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Solving a Dynamic Traveling Salesman Problem with an Adaptive Hopfield Network

This paper mathematically solves a dynamic traveling salesman problem (DTSP) with an adaptive Hopfield network (AHN). The DTSP is an extension of the conventional TSP where intercity distances are variable parameters that depend on time; while the AHN, in contrast with current deterministic networks, has the capability to adapt itself to changes in the outside environment. The result is stated as a theorem that the AHN always produces as its final states locally-minimum approximate, feasible solutions to the DTSP. It is also expected that the theorem can provide a solid theoretical basis for developing engineering devices of the AHN to solve the DTSP.