks.
• Numerical examples validated the practical application and effectiveness.

Conclusions:

• The Kohonen algorithm is a viable and effective method for finding suboptimal solutions to the TSP.
• A neural network formulation simplifies the application and understanding of the algorithm for TSP.
• The approach offers a parameter-light alternative for solving complex routing problems.