The Improvement of Local Minima of the Hopfield NetworkM e n g k a n g Pe n g , N a r e n d r a k . G u p t a A N D A l i s t a i r F. A r m i t a g

N EU R A L N ET W O R K S , V O L. 9 , N O . 7 , P P. 1 2 4 1 - 1 2 5 3 , EL SE V I ER S C I E N C E 1 9 9 6

Problem An important property of the Hopfield model is that starting from any initial state, it will always converge to a stable state.

However, the Hopfield model faces a serious local minima problem, which seriously hinders its application as an optimizer.

LME algorithm - 1Local Minima Escape algorithm (LME algorithm)

LME algorithm can be used to find a new state which is at the same or lower energy level than the present local minimum state.

LME algorithm - 2 By randomly disturbing its network parameter a new Hopfield network. Keep a copy of the current local minima state and then set it as the initial state. The network will proceed and converge to a stable state.

LME algorithm - 3

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Performance of TSP with the LME Algorithm - 1

A and B are large enough, the valid tour constraints can always be guarantee.Normalizing parameter D and letting B = A