Boltzmann machines for travelling salesman problems

E.H.L. Aarts, J.H.M. Korst

Research output: Contribution to journalArticleScientificpeer-review

59 Citations (Scopus)


Boltzmann machines are proposed as a massively parallel alternative to the (sequential) simulated annealing algorithm. Our approach is tailored to the travelling salesman problem, but it can also be applied to a more general class of combinatorial optimization problems. For two distinct 0–1 programming formulations of the travelling salesman problem (as a linear and as a quadratic assignment problem) it is shown that near-optimal solutions can be obtained by mapping the corresponding 0–1 variables onto the logic computing elements of a Boltzmann machine, and by transforming the cost functions corresponding to the 0–1 programming formulations into the consensus function associated with the Boltzmann machine. Results of computer simulations are presented for two problem instances, i.e. with 10 cities and 30 cities, respectively.
Original languageEnglish
Pages (from-to)79-95
Number of pages17
JournalEuropean Journal of Operational Research
Issue number1
Publication statusPublished - 1989
Externally publishedYes


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