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10-city problem additional constraints algorithm ANN's AP network application assignment problem Bannister and Trivedi basins of attraction biological Brandt city distribution connection faults copt corresponding cost function cost values distributed processing system elements encoded energy function equation 11 equation Bl equations of motion example external current fault locations fault tolerance fault-free function eq global optimum hardware implementation Hopfield and Tank's inhibition initial values injected faults input lateral inhibition Liapunov function Lin-Kernighan minima minimum negative feedback network converges network solving neural network neurons nonlinear NP-complete operational amplifiers optimization network output matrix overall particular solution performance assessment performance degradation permutation matrix problem representation problem size problem sizes processor failure quadratic quality q randomly real-time represents requires shown in figure shows simulations solution quality stable stuck-at-1 faults task allocation term in equation test set Tour length transfer function traveling salesman problem valid solution valid tour