1. The Improvement of Local Minima of the Hopfield Network Mengkang Peng, Narendra k. Gupta AND Alistair F. Armitag NEURAL NETWORKS, VOL. 9, NO. 7, PP.1241-1253, ELSEVIER SCIENCE 1996

2. 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.

3. LME algorithm - 1 Local 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.

4. 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.

5. LME algorithm - 3

7. 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