Biological Cybernetics

, Volume 61, Issue 1, pp 11–19 | Cite as

A neural network algorithm for the multiple traveling salesmen problem

  • E. Wacholder
  • J. Han
  • R. C. Mann


We developed an efficient neural network algorithm for solving the Multiple Traveling Salesmen Problem (MTSP). A new transformation of the N-city M-salesmen MTSP to the standard Traveling Salesmen Problem (TSP) is introduced. The transformed problem is represented by an expanded version of Hopfield-Tank's neuromorphic city-position map with (N + M-1)-cities and a single fictitious salesmen. The dynamic model associated with the problem is based on the Basic Differential Multiplier Method (BDMM) [26] which evaluates Lagrange multipliers simultaneously with the problem's state variables. The algorithm was successfully tested on many problems with up to 30 cities and five salesmen. In all test cases, the algorithm always converged to valid solutions. The great advantage of this kind of algorithm is that it can provide solutions to complex decision making problems directly by solving a system of ordinary differential equations. No learning steps, logical if statements or adjusting of parameters are required during the computation. The algorithm can therefore be implemented in hardware to solve complex constraint satisfaction problems such as the MTSP at the speed of analog silicon VLSI devices or possibly future optical neural computers.


Silicon Differential Equation Neural Network Ordinary Differential Equation Lagrange Multiplier 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • E. Wacholder
    • 1
  • J. Han
    • 1
  • R. C. Mann
    • 1
  1. 1.Oak Ridge National LaboratoryOak RidgeUSA

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