Dual-mode dynamics neural network (D2NN) for knapsack packing problem

This paper presents a new approach for solving combinatorial optimization problems based on a novel dynamic neural network featuring a dual-mode of network dynamics: the state dynamics and the weight dynamics. The proposed scheme solves the problems encountered by: 1) maintaining the objective function separately from the network energy function, rather than mapping it onto the network, and 2) introducing the weight dynamics utilizing the objective function to overcome the local minima problem. The state dynamics defines the state trajectories in a direction to minimize the network energy specified by the current weights and states, whereas the weight dynamics generates the weight trajectories in a direction to minimize the preassigned external objective function at the current state. The simulation results for the knapsack packing problem indicate the superior performance of the D2NN.